Convergence Analysis of the LDG Method for Singularly Perturbed Two-Point Boundary Value Problems
Document Type
Article
Publication Date
12-1-2011
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
In this paper the local discontinuous Galerkin method (LDG) is considered for solving one-dimensional singularly perturbed two-point boundary value problems of convection-diffusion type and reaction-diffusion type. Error estimates are studied on Shishkin meshes. The L(2) error bounds for the LDG approximation of the solution and its derivative are uniformly valid with respect to the singular perturbation parameter. Numerical experiments indicate that the orders of convergence are sharp.
Publication Title
Communications in Mathematical Sciences
Volume
9
Issue
4
First Page
1013
Last Page
1032
Recommended Citation
Zhu, H.,
Tian, H. Y.,
Zhang, Z.
(2011). Convergence Analysis of the LDG Method for Singularly Perturbed Two-Point Boundary Value Problems. Communications in Mathematical Sciences, 9(4), 1013-1032.
Available at: https://aquila.usm.edu/fac_pubs/623