Discontinuous Galerkin method for the fully dynamic Biot's model

被引：4

作者：

Wen, Jing ^{[1
]}

He, Yinnian ^{[1
]}

Chen, Hongbin ^{[1
]}

机构：

[1] Xi An Jiao Tong Univ, Dept Math & Stat, Xian 710049, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 485卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Fully dynamic Biot's model; Discontinuous Galerkin method; Fully discrete scheme; Priori error estimates; FINITE-ELEMENT METHODS; POROELASTICITY; ELASTICITY;

D O I：

10.1016/j.jmaa.2019.123837

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a fully discrete scheme of the fully dynamic Biot's model problem is proposed, which is constructed by using interior penalty discontinuous Galerkin method for the spatial approximation and a tailor difference scheme to approximate the first and second order temporal derivative terms. First of all, we prove the existence and uniqueness of solutions of proposed fully discrete scheme in proper norms. Then, based on the error equations a priori error estimates shall be derived for both primal variables displacement and pore pressure. Finally, a series of numerical examples are given to examine the convergence results by using the proposed numerical scheme to solve the fully dynamic Biot's model problem. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：21

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