DISCONTINUOUS DISCRETIZATION FOR LEAST-SQUARES FORMULATION OF SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS IN ONE AND TWO DIMENSIONS

被引：37
作者：
Lin, Runchang [1 ]
机构：
[1] Texas A&M Int Univ, Dept Math & Phys Sci, Laredo, TX 78041 USA
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2008年 / 47卷 / 01期
关键词：
least-squares methods; local discontinuous Galerkin methods; singular perturbation problems; reaction-diffusion problems;
D O I：
10.1137/070700267
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the singularly perturbed reaction-diffusion problem in one and two dimensions. The boundary value problem is decomposed into a first-order system to which a suitable weighted least-squares formulation is proposed. A robust, stable, and efficient approach is developed based on local discontinuous Galerkin (LDG) discretization for the weak form. Uniform error estimates are derived. Numerical examples are presented to illustrate the method and the theoretical results. Comparison studies are made between the proposed method and other methods.
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页码：89 / 108
页数：20
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