Stability Analysis and Error Estimates of Local Discontinuous Galerkin Method for Convection-Diffusion Equations on Overlapping Mesh with Non-Periodic Boundary Conditions
Year: 2021
Author: Nattaporn Chuenjarern, Kanognudge Wuttanachamsri, Yang Yang
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 6 : pp. 788–810
Abstract
A new local discontinuous Galerkin (LDG) method for convection-diffusion equations on overlapping meshes with periodic boundary conditions was introduced in [14]. With the new method, the primary variable $u$ and the auxiliary variable $p = u_x$ are solved on different meshes. In this paper, we will extend the idea to convection-diffusion equations with non-periodic boundary conditions, i.e. Neumann and Dirichlet boundary conditions. The main difference is to adjust the boundary cells. Moreover, we study the stability and suboptimal error estimates. Finally, numerical experiments are given to verify the theoretical findings.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-19950
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 6 : pp. 788–810
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Local discontinuous Galerkin method stability error analysis overlapping meshes.