Robust three-field finite element methods for Biot's consolidation model in poroelasticity
The article presents a numerical scheme for approximating the Biot's consolidation model. Besides medium displacement and fluid pressure, a third variable is introduced for the product of the permeability tensor and pressure gradient. The resulting three-field model is approximated in space by finite elements, based on Raviart-Thomas, piecewise constant and Mardal-Tai-Winther elements. The temporal approximation is based on the backward Euler scheme. Error analysis for the semi-discrete and fully discrete solutions are presented, which avoid using Gronwall's inequality and yield favourable error bounds. Moreover, the error bounds are uniformly bounded for arbitrarily large Lame coefficients and small storage coefficients.
scientific article; zbMATH DE number 6894728
scientific article