| Citation: |
Yaxiang Li, Jiangxing Wang. HIGH ORDER PARAMETER-UNIFORM CONVERGENT HDG METHOD FOR SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1466-1474. doi: 10.11948/20210283
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HIGH ORDER PARAMETER-UNIFORM CONVERGENT HDG METHOD FOR SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM
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Abstract
In this paper, a high order hybridizable discontinuous Galerkin method (HDG) on two layer-adapted meshes have been developed for the singularly perturbed convection-diffusion problems in one and two-dimensional. The existence and uniqueness of the HDG solutions are verified. Thanks to the implementation of two-type different anisotropic meshes, i.e., the Shishkin and an improved grade meshes, the uniform 2k + 1 -order super-convergence is obtained for both one-dimensional and two-dimensional cases.
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References
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Yaxiang Li, Jiangxing Wang. HIGH ORDER PARAMETER-UNIFORM CONVERGENT HDG METHOD FOR SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1466-1474. doi: 10.11948/20210283
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Figure 1.
$ u $ and$ \hat{u}_h $ (left),$ q $ and$ \hat{q}_h $ (right) under uniform mesh,$ N=32, k=1, \epsilon=10^{-6} $ . -
Figure 2. From left to right: exact solution, Numerical solution
$ k=2, $ and Numerical solution$ k=3 $ for$ \epsilon=1.0e-6 $