A hybridizable discontinuous Galerkin method for second order elliptic equations with Dirac delta source

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2022-01-14 DOI:10.1051/m2an/2022005

Haitao Leng, Yanping Chen

引用次数: 4

Abstract

In this paper, we investigate a hybridizable discontinuous Galerkin method for second order elliptic equations with Dirac measures. Under assumption that the domain is convex and the mesh is quasi-uniform, a priori error estimate for the error in $L^2$-norm is proved. By duality argument and Oswald interpolation, a posteriori error estimates for the errors in $L^2$-norm and $W^{1,p}$-seminorm are also obtained. Finally, numerical examples are provided to validate the theoretical analysis.

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二阶椭圆方程的可杂化不连续Galerkin方法

研究了具有Dirac测度的二阶椭圆方程的可杂化不连续Galerkin方法。在假设域是凸的，网格是准均匀的情况下，证明了L^2$-范数误差的先验误差估计。通过对偶论证和Oswald插值，得到了$L^2$-norm和$W^{1,p}$- semormare误差的后验误差估计。最后通过数值算例验证了理论分析的正确性。

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

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.