Convergence Analysis of the LDG Method for Singularly Perturbed Two-Point Boundary Value Problems
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.
Communications in Mathematical Sciences
Tian, H. Y.,
(2011). Convergence Analysis of the LDG Method for Singularly Perturbed Two-Point Boundary Value Problems. Communications in Mathematical Sciences, 9(4), 1013-1032.
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