Uniform Convergence Analysis of the Discontinuous Galerkin Method on Layer-Adapted Meshes for Singularly Perturbed Problem

Uniform Convergence Analysis of the Discontinuous Galerkin Method on Layer-Adapted Meshes for Singularly Perturbed Problem

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-adapt...

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Veröffentlicht in:Wuhan University journal of natural sciences 2023-10, Vol.28 (5), p.411-420
Hauptverfasser: SHI, Jiamin, LU, Zhongshu, ZHANG, Luyi, LU, Sunjia, CHENG, Yao
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container_issue 5
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container_title Wuhan University journal of natural sciences
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creator SHI, Jiamin
LU, Zhongshu
ZHANG, Luyi
LU, Sunjia
CHENG, Yao
description 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 L 2 -error estimate if the true solution has a special regular component. Numerical experiments are also given.
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title Uniform Convergence Analysis of the Discontinuous Galerkin Method on Layer-Adapted Meshes for Singularly Perturbed Problem
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