01352nam a2200145 a 450000500170000000800400001710000160005724500710007326400160014433600090016033800200016952009050018950600460109485600660114020260901030411.0250101s2019    xx     o     000 0 eng d1 aChunyan Niu10aA Stabilized Hybrid Mixed Finite Element Method for Poroelasticity 1barXivc2019  atext  aonline resource  aIn 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-posed0 aOpen access — freely available to read.40uhttps://arxiv.org/pdf/1906.00885v2yRead the full paper (PDF)