二阶椭圆型问题的内罚杂交不连续Galerkin方法族

IF 3.8 2区数学 Q1 MATHEMATICS

Journal of Numerical Mathematics Pub Date : 2019-09-06 DOI:10.1515/jnma-2019-0027

M. Fabien, M. Knepley, B. Rivière

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引用次数: 6

摘要

摘要本文重点分析了二阶椭圆型问题的可杂交内罚不连续伽辽金方法族。我们在能量范数中推导出相对于网格尺寸最优的先验误差估计。证明了次优l2范数误差估计。这些结果在二维和三维中都是有效的。数值结果支持了我们的理论发现，并说明了该方法的计算成本。

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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Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems

Abstract The focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive a priori error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal L2-norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.

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来源期刊

Journal of Numerical Mathematics 数学-数学

CiteScore

5.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Numerical Mathematics (formerly East-West Journal of Numerical Mathematics) contains high-quality papers featuring contemporary research in all areas of Numerical Mathematics. This includes the development, analysis, and implementation of new and innovative methods in Numerical Linear Algebra, Numerical Analysis, Optimal Control/Optimization, and Scientific Computing. The journal will also publish applications-oriented papers with significant mathematical content in computational fluid dynamics and other areas of computational engineering, finance, and life sciences.