Virtual element methods for the three-field formulation of time-dependent linear poroelasticity
Numerical Analysis
2019-12-13 v1 Numerical Analysis
Abstract
A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in [R. Oyarz\'ua and R. Ruiz-Baier, Locking-free finite element methods for poroelasticity, SIAM J. Numer. Anal. 54 (2016) 2951--2973] 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. Furthermore, the accuracy of the method is verified numerically through a set of computational tests.
Cite
@article{arxiv.1912.06029,
title = {Virtual element methods for the three-field formulation of time-dependent linear poroelasticity},
author = {Raimund Bürger and Sarvesh Kumar and David Mora and Ricardo Ruiz-Baier and Nitesh Verma},
journal= {arXiv preprint arXiv:1912.06029},
year = {2019}
}