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A uniformly convergent continuous-discontinuous Galerkin method for singularly perturbed problems of convection-diffusion type |
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| Authors: | Peng Zhu Ziqing Xie |
| Institution: | a Institute of Mathematics, Jiaxing University, Jiaxing, Zhejiang 314001, China b College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China c College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China |
| Abstract: | In this paper, we introduce a coupled approach of local discontinuous Galerkin and standard finite element method for solving singularly perturbed convection-diffusion problems. On Shishkin mesh with linear elements, a rate O(N-1lnN) in an associated norm is established, where N is the number of elements. Numerical experiments complement the theoretical results. Moreover, a rate O(N-2ln2N) in a discrete L∞ norm, and O(N-2) in L2 norm, are observed numerically on the Shishkin mesh. |
| Keywords: | Convection diffusion equation Local discontinuous Galerkin method Finite element method Shishkin mesh Uniform convergence |
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