Superconvergence analysis of FEM and SDFEM on graded meshes for a problem with characteristic layers

被引：4

作者：

Brdar, M. ^{[1
]}

Radojev, G. ^{[2
]}

Roos, H-G ^{[3
]}

Teofanov, Lj ^{[4
]}

机构：

[1] Univ Novi Sad, Fac Technol, Bulevar Cara Lazara 1, Novi Sad 21000, Serbia

[2] Univ Novi Sad, Fac Sci, Dept Math & Informat, Trg Dositeja Obradovica 4, Novi Sad 21000, Serbia

[3] Tech Univ Dresden, Inst Numer Math, D-01062 Dresden, Germany

[4] Univ Novi Sad, Fac Tech Sci, Trg Dositeja Obradovica 6, Novi Sad 21000, Serbia

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2021年 / 93卷

关键词：

Singular perturbation; Characteristic layers; Finite element method; Streamline diffusion method; Graded mesh; Superconvergence; CONVECTION-DIFFUSION PROBLEMS; FINITE-ELEMENT APPROXIMATION; BOUNDARY-VALUE-PROBLEMS; SCHEMES; CONVERGENCE; GALERKIN;

D O I：

10.1016/j.camwa.2021.04.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a singularly perturbed convection-diffusion boundary value problem whose solution contains exponential and characteristic boundary layers. The problem is numerically solved by the FEM and SDFEM method with bilinear elements on a graded mesh. For the FEM we prove almost uniform convergence and superconvergence. The use of a graded mesh allows for the SDFEM to yield almost uniform estimates in the SD norm, which is not possible for Shishkin type meshes. Numerical results are presented to support theoretical bounds.

引用

页码：50 / 57

页数：8

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