Superconvergence of discontinuous Galerkin method with interior penalties for singularly perturbed two-point boundary-value problems

被引：11

作者：

Singh, Gautam ^{[1
]}

Natesan, Srinivasan ^{[1
]}

机构：

[1] Indian Inst Technol Guwahati, Dept Math, Gauhati 781039, Assam, India

来源：

CALCOLO | 2018年 / 55卷 / 04期

关键词：

Singularly perturbed differential equation; Discontinuous Galerkin finite element method; Shishkin mesh; Superconvergence; FINITE-ELEMENT SUPERCONVERGENCE; CONVECTION-DIFFUSION PROBLEMS; SHISHKIN MESH;

D O I：

10.1007/s10092-018-0297-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, superconvergence properties of the discontinuous Galerkin method for singularly perturbed two-point boundary-value problems of reaction-diffusion and convection-diffusion types are studied. By using piecewise polynomials of degree k on modified Shishkin mesh, superconvergence error bounds of (N-1 ln N)(k+1) in the discrete energy norm are established, where N is the number of elements. Finally, the convergence result is verified numerically.

引用

页数：30

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