Uniform Convergence of a Coupled Method for Convection-diffusion Problems in 2-d Shishkin Mesh
نویسندگان
چکیده
In this paper, we introduce a coupled approach of local discontinuous Galerkin (LDG) and continuous finite element method (CFEM) for solving singularly perturbed convection-diffusion problems. When the coupled continuous-discontinuous linear FEM is used under the Shishkin mesh, a uniform convergence rate O(N−1 ln N) in an associated norm is established, where N is the number of elements. Numerical experiments complement the theoretical results. Moreover, a uniform convergence rate O(N−2) in L2 norm, is observed numerically on the Shishkin mesh.
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