层适配 Shishkin 网格上四阶抛物线奇异扰动问题的弱 Galerkin 有限元方法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-09-23 DOI:10.1016/j.apnum.2024.09.019

Aayushman Raina, Srinivasan Natesan

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引用次数: 0

摘要

本文针对一类四阶奇异扰动抛物线问题提出了一种弱 Galerkin 有限元近似方法。该问题具有边界层，因此我们考虑了与层相适应的三角网格，特别是空间域的 Shishkin 三角网格。在时间离散化方面，我们采用了均匀网格上的 Crank-Nicolson 方案。我们已经证明了该方法的稳定性、误差估计值以及均匀收敛性。其中的数值示例验证了我们的分析。

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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A weak Galerkin finite element method for fourth-order parabolic singularly perturbed problems on layer adapted Shishkin mesh

In this paper, we propose a weak Galerkin finite element approximation for a class of fourth-order singularly perturbed parabolic problems. The problem exhibits boundary layers and so we have considered layer adapted triangulations, in particular Shishkin triangular mesh in the spatial domain. For temporal discretization, we utilize the Crank-Nicolson scheme on a uniform mesh. Stability and error estimates along with the uniform convergence of the method has been proved. Numerical examples are included which verifies our analysis.

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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.