Discontinuous Galerkin method of lines for solving nonstationary singularly perturbed linear problems

M. Feistauer, Karel Svadlenka
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引用次数: 43

Abstract

The subject-matter is the analysis of the discontinuous Galerkin finite element method of lines applied to a linear nonstationary convection–diffusion–reaction problem. In the contrary to the standard FEM the requirement of the conforming properties is omitted. The discretization is carried out with respect to space variables, whereas time remains continuous. In the discontinuous Galerkin discretization, the nonsymmetric stabilization of diffusion terms combined with interior and boundary penalty is applied. In the evaluation of fluxes the idea of upwinding is used. This allows to obtain an optimal error estimate, also verified by numerical experiments.
求解非平稳奇摄动线性问题的不连续伽辽金线法
本文的主题是分析不连续伽辽金线有限元法在求解线性非平稳对流-扩散-反应问题中的应用。与标准有限元法相反,省去了对符合特性的要求。离散化是对空间变量进行的,而时间是连续的。在不连续伽辽金离散化中,应用了扩散项的非对称镇定,并结合了内惩罚和边界惩罚。在通量的评估中使用了上绕的概念。这可以获得最优的误差估计,也通过数值实验验证。
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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