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Pointwise Error Estimates for the LDG Method Applied to 1-d Singularly Perturbed Reaction-Diffusion Problems
-
Huiqing Zhu
and
Zhimin Zhang
Published/Copyright:
January 3, 2013
Abstract.
The local discontinuous Galerkin method (LDG) is considered for
solving one-dimensional singularly perturbed two-point boundary
value problems of reaction-diffusion type. Pointwise error
estimates for the LDG approximation to the solution and its
derivative are established on a Shishkin-type mesh. Numerical
experiments are presented. Moreover, a superconvergence of order 
of the numerical traces is observed numerically.
Published Online: 2013-01-03
Published in Print: 2013-01-01
© 2013 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- A Robust Preconditioned MinRes Solver for Time-periodic Eddy Current Problems
- Robust Approximation of Singularly Perturbed Delay Differential Equations by the hp Finite Element Method
- On Cardinal Spline Interpolation
- Convection Problems on Anisotropic Meshes
- Pointwise Error Estimates for the LDG Method Applied to 1-d Singularly Perturbed Reaction-Diffusion Problems
- Implementing Galerkin Finite Element Methods for Semilinear Elliptic Differential Inclusions
Articles in the same Issue
- Masthead
- A Robust Preconditioned MinRes Solver for Time-periodic Eddy Current Problems
- Robust Approximation of Singularly Perturbed Delay Differential Equations by the hp Finite Element Method
- On Cardinal Spline Interpolation
- Convection Problems on Anisotropic Meshes
- Pointwise Error Estimates for the LDG Method Applied to 1-d Singularly Perturbed Reaction-Diffusion Problems
- Implementing Galerkin Finite Element Methods for Semilinear Elliptic Differential Inclusions
