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Volume 18, Issue 6
Stability Analysis and Error Estimates of Local Discontinuous Galerkin Method for Convection-Diffusion Equations on Overlapping Mesh with Non-Periodic Boundary Conditions

Nattaporn Chuenjarern, Kanognudge Wuttanachamsri & Yang Yang

Int. J. Numer. Anal. Mod., 18 (2021), pp. 788-810.

Published online: 2021-11

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  • 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.

  • Keywords

Local discontinuous Galerkin method, stability, error analysis, overlapping meshes.

  • AMS Subject Headings

65M12, 65M15, 65M20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-18-788, author = {Chuenjarern , NattapornWuttanachamsri , Kanognudge and Yang , Yang}, title = {Stability Analysis and Error Estimates of Local Discontinuous Galerkin Method for Convection-Diffusion Equations on Overlapping Mesh with Non-Periodic Boundary Conditions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {6}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/19950.html} }
TY - JOUR T1 - Stability Analysis and Error Estimates of Local Discontinuous Galerkin Method for Convection-Diffusion Equations on Overlapping Mesh with Non-Periodic Boundary Conditions AU - Chuenjarern , Nattaporn AU - Wuttanachamsri , Kanognudge AU - Yang , Yang JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 788 EP - 810 PY - 2021 DA - 2021/11 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/19950.html KW - Local discontinuous Galerkin method, stability, error analysis, overlapping meshes. AB -

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.

Chuenjarern , NattapornWuttanachamsri , Kanognudge and Yang , Yang. (2021). Stability Analysis and Error Estimates of Local Discontinuous Galerkin Method for Convection-Diffusion Equations on Overlapping Mesh with Non-Periodic Boundary Conditions. International Journal of Numerical Analysis and Modeling. 18 (6). 788-810. doi:
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