On the local discontinuous Galerkin method for singularly perturbed problem with two parameters

摘要

The local discontinuous Galerkin method is studied for a singularly perturbed problem with two parameters. We use a layer-adapted mesh in terms of mesh generating functions, which are discussed in an abstract form and satisfy several assumptions. Robust or almost robust convergence is established in different norms including the energy, L-2, balanced, and maximum norms. Our analysis is based on several projections, i.e., different combinations of local L-2 and local Gauss-Radau projections. By careful approximation error estimation on anisotropic meshes, we establish different error estimates in the mentioned norms. Numerical experiments are also included to test the theoretical results. (C) 2021 Elsevier B.V. All rights reserved.