UNIFORM SUPERCONVERGENCE OF GALERKIN METHODS FOR SINGULARLY PERTURBED PROBLEMS  

作　　者：Ying Chen Min Huang 

机构地区：[1]Department of Mathematics, University of California, lrvine, CA 92697, USA [2]Department of Computer Science, Purdue University, West Lafayette, IN ~ 7907, USA

出　　处：《Journal of Computational Mathematics》2010年第2期273-288,共16页计算数学（英文）

摘　　要：In this paper, we are concerned with uniform superconvergence of Galerkin methods for singularly perturbed reaction-diffusion problems by using two Shishkin-type meshes. Based on an estimate of the error between spline interpolation of the exact solution and its numerical approximation, an interpolation post-processing technique is applied to the original numerical solution. This results in approximation exhibit superconvergence which is uniform in the weighted energy norm. Numerical examples are presented to demonstrate the effectiveness of the interpolation post-processing technique and to verify the theoretical results obtained in this paper.In this paper, we are concerned with uniform superconvergence of Galerkin methods for singularly perturbed reaction-diffusion problems by using two Shishkin-type meshes. Based on an estimate of the error between spline interpolation of the exact solution and its numerical approximation, an interpolation post-processing technique is applied to the original numerical solution. This results in approximation exhibit superconvergence which is uniform in the weighted energy norm. Numerical examples are presented to demonstrate the effectiveness of the interpolation post-processing technique and to verify the theoretical results obtained in this paper.

关 键 词：singularly perturbed Hermite splines Shishkin-type meshes Interpolation post-processing Uniform superconvergence. 

分 类 号：O175.29[理学—数学] O241.82[理学—基础数学]