两个小参数奇异扰动问题的巴赫瓦洛夫型网格上 NIPG 方法的超封闭性

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED Applied Numerical Mathematics Pub Date : 2024-09-19 DOI:10.1016/j.apnum.2024.09.016

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引用次数: 0

摘要

本文针对具有两个小参数的奇异扰动问题，提出了巴赫瓦洛夫网格上的非对称内部惩罚伽勒金（NIPG）方法。为了更准确地反映层的行为，本文引入了平衡规范而非普通能量规范。通过在不同网格点选择特殊的惩罚参数，我们建立了 k+12 阶的超松性，并证明了平衡规范中均匀收敛的最优阶。我们提出了数值实验来证实我们的理论结果。

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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Supercloseness of the NIPG method on a Bakhvalov-type mesh for a singularly perturbed problem with two small parameters

In this paper, the nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov-type mesh is proposed for a singularly perturbed problem with two small parameters. In order to reflect the behavior of layers more accurately, a balanced norm, rather than the common energy norm, is introduced. By selecting special penalty parameters at different mesh points, we establish the supercloseness of

k + \frac{1}{2}

order, and prove an optimal order of uniform convergence in a balanced norm. Numerical experiments are proposed to confirm our theoretical results.

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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.