抛物型方程弱Galerkin有限元变时步BDF2隐式格式的收敛性分析

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-02-21 DOI:10.1016/j.apnum.2025.02.015

Chenxing Li , Fuzheng Gao , Jintao Cui

引用次数: 0

摘要

本文给出了求解抛物型问题的一种完全离散隐式方法。在时间上采用变时间步长BDF2方法，在空间上采用弱伽辽金有限元法。在时间步长比为0<；rk≤4.8645的条件下，得到了h1 -范数0 （hr+τ2）和l2 -范数0 （hr+1+τ2）的最优误差估计。数值实验证实了理论结果。在此基础上，提出了一种自适应算法，并进行了验证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Convergence analysis of weak Galerkin finite element variable-time-step BDF2 implicit scheme for parabolic equations

In this paper, we propose a fully discrete implicit method for parabolic problem. The variable-time-step BDF2 method is applied in time combining with the weak Galerkin finite element method in space. Optimal error estimates of

O (h^{r} + τ^{2})

H^{1}

-norm and

O (h^{r + 1} + τ^{2})

L^{2}

-norm are derived under the time-step ratio

0 < r_{k} ⩽ 4.8645

. Numerical experiments confirm the theoretical findings. Furthermore, an adaptive scheme is introduced and validated to enhance the computational performance.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.