Local Discontinuous Galerkin Method for a Third-Order Singularly Perturbed Problem of Convection-Diffusion Type-Reference-Cited by-同舟云学术

Local Discontinuous Galerkin Method for a Third-Order Singularly Perturbed Problem of Convection-Diffusion Type

Published:2022-12-06 Issue:0 Volume:0 Page:
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Yan Li¹,Wang Zhoufeng²,Cheng Yao¹^ORCID

Affiliation:

1. School of Mathematical Sciences , Suzhou University of Science and Technology , Jiangsu , P. R. China

2. School of Mathematics and Statistics , Henan University of Science and Technology , Henan , P. R. China

Abstract

Abstract The local discontinuous Galerkin (LDG) method is studied for a third-order singularly perturbed problem of convection-diffusion type. Based on a regularity assumption for the exact solution, we prove almost O ⁢ ( N - ( k + 1 2 ) )

{O(N^{-(k+\frac{1}{2})})}

(up to a logarithmic factor) energy-norm convergence uniformly in the perturbation parameter. Here, k ≥ 0

{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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2022-0176/pdf

Reference19 articles.

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2. Y. Cheng, Y. Mei and H.-G. Roos, The local discontinuous Galerkin method on layer-adapted meshes for time-dependent singularly perturbed convection-diffusion problems, Comput. Math. Appl. 117 (2022), 245–256.

3. Y. Cheng, L. Yan, X. Wang and Y. Liu, Optimal maximum-norm estimate of the LDG method for singularly perturbed convection-diffusion problem, Appl. Math. Lett. 128 (2022), Paper No. 107947.

4. Y. Cheng and Q. Zhang, Local analysis of the local discontinuous Galerkin method with generalized alternating numerical flux for one-dimensional singularly perturbed problem, J. Sci. Comput. 72 (2017), no. 2, 792–819.

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