Virtual element methods for the three-field formulation of time-dependent linear poroelasticity

• Published in: Advances in computational mathematics Vol. 47; no. 1
• Main Authors: Bürger, Raimund, Kumar, Sarvesh, Mora, David, Ruiz-Baier, Ricardo, Verma, Nitesh
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2021; Springer Nature B.V
• Subjects: 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; A priori error analysis; Time-dependent problems; 74F10; Biot equations; 65M60; 35K57; 74L15; Virtual element method
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-020-09826-7

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.