Local Discontinuous Galerkin Method for a Third-Order Singularly Perturbed Problem of Convection-Diffusion Type

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2022-12-06 DOI:10.1515/cmam-2022-0176

Li Yan, Zhoufeng Wang, Yao Cheng

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引用次数: 0

Abstract

The local discontinuous Galerkin (LDG) method is studied for a third-order singularly perturbed problem of convection-diffusion type. Based on a regularity assumption for the exact solution, we prove almost O ⁢ ( N - ( k + 1 2 ) )

{O(N^{-(k+\frac{1}{2})})}

(up to a logarithmic factor) energy-norm convergence uniformly in the perturbation parameter. Here, k ≥ 0

{k\geq 0}

is the maximum degree of piecewise polynomials used in discrete space, and N is the number of mesh elements. The results are valid for the three types of layer-adapted meshes: Shishkin-type, Bakhvalov–Shishkin-type, and Bakhvalov-type. Numerical experiments are conducted to test the theoretical results.

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一类三阶对流扩散型奇摄动问题的局部不连续伽辽金方法

研究了一类三阶对流扩散型奇异摄动问题的局部不连续伽辽金方法。基于精确解的正则性假设，我们证明了几乎O(N -(k+ 1 2)) {O(N^{-(k+ \frac{1}{2}))}(直到一个对数因子)能量范数在扰动参数上一致收敛。其中，k≥0 }k{\geq 0为}离散空间中使用分段多项式的最大程度，N为网格单元个数。结果适用于三种类型的层适应网格:shishkin型、bakhvalov - shishkin型和bakhvalov型。数值实验对理论结果进行了验证。

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.