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.
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页数：30
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