ROBUST DPG METHOD FOR CONVECTION-DOMINATED DIFFUSION PROBLEMS

被引：79

作者：

Demkowicz, Leszek ^{[1
]}

Heuer, Norbert ^{[2
]}

机构：

[1] Univ Texas Austin, Inst Computat Engn & Sci, Austin, TX 78712 USA

[2] Pontificia Univ Catolica Chile, Fac Matemat, Santiago, Chile

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2013年 / 51卷 / 05期

关键词：

convection-dominated diffusion; hp-adaptivity; discontinuous Petrov-Galerkin method; ADAPTIVITY; EQUATIONS;

D O I：

10.1137/120862065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose and analyze a discontinuous Petrov-Galerkin (DPG) method for convection-dominated diffusion problems that provides robust L-2 error estimates for the field variables which are quasi-optimal in the energy norm. A key feature of the method is to construct test functions defined by a variational formulation with bilinear form (test norm) specifically designed for the goal of robustness. A main theoretical ingredient is a stability analysis of the adjoint problem. Numerical experiments underline our theoretical results and, in particular, confirm robustness of the DPG method for well-chosen test norms.

引用

页码：2514 / 2537

页数：24

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