Abstract

In this talk, we will present a hybrid mixed finite element method for poroelasticity model. The hybrid P1-RT0-P0 discretization of the displacement-pressure-Darcy’s velocity system of Biot’s model presented is not uniformly stable with respect to the physical parameters, resulting in some issues in numerical simulations. To alleviate such problems,  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-posedness of the eliminated system, we design block preconditioners that are parameter robust. Numerical experiments are presented to confirm the theoretical results of the stabilized scheme as well as the block preconditioners. We will also present some other works on poroelastic problem simply.

个人简介

芮洪兴，男，理学博士，山东大学教授，博士生导师，山东大学数学学院副院长。主要从事计算数学和应用数学研究，包括有限元和混合元方法，有限体积元，差分算法，特征线算法等偏微分方程数值解法，流体及渗流力学问题数值模拟方法及应用软件。发表论文150余篇，其中 SCI收录近百余篇。现任中国工业与应用数学学会常务理事、中国计算物理学会常务理事，曾任中国计算数学学会常务理事。