Virtual element methods for the three-field formulation of time-dependent linear poroelasticity
A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in R. Oyarzúa and R. Ruiz-Baier, ( SIAM J. Numer. Anal. 54 2951–2973, 2016 ) is proposed. The treatment is extended to include also the transient case. Appropriate poro...
Saved in:
| Published in | Advances in computational mathematics Vol. 47; no. 1 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.02.2021
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in R. Oyarzúa and R. Ruiz-Baier, (
SIAM J. Numer. Anal.
54
2951–2973,
2016
) is proposed. The treatment is extended to include also the transient case. Appropriate poroelasticity projector operators are introduced and they assist in deriving energy bounds for the time-dependent discrete problem. Under standard assumptions on the computational domain, optimal a priori error estimates are established. These estimates are valid independently of the values assumed by the dilation modulus and the specific storage coefficient, implying that the formulation is locking-free. Furthermore, the accuracy of the method is verified numerically through a set of computational tests. |
|---|---|
| AbstractList | A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in R. Oyarzúa and R. Ruiz-Baier, (
SIAM J. Numer. Anal.
54
2951–2973,
2016
) is proposed. The treatment is extended to include also the transient case. Appropriate poroelasticity projector operators are introduced and they assist in deriving energy bounds for the time-dependent discrete problem. Under standard assumptions on the computational domain, optimal a priori error estimates are established. These estimates are valid independently of the values assumed by the dilation modulus and the specific storage coefficient, implying that the formulation is locking-free. Furthermore, the accuracy of the method is verified numerically through a set of computational tests. A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in R. Oyarzúa and R. Ruiz-Baier, (SIAM J. Numer. Anal.54 2951–2973, 2016) is proposed. The treatment is extended to include also the transient case. Appropriate poroelasticity projector operators are introduced and they assist in deriving energy bounds for the time-dependent discrete problem. Under standard assumptions on the computational domain, optimal a priori error estimates are established. These estimates are valid independently of the values assumed by the dilation modulus and the specific storage coefficient, implying that the formulation is locking-free. Furthermore, the accuracy of the method is verified numerically through a set of computational tests. |
| ArticleNumber | 2 |
| Author | Mora, David Ruiz-Baier, Ricardo Verma, Nitesh Bürger, Raimund Kumar, Sarvesh |
| Author_xml | – sequence: 1 givenname: Raimund surname: Bürger fullname: Bürger, Raimund organization: Centro de Investigación en Ingeniería Matemática (CI2MA) and Departamento de Ingeniería Matemática, Universidad de Concepción – sequence: 2 givenname: Sarvesh surname: Kumar fullname: Kumar, Sarvesh email: sarvesh@iist.ac.in organization: Department of Mathematics, Indian Institute of Space Science and Technology – sequence: 3 givenname: David surname: Mora fullname: Mora, David organization: GIMNAP, Departamento de Matemática, Universidad del Bío-Bío, CI2MA, Universidad de Concepción – sequence: 4 givenname: Ricardo surname: Ruiz-Baier fullname: Ruiz-Baier, Ricardo organization: School of Mathematical Sciences, Monash University, Laboratory of Mathematical Modelling, Institute of Personalised Medicine, Sechenov University – sequence: 5 givenname: Nitesh surname: Verma fullname: Verma, Nitesh organization: Department of Mathematics, Indian Institute of Space Science and Technology |
| BookMark | eNp9kE1LxDAQhoOs4O7qH_BU8BxN0rRpjrL4BYIX9RrSdupmaZOapIf992a3guBhGcIMyftMZt4VWlhnAaFrSm4pIeIuUMI5x4QRTGTFSizO0JIWgmGZHhapJlRiQcvqAq1C2BFCZCmKJVKfxsdJ9xn0MICN2QBx69qQdc5ncQvpeADcGejbw90w9ToaZzPXZdEMgFsYwbYHsjcWtM9G5x30OkTTmLi_ROed7gNc_eY1-nh8eN8849e3p5fN_StuciojLqio0gINyzUvy1bUNVQgBWtJU8kCcp2XWsiy5LpoAUDLmjdApayKXLc1Zfka3cx9R---JwhR7dzkbfpSMS4lJymKpKpmVeNdCB46lWY87hO9Nr2iRB3sVLOdKtmpjnYqkVD2Dx29GbTfn4byGQpJbL_A_011gvoBa6aLNA |
| CitedBy_id | crossref_primary_10_1016_j_camwa_2022_09_005 crossref_primary_10_1002_num_23083 crossref_primary_10_1007_s10915_023_02188_4 crossref_primary_10_1016_j_apnum_2024_09_017 crossref_primary_10_1007_s10915_023_02444_7 crossref_primary_10_1016_j_camwa_2023_01_034 crossref_primary_10_1016_j_cma_2024_117353 crossref_primary_10_1007_s10915_023_02365_5 crossref_primary_10_1016_j_camwa_2025_03_004 crossref_primary_10_2139_ssrn_3967210 crossref_primary_10_1016_j_amc_2025_129285 crossref_primary_10_1007_s10915_024_02562_w crossref_primary_10_1016_j_apnum_2024_06_004 crossref_primary_10_1016_j_cam_2024_115754 crossref_primary_10_1016_j_camwa_2023_04_022 crossref_primary_10_11948_20210381 crossref_primary_10_1093_imanum_drae093 crossref_primary_10_3846_mma_2022_15542 crossref_primary_10_1016_j_camwa_2021_03_008 crossref_primary_10_1002_num_23059 crossref_primary_10_1007_s10092_021_00440_7 crossref_primary_10_1007_s10915_022_01960_2 crossref_primary_10_1016_j_jcp_2022_111464 |
| Cites_doi | 10.1007/s00211-010-0358-8 10.1007/s10543-017-0688-3 10.1093/imanum/dry063 10.2478/cmam-2002-0008 10.1051/m2an/2020064 10.1137/15M1008117 10.1016/j.camwa.2014.02.005 10.1093/imanum/drz001 10.2118/119084-PA 10.1007/978-0-387-75934-0 10.1553/etna_vol48s202 10.1137/15M1050082 10.1137/15M1025505 10.1137/19M1268343 10.1051/m2an/2019063 10.1002/num.21775 10.1016/j.camwa.2020.06.004 10.1142/S0218202518500057 10.1142/S0218202515500372 10.1137/15M1029473 10.1090/mcom/3331 10.1137/16M1056109 10.1016/j.cam.2016.06.003 10.2478/cmam-2006-0017 10.1137/18M1182395 10.1115/1.1611512 10.1016/j.camwa.2018.09.029 10.1142/S0218202512500492 10.1016/j.aml.2016.12.019 10.1007/s10596-018-9736-6 10.1006/jmaa.2000.7048 10.1016/j.apm.2007.09.024 10.1051/m2an/2016032 10.1002/num.21982 10.1016/j.cam.2019.06.028 10.1093/imanum/drw002 10.1016/j.camwa.2013.05.015 10.1007/978-3-642-61623-5 10.1137/0733052 10.1051/m2an/2015066 10.1007/s10596-012-9318-y 10.1142/S0218202511005039 10.1007/s00211-017-0891-9 10.1016/j.compgeo.2013.09.014 10.1007/s10596-019-09831-w 10.1515/cmam-2017-0008 10.1007/s10596-013-9393-8 10.1142/S0218202516500160 10.1137/13091141X 10.1080/00036811.2021.1877677 10.4171/078 10.1016/j.camwa.2016.12.030 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media, LLC, part of Springer Nature 2021 Springer Science+Business Media, LLC, part of Springer Nature 2021. |
| Copyright_xml | – notice: Springer Science+Business Media, LLC, part of Springer Nature 2021 – notice: Springer Science+Business Media, LLC, part of Springer Nature 2021. |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s10444-020-09826-7 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1572-9044 |
| ExternalDocumentID | 10_1007_s10444_020_09826_7 |
| GrantInformation_xml | – fundername: Department of Science and Technology (DST-SERB), India grantid: MATRICS grant MTR/2019/000519 – fundername: Fondo Nacional de Desarrollo Científico y Tecnológico grantid: FONDECYT 1170473 funderid: https://doi.org/10.13039/501100002850 – fundername: Transnationale Universiteit Limburg grantid: Grant HPC175QA9K funderid: https://doi.org/10.13039/501100009164 – fundername: Fondo Nacional de Desarrollo Científico y Tecnológico grantid: FONDECYT 1180913 funderid: https://doi.org/10.13039/501100002850 |
| GroupedDBID | -52 -59 -5G -BR -EM -Y2 -~C .4S .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 2.D 203 23M 28- 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARCSS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BBWZM BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP EBLON EBS EDO EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAK LLZTM M4Y MA- MK~ N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9O PF0 PT4 PT5 QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SCO SDD SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z83 ZMTXR ZWQNP ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION ABRTQ |
| ID | FETCH-LOGICAL-c319t-5178444c23a466d7bbe8e972d0c895e3a36a79664a5deeea9b4ce199853adb123 |
| IEDL.DBID | U2A |
| ISSN | 1019-7168 |
| IngestDate | Fri Jul 25 11:02:22 EDT 2025 Thu Apr 24 23:08:20 EDT 2025 Tue Jul 01 02:55:34 EDT 2025 Fri Feb 21 02:48:55 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | A priori error analysis Time-dependent problems 74F10 Biot equations 65M60 35K57 74L15 Virtual element method |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c319t-5178444c23a466d7bbe8e972d0c895e3a36a79664a5deeea9b4ce199853adb123 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2499404045 |
| PQPubID | 2043875 |
| ParticipantIDs | proquest_journals_2499404045 crossref_citationtrail_10_1007_s10444_020_09826_7 crossref_primary_10_1007_s10444_020_09826_7 springer_journals_10_1007_s10444_020_09826_7 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2021-02-01 |
| PublicationDateYYYYMMDD | 2021-02-01 |
| PublicationDate_xml | – month: 02 year: 2021 text: 2021-02-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Advances in computational mathematics |
| PublicationTitleAbbrev | Adv Comput Math |
| PublicationYear | 2021 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | Lee, Piersanti, Mardal, Rognes (CR37) 2019; 41 Boffi, Botti, Di Pietro (CR14) 2016; 38 Antonietti, Beirão da Veiga, Mora, Verani (CR5) 2014; 52 (CR25) 2002; 2 Fu (CR24) 2019; 77 Mikelić, Wang, Wheeler (CR39) 2014; 18 CR34 Kolesov, Vabishchevich, Vasilyeva (CR32) 2014; 67 Anaya, De Wijn, Gómez-Vargas, Mora, Ruiz Baier (CR4) 2020; 42 Mora, Rivera (CR41) 2020; 40 Asadi, Ataie-Ashtiani, Simmons (CR8) 2014; 55 Mikelić, Wheeler (CR40) 2013; 17 Kim, Tchelepi, Juanes (CR31) 2011; 16 Mora, Rivera, Rodríguez (CR42) 2015; 25 CR49 Brenner, Guan, Sung (CR18) 2017; 17 Kumar, Oyarzúa, Ruiz-Baier, Sandilya (CR33) 2020; 54 Cáceres, Gatica (CR20) 2017; 37 Antonietti, Beirão da Veiga, Scacchi, Verani (CR6) 2016; 54 Hong, Kraus (CR29) 2018; 48 Vacca (CR50) 2018; 28 Lee (CR36) 2018; 58 Ahmad, Alsaedi, Brezzi, Marini, Russo (CR1) 2013; 66 Ahmed, Nordbotten, Radu (CR2) 2020; 364 Arega, Hayter (CR7) 2008; 32 CR19 Yi (CR53) 2013; 29 CR17 Perugia, Pietra, Russo (CR46) 2016; 50 CR52 Beirão da Veiga, Mora, Rivera (CR13) 2019; 88 Cangiani, Georgoulis, Pryer, Sutton (CR21) 2017; 137 Mauck, Hung, Ateshian (CR38) 2003; 125 Oyarzúa, Ruiz-Baier (CR45) 2016; 54 Hu, Rodrigo, Gaspar, Zikatanov (CR30) 2017; 310 Vacca, Beirão da Veiga (CR51) 2015; 31 Borregales, Radu, Kumar, Nordbotten (CR15) 2018; 22 Murad, Thomée, Loula (CR43) 1996; 33 Naumovich (CR44) 2006; 6 Beirão da Veiga, Lovadina, Vacca (CR11) 2017; 51 Coulet, Faille, Girault, Guy, Nataf (CR23) 2020; 24 Beirão da Veiga, Mora (CR12) 2011; 117 Showalter (CR48) 2000; 251 Anaya, Bendahmane, Mora, Sepúlveda (CR3) 2020; 40 CR28 CR27 Girault, Pencheva, Wheeler, Wildey (CR26) 2011; 21 Beirão da Veiga, Brezzi, Marini, Russo (CR10) 2016; 26 Rivière, Tan, Thompson (CR47) 2017; 73 Both, Borregales, Nordbotten, Kumar, Radu (CR16) 2017; 68 Cangiani, Manzini, Sutton (CR22) 2017; 37 Yi (CR54) 2017; 55 Beirão da Veiga, Brezzi, Cangiani, Manzini, Marini, Russo (CR9) 2013; 23 Lee, Mardal, Winther (CR35) 2017; 39 A Mikelić (9826_CR39) 2014; 18 L Beirão da Veiga (9826_CR12) 2011; 117 L Beirão da Veiga (9826_CR10) 2016; 26 9826_CR19 PF Antonietti (9826_CR6) 2016; 54 9826_CR17 R Asadi (9826_CR8) 2014; 55 J Kim (9826_CR31) 2011; 16 B Ahmad (9826_CR1) 2013; 66 M Borregales (9826_CR15) 2018; 22 JJ Lee (9826_CR35) 2017; 39 D Mora (9826_CR41) 2020; 40 D Boffi (9826_CR14) 2016; 38 F Arega (9826_CR7) 2008; 32 A Cangiani (9826_CR21) 2017; 137 X Hu (9826_CR30) 2017; 310 9826_CR52 A Mikelić (9826_CR40) 2013; 17 JJ Lee (9826_CR36) 2018; 58 AE Kolesov (9826_CR32) 2014; 67 RE Showalter (9826_CR48) 2000; 251 9826_CR49 R Oyarzúa (9826_CR45) 2016; 54 D Mora (9826_CR42) 2015; 25 V Anaya (9826_CR3) 2020; 40 S-Y Yi (9826_CR54) 2017; 55 PF Antonietti (9826_CR5) 2014; 52 E Cáceres (9826_CR20) 2017; 37 S Kumar (9826_CR33) 2020; 54 JW Both (9826_CR16) 2017; 68 E Ahmed (9826_CR2) 2020; 364 JJ Lee (9826_CR37) 2019; 41 J Coulet (9826_CR23) 2020; 24 Gaspar, F.J., Lisbona, F.J. and Vabishchevich, P.N. (9826_CR25) 2002; 2 B Rivière (9826_CR47) 2017; 73 L Beirão da Veiga (9826_CR9) 2013; 23 V Anaya (9826_CR4) 2020; 42 MA Murad (9826_CR43) 1996; 33 Q Hong (9826_CR29) 2018; 48 A Naumovich (9826_CR44) 2006; 6 9826_CR34 G Fu (9826_CR24) 2019; 77 L Beirão da Veiga (9826_CR13) 2019; 88 L Beirão da Veiga (9826_CR11) 2017; 51 V Girault (9826_CR26) 2011; 21 A Cangiani (9826_CR22) 2017; 37 9826_CR27 9826_CR28 RT Mauck (9826_CR38) 2003; 125 G Vacca (9826_CR50) 2018; 28 I Perugia (9826_CR46) 2016; 50 SC Brenner (9826_CR18) 2017; 17 G Vacca (9826_CR51) 2015; 31 S-Y Yi (9826_CR53) 2013; 29 |
| References_xml | – volume: 364 start-page: 112312 year: 2020 ident: CR2 article-title: Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problems publication-title: J. Comput. Appl. Math. – ident: CR49 – volume: 17 start-page: 455 year: 2013 end-page: 461 ident: CR40 article-title: Convergence of iterative coupling for coupled flow and geomechanics publication-title: Comput. Geosci. – volume: 23 start-page: 199 year: 2013 end-page: 214 ident: CR9 article-title: Basic principles of virtual element methods publication-title: Math.Models Methods Appl.Sci. – volume: 66 start-page: 376 year: 2013 end-page: 391 ident: CR1 article-title: Equivalent projectors for virtual element methods publication-title: Comput. Math. Appl. – volume: 40 start-page: 1544 issue: 2 year: 2020 end-page: 1576 ident: CR3 article-title: A virtual element method for a nonlocal FitzHugh-Nagumo model of cardiac electrophysiology publication-title: IMA J.Numer.Anal. – volume: 25 start-page: 1421 year: 2015 end-page: 1445 ident: CR42 article-title: A virtual element method for the Steklov eigenvalue problem publication-title: Math. Models Methods Appl.Sci. – volume: 50 start-page: 783 year: 2016 end-page: 808 ident: CR46 article-title: A plane wave virtual element method for the Helmholtz problem publication-title: ESAIM Math. Model. Numer. Anal. – volume: 88 start-page: 149 year: 2019 end-page: 178 ident: CR13 article-title: Virtual Elements for a shear-deflection formulation of Reissner-Mindlin plates publication-title: Math. Comp. – volume: 32 start-page: 2413 year: 2008 end-page: 2428 ident: CR7 article-title: Coupled consolidation and contaminant transport model for simulating migration of contaminants through the sediment and a cap publication-title: Appl. Math. Model. – volume: 48 start-page: 202 year: 2018 end-page: 226 ident: CR29 article-title: Parameter-robust stability of classical three-field formulation of Biot’s consolidation model publication-title: Electron. Trans. Numer. Anal. – volume: 29 start-page: 1749 issue: 5 year: 2013 end-page: 1777 ident: CR53 article-title: A coupling of nonconforming and mixed finite element methods for Biot’s consolidation model publication-title: Numer. Methods Partial Differential Equations – volume: 77 start-page: 237 year: 2019 end-page: 252 ident: CR24 article-title: A high-order HDG method for the Biot’s consolidation model publication-title: Comput.Math.Appl. – ident: CR19 – volume: 2 start-page: 132 year: 2002 end-page: 142 ident: CR25 article-title: Finite difference schemes for poroelastic problems publication-title: Comput.Methods Appl.Math. – volume: 54 start-page: 273 issue: 1 year: 2020 end-page: 299 ident: CR33 article-title: Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity publication-title: ESAIM: Math.Model.Numer.Anal. – volume: 55 start-page: 1915 year: 2017 end-page: 1936 ident: CR54 article-title: A study of two modes of locking in poroelasticity publication-title: SIAM J.Numer.Anal. – volume: 73 start-page: 666 year: 2017 end-page: 683 ident: CR47 article-title: Error analysis of primal discontinuous Galerkin methods for a mixed formulation of the Biot equations publication-title: Comput.Math.Appl. – volume: 117 start-page: 425 year: 2011 end-page: 462 ident: CR12 article-title: A mimetic discretization of the Reissner-Mindlin plate bending problem publication-title: Numer. Math. – volume: 68 start-page: 101 year: 2017 end-page: 108 ident: CR16 article-title: Robust fixed stress splitting for Biot’s equations in heterogeneous media publication-title: Appl. Math. Lett. – volume: 310 start-page: 143 year: 2017 end-page: 154 ident: CR30 article-title: A non-conforming finite element method for the Biot’s consolidation model in poroelasticity publication-title: J. Comput. Appl. Math. – volume: 67 start-page: 2185 year: 2014 end-page: 2198 ident: CR32 article-title: Splitting schemes for poroelasticity and thermoelasticity problems publication-title: Comput. Math. Appl. – volume: 58 start-page: 347 year: 2018 end-page: 372 ident: CR36 article-title: Robust three-field finite element methods for Biot’s consolidation model in poroelasticity publication-title: Bit Numer Math – volume: 17 start-page: 553 year: 2017 end-page: 574 ident: CR18 article-title: Some estimates for virtual element methods publication-title: Comput. Methods Appl Math. – volume: 22 start-page: 1021 year: 2018 end-page: 1038 ident: CR15 article-title: Robust iterative schemes for nonlinear poromechanics publication-title: Comput. Geosci – volume: 33 start-page: 1065 year: 1996 end-page: 1083 ident: CR43 article-title: Asymptotic behavior of semi discrete finite-element approximations of Biot’s consolidation problem publication-title: SIAM J.Numer.Anal. – volume: 54 start-page: 2951 year: 2016 end-page: 2973 ident: CR45 article-title: Locking-free finite element methods for poroelasticity publication-title: SIAM J.Numer.Anal. – volume: 24 start-page: 381 year: 2020 end-page: 403 ident: CR23 article-title: A fully coupled scheme using virtual element method and finite volume for poroelasticity publication-title: Comput.Geosci. – volume: 16 start-page: 119084 issue: 02 year: 2011 ident: CR31 article-title: Stability, accuracy and efficiency of sequential methods for coupled flow and geomechanics publication-title: SPE J. – volume: 51 start-page: 509 year: 2017 end-page: 535 ident: CR11 article-title: Divergence free virtual elements for the Stokes problem on polygonal meshes publication-title: ESAIM: Math. Model. Numer. Anal. – volume: 38 start-page: A1508 year: 2016 end-page: A1537 ident: CR14 article-title: A nonconforming high-order method for the Biot problem on general meshes publication-title: SIAM J.Sci.Comput. – volume: 251 start-page: 310 year: 2000 end-page: 340 ident: CR48 article-title: Diffusion in poro-elastic media publication-title: J. Math. Anal. Appl. – volume: 39 start-page: A1 year: 2017 end-page: A24 ident: CR35 article-title: Parameter-robust discretization and preconditioning of Biot’s consolidation model publication-title: SIAM J.Sci.Comput. – volume: 52 start-page: 386 year: 2014 end-page: 404 ident: CR5 article-title: A stream virtual element formulation of the Stokes problem on polygonal meshes publication-title: SIAM J.Numer.Anal. – volume: 54 start-page: 36 year: 2016 end-page: 56 ident: CR6 article-title: A c1 virtual element method for the Cahn–Hilliard equation with polygonal meshes publication-title: SIAM J. Numer. Anal. – ident: CR27 – volume: 41 start-page: A722 year: 2019 end-page: A747 ident: CR37 article-title: A mixed finite element method for nearly incompressible multiple-network poroelasticity publication-title: SIAM J.Sci.Comput. – volume: 26 start-page: 729 year: 2016 end-page: 750 ident: CR10 article-title: Virtual element method for general second-order elliptic problems on polygonal meshes publication-title: Math. Models Methods Appl. Sci. – volume: 18 start-page: 325 year: 2014 end-page: 34 ident: CR39 article-title: Numerical convergence study of iterative coupling for coupled flow and geomechanics publication-title: Comput. Geosci. – volume: 21 start-page: 169 year: 2011 end-page: 213 ident: CR26 article-title: Domain decomposition for poroelasticity and elasticity with DG jumps and mortars publication-title: Math. Models methods appl Sci. – volume: 42 start-page: B225 issue: 1 year: 2020 end-page: B249 ident: CR4 article-title: Rotation-based mixed formulations for an elasticity-poroelasticity interface problem publication-title: SIAM J.Sci.Comput. – ident: CR52 – ident: CR17 – volume: 6 start-page: 306 year: 2006 end-page: 325 ident: CR44 article-title: On finite volume discretization of the three-dimensional Biot poroelasticity system in multilayer domains publication-title: Comput. Methods Appl.Math. – volume: 37 start-page: 1317 year: 2017 end-page: 1354 ident: CR22 article-title: Conforming and nonconforming virtual element methods for elliptic problems publication-title: IMA J.Numer.Anal. – ident: CR34 – volume: 40 start-page: 322 issue: 1 year: 2020 end-page: 357 ident: CR41 article-title: A priori and a posteriori error estimates for a virtual element spectral analysis for the elasticity equations publication-title: IMA J.Numer.Anal. – volume: 137 start-page: 857 year: 2017 end-page: 893 ident: CR21 article-title: A posteriori error estimates for the virtual element method publication-title: Numer.Math. – volume: 31 start-page: 2110 year: 2015 end-page: 2134 ident: CR51 article-title: Virtual element methods for parabolic problems on polygonal meshes publication-title: Numer. Methods Partial Differential Equations – volume: 37 start-page: 296 year: 2017 end-page: 331 ident: CR20 article-title: A mixed virtual element method for the pseudostress-velocity formulation of the Stokes problem publication-title: IMA J. Numer. Anal. – ident: CR28 – volume: 28 start-page: 159 year: 2018 end-page: 194 ident: CR50 article-title: An h1-conforming virtual element for Darcy and Brinkman equations publication-title: Math. Models Methods Appl.Sci. – volume: 55 start-page: 494 year: 2014 end-page: 505 ident: CR8 article-title: Finite volume coupling strategies for the solution of a Biot consolidation model publication-title: Comput. Geotech. – volume: 125 start-page: 602 year: 2003 end-page: 614 ident: CR38 article-title: Modelling of neutral solute transport in a dynamically loaded porous permeable gel: implications for articular cartilage biosynthesis and tissue engineering publication-title: J. Biomech. Engrg. – volume: 117 start-page: 425 year: 2011 ident: 9826_CR12 publication-title: Numer. Math. doi: 10.1007/s00211-010-0358-8 – volume: 58 start-page: 347 year: 2018 ident: 9826_CR36 publication-title: Bit Numer Math doi: 10.1007/s10543-017-0688-3 – volume: 40 start-page: 322 issue: 1 year: 2020 ident: 9826_CR41 publication-title: IMA J.Numer.Anal. doi: 10.1093/imanum/dry063 – volume: 2 start-page: 132 year: 2002 ident: 9826_CR25 publication-title: Comput.Methods Appl.Math. doi: 10.2478/cmam-2002-0008 – ident: 9826_CR49 doi: 10.1051/m2an/2020064 – volume: 54 start-page: 36 year: 2016 ident: 9826_CR6 publication-title: SIAM J. Numer. Anal. doi: 10.1137/15M1008117 – volume: 67 start-page: 2185 year: 2014 ident: 9826_CR32 publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2014.02.005 – volume: 40 start-page: 1544 issue: 2 year: 2020 ident: 9826_CR3 publication-title: IMA J.Numer.Anal. doi: 10.1093/imanum/drz001 – volume: 16 start-page: 119084 issue: 02 year: 2011 ident: 9826_CR31 publication-title: SPE J. doi: 10.2118/119084-PA – ident: 9826_CR19 doi: 10.1007/978-0-387-75934-0 – volume: 48 start-page: 202 year: 2018 ident: 9826_CR29 publication-title: Electron. Trans. Numer. Anal. doi: 10.1553/etna_vol48s202 – volume: 54 start-page: 2951 year: 2016 ident: 9826_CR45 publication-title: SIAM J.Numer.Anal. doi: 10.1137/15M1050082 – volume: 38 start-page: A1508 year: 2016 ident: 9826_CR14 publication-title: SIAM J.Sci.Comput. doi: 10.1137/15M1025505 – volume: 42 start-page: B225 issue: 1 year: 2020 ident: 9826_CR4 publication-title: SIAM J.Sci.Comput. doi: 10.1137/19M1268343 – volume: 54 start-page: 273 issue: 1 year: 2020 ident: 9826_CR33 publication-title: ESAIM: Math.Model.Numer.Anal. doi: 10.1051/m2an/2019063 – volume: 29 start-page: 1749 issue: 5 year: 2013 ident: 9826_CR53 publication-title: Numer. Methods Partial Differential Equations doi: 10.1002/num.21775 – ident: 9826_CR17 doi: 10.1016/j.camwa.2020.06.004 – volume: 28 start-page: 159 year: 2018 ident: 9826_CR50 publication-title: Math. Models Methods Appl.Sci. doi: 10.1142/S0218202518500057 – volume: 25 start-page: 1421 year: 2015 ident: 9826_CR42 publication-title: Math. Models Methods Appl.Sci. doi: 10.1142/S0218202515500372 – volume: 39 start-page: A1 year: 2017 ident: 9826_CR35 publication-title: SIAM J.Sci.Comput. doi: 10.1137/15M1029473 – volume: 88 start-page: 149 year: 2019 ident: 9826_CR13 publication-title: Math. Comp. doi: 10.1090/mcom/3331 – volume: 55 start-page: 1915 year: 2017 ident: 9826_CR54 publication-title: SIAM J.Numer.Anal. doi: 10.1137/16M1056109 – volume: 310 start-page: 143 year: 2017 ident: 9826_CR30 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2016.06.003 – volume: 6 start-page: 306 year: 2006 ident: 9826_CR44 publication-title: Comput. Methods Appl.Math. doi: 10.2478/cmam-2006-0017 – volume: 41 start-page: A722 year: 2019 ident: 9826_CR37 publication-title: SIAM J.Sci.Comput. doi: 10.1137/18M1182395 – volume: 125 start-page: 602 year: 2003 ident: 9826_CR38 publication-title: J. Biomech. Engrg. doi: 10.1115/1.1611512 – volume: 77 start-page: 237 year: 2019 ident: 9826_CR24 publication-title: Comput.Math.Appl. doi: 10.1016/j.camwa.2018.09.029 – volume: 23 start-page: 199 year: 2013 ident: 9826_CR9 publication-title: Math.Models Methods Appl.Sci. doi: 10.1142/S0218202512500492 – volume: 68 start-page: 101 year: 2017 ident: 9826_CR16 publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2016.12.019 – volume: 22 start-page: 1021 year: 2018 ident: 9826_CR15 publication-title: Comput. Geosci doi: 10.1007/s10596-018-9736-6 – volume: 251 start-page: 310 year: 2000 ident: 9826_CR48 publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.2000.7048 – volume: 32 start-page: 2413 year: 2008 ident: 9826_CR7 publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2007.09.024 – volume: 51 start-page: 509 year: 2017 ident: 9826_CR11 publication-title: ESAIM: Math. Model. Numer. Anal. doi: 10.1051/m2an/2016032 – volume: 31 start-page: 2110 year: 2015 ident: 9826_CR51 publication-title: Numer. Methods Partial Differential Equations doi: 10.1002/num.21982 – volume: 364 start-page: 112312 year: 2020 ident: 9826_CR2 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2019.06.028 – volume: 37 start-page: 296 year: 2017 ident: 9826_CR20 publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drw002 – ident: 9826_CR34 – volume: 66 start-page: 376 year: 2013 ident: 9826_CR1 publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2013.05.015 – ident: 9826_CR27 doi: 10.1007/978-3-642-61623-5 – volume: 33 start-page: 1065 year: 1996 ident: 9826_CR43 publication-title: SIAM J.Numer.Anal. doi: 10.1137/0733052 – volume: 50 start-page: 783 year: 2016 ident: 9826_CR46 publication-title: ESAIM Math. Model. Numer. Anal. doi: 10.1051/m2an/2015066 – volume: 37 start-page: 1317 year: 2017 ident: 9826_CR22 publication-title: IMA J.Numer.Anal. – volume: 17 start-page: 455 year: 2013 ident: 9826_CR40 publication-title: Comput. Geosci. doi: 10.1007/s10596-012-9318-y – volume: 21 start-page: 169 year: 2011 ident: 9826_CR26 publication-title: Math. Models methods appl Sci. doi: 10.1142/S0218202511005039 – volume: 137 start-page: 857 year: 2017 ident: 9826_CR21 publication-title: Numer.Math. doi: 10.1007/s00211-017-0891-9 – volume: 55 start-page: 494 year: 2014 ident: 9826_CR8 publication-title: Comput. Geotech. doi: 10.1016/j.compgeo.2013.09.014 – volume: 24 start-page: 381 year: 2020 ident: 9826_CR23 publication-title: Comput.Geosci. doi: 10.1007/s10596-019-09831-w – volume: 17 start-page: 553 year: 2017 ident: 9826_CR18 publication-title: Comput. Methods Appl Math. doi: 10.1515/cmam-2017-0008 – volume: 18 start-page: 325 year: 2014 ident: 9826_CR39 publication-title: Comput. Geosci. doi: 10.1007/s10596-013-9393-8 – volume: 26 start-page: 729 year: 2016 ident: 9826_CR10 publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202516500160 – volume: 52 start-page: 386 year: 2014 ident: 9826_CR5 publication-title: SIAM J.Numer.Anal. doi: 10.1137/13091141X – ident: 9826_CR52 doi: 10.1080/00036811.2021.1877677 – ident: 9826_CR28 doi: 10.4171/078 – volume: 73 start-page: 666 year: 2017 ident: 9826_CR47 publication-title: Comput.Math.Appl. doi: 10.1016/j.camwa.2016.12.030 |
| SSID | ssj0009675 |
| Score | 2.4088702 |
| Snippet | A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in R. Oyarzúa and R.... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| SubjectTerms | Computational mathematics Computational Mathematics and Numerical Analysis Computational Science and Engineering Locking Mathematical analysis Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Poroelasticity Time dependence Visualization |
| Title | Virtual element methods for the three-field formulation of time-dependent linear poroelasticity |
| URI | https://link.springer.com/article/10.1007/s10444-020-09826-7 https://www.proquest.com/docview/2499404045 |
| Volume | 47 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED5Bu8DAo4AolMoDG1giie3EY4taKlA7UVSmKI-LhAQtSsLAv-ecOi0gQGKIIsWOh7uz_Z3u8QGcY6QUJq5hDdAxF16a8UAIlystZJI5macqbsDxRI2m4nYmZ7YorKiz3euQZHVSfyp2E0Jw4-5caQLF3N-EpjS-O1nx1O2tW-2qqr0u2Zrm5A0EtlTm5zW-XkdrjPktLFrdNsM92LEwkfWWet2HDZy3YNdCRmY3ZNGC7fGq7WpxAOHDU27qQRguk8LZkh-6YIRMGc2jJ0fkVdaa-fZiubvYImOGZJ7XlLglM-gzyhmh8wUSwDa51-X7IUyHg_vrEbcMCjyhrVVy6fgkeUG6iIRSqR_HGKD23fQqCbREL_JU5JPDIyKZImKkY5GgqbqTXpTGdKkdQWO-mOMxMCeRXkZgzAliLQI65xwMdGDi1rR0FidtcGpBholtL25YLp7DdWNkI_yQhB9Wwg_9Nlys_nldNtf4c3an1k9oN1oRkveoBR1EQrbhstbZevj31U7-N_0UtlyTzVLla3egUeZveEZwpIy70OwN-_2Jed883g26lTV-ABs91-8 |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED5BGYCBN6I8PbCBJZI4jj1WCFSg7UQRm5XHRUKCFjVh4N9zTpwGECAxZEkuHu78-E7-7j6AU4ylxNS3qgE64SLIcq6E8LnUIkxzLw9kpQ04HMn-WNw-ho-uKKxo2O7NlWS1U38qdhNCcJvuXGgCxTxahCUCA8oSucZ-r221K6v2ujTXNKdsQLlSmZ_H-HoctRjz27Voddpcb8Cag4msV8d1ExZwsgXrDjIytyCLLVgdztuuFttgHp5mth6EYU0KZ7U-dMEImTKyo2eGyCvWmn334rS72DRnVmSeN5K4JbPoM54xQudTJIBtudfl-w6Mr6_uL_vcKSjwlJZWyUMvIs8LikUspMyiJEGFOvKzi1TpEIM4kHFECY-IwwwRY52IFG3VXRjEWUKH2i50JtMJ7gHz0jDICYx5KtFC0T7nodLK3lvT0HmSdsFrHGlS117cqlw8m7YxsnW-Ieebyvkm6sLZ_J_XurnGn9aHTXyMW2iFoexRC9qIRNiF8yZm7effR9v_n_kJLPfvhwMzuBndHcCKb5ktFXf7EDrl7A2PCJqUyXE1Ez8A5sDX0g |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED5BkRAMPAqIQgEPbGC1SRwnHiugKo9WDBR1s_K4SEjQVmkY-Pec82gLAiSGLInj4e5sfyfffR_AOQZSYmQb1QAVcuHECfeFsLlUwo0SK3Fkrg3YH8jeUNyN3NFSF39e7V5dSRY9DYalaZy1pnHSWmp8E0Jwk_q0FQFk7q3CGm3Hlonrod1Z0O7KnGqX4k5xygz8sm3m5zm-Hk0LvPntijQ_ebo7sFVCRtYpfLwLKziuw3YJH1m5OGd12OzPKVhne6CfX1LTG8KwKBBnhVb0jBFKZTSOnhSR5xVs5t1bqePFJgkzgvO8ksfNmEGiQcoIqU-QwLapw84-9mHYvXm66vFSTYFHZJeMu5ZHXhDkl0BIGXthiD4qz47bka9cdAJHBh4lPyJwY0QMVCgiNB14rhPEIR1wB1AbT8Z4CMyKXCchYGb5oRI-7XkW-so3d9g0dRJGDbAqQ-qopBo3ihevekGSbIyvyfg6N772GnAx_2daEG38ObpZ-UeXi26mKZNUgjYl4TbgsvLZ4vPvsx39b_gZrD9ed_XD7eD-GDZsU-SSl3E3oZal73hCKCULT_NA_ASRYNwO |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Virtual+element+methods+for+the+three-field+formulation+of+time-dependent+linear+poroelasticity&rft.jtitle=Advances+in+computational+mathematics&rft.au=B%C3%BCrger%2C+Raimund&rft.au=Kumar%2C+Sarvesh&rft.au=Mora%2C+David&rft.au=Ruiz-Baier%2C+Ricardo&rft.date=2021-02-01&rft.pub=Springer+US&rft.issn=1019-7168&rft.eissn=1572-9044&rft.volume=47&rft.issue=1&rft_id=info:doi/10.1007%2Fs10444-020-09826-7&rft.externalDocID=10_1007_s10444_020_09826_7 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1019-7168&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1019-7168&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1019-7168&client=summon |