非凸域上扩散和次扩散问题的XFEM

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2025-09-01 DOI:10.1016/j.camwa.2025.08.027

Tao Wang , Yanping Chen , Xiangquan Li , Fangfang Qin

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引用次数: 0

摘要

本文提出了一种求解非凸域上扩散和次扩散问题的时空有限元方法。该方法采用不连续伽辽金法（DG）进行时间离散，采用扩展有限元法（XFEM）进行空间离散，具有比标准线性有限元法更高的精度。对具有光滑和非光滑初始数据的扩散和次扩散问题，用统一的方法导出了尖锐误差估计。最后，给出了两个数值算例来验证理论结果。

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XFEM for the diffusion and sub-diffusion problems in a non-convex domain

This paper proposes a space-time finite element method for solving diffusion and sub-diffusion problems in a non-convex domain. This method employs the discontinuous Galerkin (DG) method for temporal discretization and the eXtended Finite Element Method (XFEM) for spatial discretization, which offers higher accuracy than the standard linear finite element method. Sharp error estimates are derived for diffusion and sub-diffusion problems with smooth and non-smooth initial data in a unified approach. Finally, two numerical examples are provided to verify the theoretical results.

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来源期刊

Computers & Mathematics with Applications 工程技术-计算机：跨学科应用

CiteScore

5.10

自引率

10.30%

发文量

396

审稿时长

9.9 weeks

期刊介绍： Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).