TY  - BOOK
AU  - Chunyan Niu
TI  - A Stabilized Hybrid Mixed Finite Element Method for Poroelasticity
PY  - 2019///
PB  - arXiv
N1  - Open access — freely available to read
N2  - In this work, we consider a hybrid mixed finite element method for Biot's model. The hybrid P1-RT0-P0 discretization of the displacement-pressure-Darcy's velocity system of Biot's model presented in \cite{C. Niu} is not uniformly stable with respect to the physical parameters, resulting in some issues in numerical simulations. To alleviate such problems, following \cite{V. Girault}, we stabilize the hybrid scheme with face bubble functions and show the well-posedness with respect to physical and discretization parameters, which provide optimal error estimates of the stabilized method. We introduce a perturbation of the bilinear form of the displacement which allows for the elimination of the bubble functions. Together with eliminating Darcy's velocity by hybridization, we obtain an eliminated system whose size is the same as the classical P1-RT0-P0 discretization. Based on the well-posed
UR  - https://arxiv.org/pdf/1906.00885v2
ER  -