| Issue |
Wuhan Univ. J. Nat. Sci.
Volume 28, Number 5, October 2023
|
|
|---|---|---|
| Page(s) | 411 - 420 | |
| DOI | https://doi.org/10.1051/wujns/2023285411 | |
| Published online | 10 November 2023 | |
Mathematics
CLC number: O241
Uniform Convergence Analysis of the Discontinuous Galerkin Method on Layer-Adapted Meshes for Singularly Perturbed Problem
School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China
† To whom correspondence should be addressed. E-mail: ycheng@usts.edu.cn
Received:
2
March
2023
This paper concerns a discontinuous Galerkin (DG) method for a one-dimensional singularly perturbed problem which possesses essential characteristic of second order convection-diffusion problem after some simple transformations. We derive an optimal convergence of the DG method for eight layer-adapted meshes in a general framework. The convergence rate is valid independent of the small parameter. Furthermore, we establish a sharper L2-error estimate if the true solution has a special regular component. Numerical experiments are also given.
Key words: layer-adapted meshes / singularly perturbed problem / uniform convergence / discontinuous Galerkin method
Biography: SHI Jiamin, female, Undergraduate, research direction: computational method. E-mail: 21200210103@qq.com
Fundation item: Supported by the National Natural Science Foundation of China (11801396) and National College Students Innovation and Entrepreneurship Training Project (202210332019Z)
© Wuhan University 2023
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