New stabilized mixed finite element methods for two-field poroelasticity with low permeability

作     者：He, Linshuang Jing, Luru Feng, Minfu 

作者机构：Sichuan Univ Sch Math Chengdu 610065 Peoples R China 

出 版 物：《APPLIED MATHEMATICS AND COMPUTATION》 (Appl. Math. Comput.)

年 卷 期：2025年第494卷

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China 

主　　题：Poroelasticity Low permeability Stabilized method Mixed finite element method 

摘      要：In this paper, we develop new stabilized mixed finite element (MFE) methods for two-field Biot s model of poroelasticity. We employ the H(div)-conforming element and discontinuous element to approximate the displacement and pressure variables, and use the theta-scheme to discretize time. By adding the stabilization term based on polynomial pressure projection, the fully-discrete and stabilized MFE methods are obtained. Our methods work well for both inf-sup stable and unstable element pairs, and provide oscillation-free pressure solutions in heterogeneous materials with low-permeable layers or interfaces. These methods are also volumetric locking-free and locally mass-conservative. We establish optimal apriori error estimates and perform numerical examples, which show the uniform robustness of the proposed methods for low permeability.