Communications in Mathematical Sciences
Volume 9 (2011)
Convergence analysis of the LDG method for singularly perturbed two-point boundary value problems
Pages: 1013 – 1032
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 L² 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.
local discontinuous Galerkin method, singularly perturbed, Shishkin mesh
2010 Mathematics Subject Classification
65L11, 65N15, 65N30