Mixed and multipoint finite element methods for rotation-based poroelasticity
Abstract
This work proposes a mixed finite element method for the Biot poroelasticity equations that employs the lowest-order Raviart-Thomas finite element space for the solid displacement and piecewise constants for the fluid pressure. The method is based on the formulation of linearized elasticity as a weighted vector Laplace problem. By introducing the solid rotation and fluid flux as auxiliary variables, we form a four-field formulation of the Biot system, which is discretized using conforming mixed finite element spaces. The auxiliary variables are subsequently removed from the system in a local hybridization technique to obtain a multipoint rotation-flux mixed finite element method. Stability and convergence of the four-field and multipoint mixed finite element methods are shown in terms of weighted norms, which additionally leads to parameter-robust preconditioners. Numerical experiments confirm the theoretical results.
Cite
@article{arxiv.2212.12448,
title = {Mixed and multipoint finite element methods for rotation-based poroelasticity},
author = {Wietse M. Boon and Alessio Fumagalli and Anna Scotti},
journal= {arXiv preprint arXiv:2212.12448},
year = {2022}
}