An efficient weak Galerkin FEM for third-order singularly perturbed convection-diffusion differential equations on layer-adapted meshes

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-06-12 DOI:10.1016/j.apnum.2024.06.009

Suayip Toprakseven , Natesan Srinivasan

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引用次数: 0

Abstract

In this article, we study the weak Galerkin finite element method to solve a class of a third order singularly perturbed convection-diffusion differential equations. Using some knowledge on the exact solution, we prove a robust uniform convergence of order $O (N^{- (k - 1 / 2)})$ on the layer-adapted meshes including Bakhvalov-Shishkin type, and Bakhvalov-type and almost optimal uniform error estimates of order $O ({(N^{- 1} \ln N)}^{(k - 1 / 2)})$ on Shishkin-type mesh with respect to the perturbation parameter in the energy norm using high-order piecewise discontinuous polynomials of degree k. Here N is the number mesh intervals. We conduct numerical examples to support our theoretical results.

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层适应网格上三阶奇异扰动对流扩散微分方程的高效弱 Galerkin 有限元模型

本文研究用弱 Galerkin 有限元方法求解一类三阶奇异扰动对流扩散微分方程。利用关于精确解的一些知识，我们证明了在层适应网格（包括 Bakhvalov-Shishkin 型和 Bakhvalov 型）上阶数为 O(N-(k-1/2))的稳健均匀收敛性，以及在 Shishkin 型网格上阶数为 O((N-1lnN)(k-1/2))的几乎最优均匀误差估计值。我们通过数值示例来支持我们的理论结果。

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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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.