多孔弹性问题多物理场间断有限元方法后验误差估计

葛志昊, 贺文龙, 马梦霞

doi:10.13371/j.cnki.chin.q.j.m.2025.03.002

数学季刊 >

2025 , Vol. 40 >Issue 3: 238 - 261

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.03.002

多孔弹性问题多物理场间断有限元方法后验误差估计

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1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China; 2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China; 3. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

GE Zhi-hao (1980-), male, native of Zhoukou, Henan, profesor of Henan University, engages in finite element method and application; HE Wen-long (1998-), male, native of Jianshui, Yunnan, doctoral student of Wuhan University, engages in finite element method; MA Meng-xia (1989-), female, native of Zhumadian, Henan, lecturer of Shijiazhuang Tiedao University, engages in computational fluid dynamics.

GE Zhi-hao (1980-), male, native of Zhoukou, Henan, profesor of Henan University, engages in finite element method and application

收稿日期: 2025-04-26

网络出版日期: 2025-09-30

基金资助

The work is supported by the National Natural Science Foundation of China (Grant Nos. 12371393 and 11971150) and Natural Science Foundation of Henan (Grant No. 242300421047).

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A Posteriori Error Estimate of Multiphysics Discontinuous Galerkin Method for a Poroelasticity#br#

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1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China; 2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China; 3. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

GE Zhi-hao (1980-), male, native of Zhoukou, Henan, profesor of Henan University, engages in finite element method and application

Received date: 2025-04-26

Online published: 2025-09-30

Supported by

The work is supported by the National Natural Science Foundation of China (Grant Nos. 12371393 and 11971150) and Natural Science Foundation of Henan (Grant No. 242300421047).

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摘要

In this paper, we design a new error estimator and give a posteriori error analysis for a poroelasticity model. To better overcome “locking phenomenon” on pressure and displacement, we proposed a new error estimators based on multiphysics discontinuous Galerkin method for the poroelasticity model. And we prove the upper and lower bound of
the proposed error estimators, which are numerically demonstrated to be computationally very efficient. Finally, we present numerical examples to verify and validate the efficiency of the proposed error estimators, which show that the adaptive scheme can overcome “locking phenomenon” and greatly reduce the computation cost.

关键词： Poroelasticity model; A posteriori error; Multiphysics discontinuous Galerkin ; method

本文引用格式

葛志昊, 贺文龙, 马梦霞 . 多孔弹性问题多物理场间断有限元方法后验误差估计[J]. 数学季刊, 2025 , 40(3) : 238 -261 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.002

Abstract

Key words： Poroelasticity model; A posteriori error; Multiphysics discontinuous Galerkin ; method

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