An Accuracy Condition for the Finite Element Discretization of Biot’s Equations on Triangular Meshes
Marco Favino, Jürg Hunziker, Klaus Holliger, Rolf Krause · 2017
Finite element solutions of Biot’s equations may be characterized by unphysical oscillations for small time-steps or low permeabilities. We analyse these numerical wiggles by comparing the Schur complement of the system with an equivalent reaction-diffusion problem. We show that the non-physical behaviour of the discrete solution is due to the fact that the discrete maximum principle is not satisfied. We provide a sufficient condition for two-dimensional problems of this kind to ensure monotonic solutions on triangular meshes.