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arXiv · 2210.13315

Local discontinuous Galerkin method for a third order singularly perturbed problem of convection-diffusion type

Li Yan·Zhoufeng Wang·Yao Cheng
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Abstract

The local discontinuous Galerkin (LDG) method is studied for a third-order singularly perturbed problem of the convection-diffusion type. Based on a regularity assumption for the exact solution, we prove almost $O(N^{-(k+1/2)})$ (up to a logarithmic factor) energy-norm convergence uniformly in the perturbation parameter. Here, $k\geq 0$ is the maximum degree of piecewise polynomials used in discrete space, and $N$ is the number of mesh elements. The results are valid for the three types of layer-adapted meshes: Shishkin-type, Bakhvalov-Shishkin type, and Bakhvalov-type. Numerical experiments are conducted to test the theoretical results.

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Li Yan, Zhoufeng Wang, Yao Cheng. 2022-10-24. Local discontinuous Galerkin method for a third order singularly perturbed problem of convection-diffusion type. https://arxiv.org/abs/2210.13315

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