非线性准静态挤压弹性问题的非连续伽勒金方法

IF 1.3 4区数学 Q1 MATHEMATICS International Journal of Numerical Analysis and Modeling Pub Date : 2024-04-01 DOI:10.4208/ijnam2024-1008

Fan Chen,Ming Cui, Chenguang Zhou

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引用次数: 0

摘要

本文致力于非线性准静态孔弹性问题的非连续伽勒金（DG）方法。利用空间近似的 DG 方法和时间离散的后向欧拉方法构建了全隐式非线性数值方案。证明了数值解的存在性和唯一性。然后，我们得出了位移的离散 $H^1$ 准则和压力的 $H^1$ 和 $L^2$ 准则的最佳收敛阶次估计。最后，通过数值实验验证了我们所提方法的理论误差估计值。

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Discontinuous Galerkin Method for Nonlinear Quasi-Static Poroelasticity Problems

This paper is devoted to a discontinuous Galerkin (DG) method for nonlinear quasi-static poroelasticity problems. The fully implicit nonlinear numerical scheme is constructed by utilizing DG method for the spatial approximation and the backward Euler method for the temporal discretization. The existence and uniqueness of the numerical solution is proved. Then we derive the optimal convergence order estimates in a discrete $H^1$ norm for the displacement and in $H^1$ and $L^2$ norms for the pressure. Finally, numerical experiments are supplied to validate the theoretical error estimates of our proposed method.

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来源期刊

International Journal of Numerical Analysis and Modeling 数学-数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.