Parameter‐uniform numerical method for singularly perturbed 2‐D parabolic convection–diffusion problem with interior layers
In this article, we devise a uniformly convergent numerical scheme for solving singularly perturbed two‐dimensional parabolic convection–diffusion problem with non‐smooth convection coefficients and source term. The solution of this kind of problem typically exhibits interior layers due to the disco...
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| Published in | Mathematical methods in the applied sciences Vol. 45; no. 5; pp. 3039 - 3057 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Freiburg
Wiley Subscription Services, Inc
30.03.2022
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0170-4214 1099-1476 |
| DOI | 10.1002/mma.7975 |
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| Abstract | In this article, we devise a uniformly convergent numerical scheme for solving singularly perturbed two‐dimensional parabolic convection–diffusion problem with non‐smooth convection coefficients and source term. The solution of this kind of problem typically exhibits interior layers due to the discontinuity of convection coefficients and source term. To capture the interior layers, the piecewise‐uniform mesh is used in the spatial directions and the uniform mesh is considered in temporal direction. To discretize the temporal and spatial derivatives, we apply an alternating direction method and upwind method, respectively. Theoretically, we prove that the proposed method is ε‐uniformly convergent. Numerical results are presented to demonstrate the theoretical estimates. |
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| AbstractList | In this article, we devise a uniformly convergent numerical scheme for solving singularly perturbed two‐dimensional parabolic convection–diffusion problem with non‐smooth convection coefficients and source term. The solution of this kind of problem typically exhibits interior layers due to the discontinuity of convection coefficients and source term. To capture the interior layers, the piecewise‐uniform mesh is used in the spatial directions and the uniform mesh is considered in temporal direction. To discretize the temporal and spatial derivatives, we apply an alternating direction method and upwind method, respectively. Theoretically, we prove that the proposed method is ε‐uniformly convergent. Numerical results are presented to demonstrate the theoretical estimates. In this article, we devise a uniformly convergent numerical scheme for solving singularly perturbed two‐dimensional parabolic convection–diffusion problem with non‐smooth convection coefficients and source term. The solution of this kind of problem typically exhibits interior layers due to the discontinuity of convection coefficients and source term. To capture the interior layers, the piecewise‐uniform mesh is used in the spatial directions and the uniform mesh is considered in temporal direction. To discretize the temporal and spatial derivatives, we apply an alternating direction method and upwind method, respectively. Theoretically, we prove that the proposed method is ε ‐uniformly convergent. Numerical results are presented to demonstrate the theoretical estimates. |
| Author | Majumdar, Anirban Natesan, Srinivasan |
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| References_xml | – volume: 96 start-page: 1313 year: 2019 end-page: 1334 article-title: An ‐uniform hybrid scheme for a singularly perturbed degenerate convection‐diffusion problem publication-title: Int J Comput Math – volume: 45 start-page: 469 year: 2003 end-page: 479 article-title: A numerical algorithm for singular perturbation problems exhibiting weak boundary layers publication-title: Comput Math Appl – volume: 20 start-page: 641 year: 2015 end-page: 657 article-title: Schemes convergent ‐uniformly for parabolic singularly perturbed problems with a degenerating convective term and a discontinuous source publication-title: Math Model Anal – year: 2009 – volume: 11 start-page: 3 year: 1975 end-page: 5 article-title: A lower bound for the smallest singular value of a matrix publication-title: Linear Algebra and Appl – volume: 40 start-page: 1375 year: 2004 end-page: 1392 article-title: Global maximum norm parameter‐uniform numerical method for a singularly perturbed convection‐diffusion problem with discontinuous convection coefficient publication-title: Math Comput Modelling – volume: 22 start-page: 49 year: 2006 end-page: 65 article-title: Fitted mesh method for singularly perturbed reaction‐convection‐diffusion problems with boundary and interior layers publication-title: J Appl Math Computing – volume: 192 start-page: 132 year: 2006 end-page: 141 article-title: An efficient numerical method for singular perturbation problems publication-title: J Comput Appl Math – volume: 313 start-page: 453 year: 2017 end-page: 473 article-title: Alternating direction numerical scheme for singularly perturbed 2d degenerate parabolic convection‐diffusion problems publication-title: Appl Math Comput – volume: 71 start-page: 153 year: 2003 end-page: 173 article-title: Numerical solution of a reaction‐diffusion elliptic interface problem with strong anisotropy publication-title: Computing – year: 2008 – volume: 166 start-page: 233 year: 2004 end-page: 245 article-title: Singularly perturbed parabolic problems with non‐smooth data publication-title: J Comput Appl Math – volume: 27 start-page: 195 year: 2004 end-page: 206 article-title: A parallel boundary value technique for singularly perturbed two‐point boundary value problems publication-title: J Supercomputs – volume: 169 start-page: 689 year: 2005 end-page: 699 article-title: A hybrid difference scheme for a singularly perturbed convection‐diffusion problem with discontinuous convection coefficient publication-title: Appl Math Comput – volume: 58 start-page: 103 year: 2011 end-page: 141 article-title: ‐uniform error estimate of hybrid numerical scheme for singularly perturbed parabolic problems with interior layers publication-title: Numer Algorithms – year: 1996 – volume: 20 start-page: 263 year: 2000 end-page: 280 article-title: An alternating direction scheme on a nonuniform mesh for reaction‐diffusion parabolic problems publication-title: IMA J Numer Anal – year: 2000 – volume: 163 start-page: 645 year: 2005 end-page: 665 article-title: Uniformly convergent finite volume difference scheme for 2d convection‐dominated problem with discontinuous coefficients publication-title: Appl Math Comput – volume: 107 start-page: 1 year: 2007 end-page: 25 article-title: A high order uniformly convergent alternating direction scheme for time dependent reaction‐diffusion singularly perturbed problems publication-title: Numer Math – volume: 10 start-page: 68 year: 2020 end-page: 101 article-title: A higher‐order hybrid numerical scheme for singularly perturbed convection‐diffusion problem with boundary and weak interior layers publication-title: Int J Math Modell Numer Optimisation – volume: 75 start-page: 2387 year: 2018 end-page: 2403 article-title: Higher‐order convergence with fractional‐step method for singularly perturbed 2d parabolic convection‐diffusion problems on shishkin mesh publication-title: Comput Math Appl – volume: 166 start-page: 133 year: 2004 end-page: 151 article-title: Singularly perturbed convection‐diffusion problems with boundary and weak interior layers publication-title: Comput Appl Math – ident: e_1_2_10_4_1 doi: 10.1142/2933 – volume-title: Difference methods for singular perturbation problems year: 2009 ident: e_1_2_10_7_1 – ident: e_1_2_10_10_1 doi: 10.1016/j.cam.2003.09.033 – ident: e_1_2_10_24_1 doi: 10.1016/0024-3795(75)90112-3 – ident: e_1_2_10_3_1 doi: 10.1080/00207160.2018.1485896 – ident: e_1_2_10_23_1 doi: 10.1016/j.amc.2017.06.010 – ident: e_1_2_10_18_1 doi: 10.1016/j.amc.2004.04.007 – ident: e_1_2_10_22_1 doi: 10.1201/9781482285727 – ident: e_1_2_10_16_1 doi: 10.1007/s11075-011-9449-6 – ident: e_1_2_10_15_1 doi: 10.3846/13926292.2015.1091041 – ident: e_1_2_10_14_1 doi: 10.1016/j.cam.2003.09.025 – ident: e_1_2_10_2_1 doi: 10.1016/j.camwa.2017.12.013 – ident: e_1_2_10_9_1 doi: 10.1023/B:SUPE.0000009322.23950.53 – ident: e_1_2_10_19_1 doi: 10.1007/s00607-003-0009-3 – ident: e_1_2_10_20_1 doi: 10.1093/imanum/20.2.263 – ident: e_1_2_10_5_1 doi: 10.1016/S0898-1221(03)80031-7 – volume-title: Robust numerical methods for singularly perturbed differential equations year: 2008 ident: e_1_2_10_6_1 – ident: e_1_2_10_13_1 doi: 10.1007/BF02896460 – ident: e_1_2_10_21_1 doi: 10.1007/s00211-007-0083-0 – ident: e_1_2_10_8_1 doi: 10.1016/j.cam.2005.04.042 – ident: e_1_2_10_11_1 doi: 10.1016/j.mcm.2005.01.025 – volume: 169 start-page: 689 year: 2005 ident: e_1_2_10_12_1 article-title: A hybrid difference scheme for a singularly perturbed convection‐diffusion problem with discontinuous convection coefficient publication-title: Appl Math Comput – ident: e_1_2_10_17_1 doi: 10.1504/IJMMNO.2020.104325 |
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| SubjectTerms | Convection Convergence Diffusion layers finite difference scheme interior layer Numerical methods piecewise‐uniform meshes Singular perturbation methods singularly perturbed 2‐D parabolic convection–diffusion problem uniform convergence |
| Title | Parameter‐uniform numerical method for singularly perturbed 2‐D parabolic convection–diffusion problem with interior layers |
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