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Volume 35, Issue 1
A New Upwind Finite Volume Element Method for Convection-Diffusion-Reaction Problems on Quadrilateral Meshes

Ang Li, Hongtao Yang, Yulong Gao & Yonghai Li

DOI: 10.4208/cicp.OA-2023-0189

Commun. Comput. Phys., 35 (2024), pp. 239-272.

Published online: 2024-01

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  • Abstract

This paper is devoted to constructing and analyzing a new upwind finite volume element method for anisotropic convection-diffusion-reaction problems on general quadrilateral meshes. We prove the coercivity, and establish the optimal error estimates in $H^1$ and $L^2$ norm respectively. The novelty is the discretization of convection term, which takes the two terms Taylor expansion. This scheme has not only optimal first-order accuracy in $H^1$ norm, but also optimal second-order accuracy in $L^2$ norm, both for dominant diffusion and dominant convection. Numerical experiments confirm the theoretical results.

  • Keywords

Convection-diffusion-reaction, upwind finite volume method, coercivity, optimal convergence rate in $L^2$ norm.

  • AMS Subject Headings

65N08, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-35-239, author = {Li , AngYang , HongtaoGao , Yulong and Li , Yonghai}, title = {A New Upwind Finite Volume Element Method for Convection-Diffusion-Reaction Problems on Quadrilateral Meshes}, journal = {Communications in Computational Physics}, year = {2024}, volume = {35}, number = {1}, pages = {239--272}, abstract = {

This paper is devoted to constructing and analyzing a new upwind finite volume element method for anisotropic convection-diffusion-reaction problems on general quadrilateral meshes. We prove the coercivity, and establish the optimal error estimates in $H^1$ and $L^2$ norm respectively. The novelty is the discretization of convection term, which takes the two terms Taylor expansion. This scheme has not only optimal first-order accuracy in $H^1$ norm, but also optimal second-order accuracy in $L^2$ norm, both for dominant diffusion and dominant convection. Numerical experiments confirm the theoretical results.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0189}, url = {http://global-sci.org/intro/article_detail/cicp/22902.html} }
TY - JOUR T1 - A New Upwind Finite Volume Element Method for Convection-Diffusion-Reaction Problems on Quadrilateral Meshes AU - Li , Ang AU - Yang , Hongtao AU - Gao , Yulong AU - Li , Yonghai JO - Communications in Computational Physics VL - 1 SP - 239 EP - 272 PY - 2024 DA - 2024/01 SN - 35 DO - http://doi.org/10.4208/cicp.OA-2023-0189 UR - https://global-sci.org/intro/article_detail/cicp/22902.html KW - Convection-diffusion-reaction, upwind finite volume method, coercivity, optimal convergence rate in $L^2$ norm. AB -

This paper is devoted to constructing and analyzing a new upwind finite volume element method for anisotropic convection-diffusion-reaction problems on general quadrilateral meshes. We prove the coercivity, and establish the optimal error estimates in $H^1$ and $L^2$ norm respectively. The novelty is the discretization of convection term, which takes the two terms Taylor expansion. This scheme has not only optimal first-order accuracy in $H^1$ norm, but also optimal second-order accuracy in $L^2$ norm, both for dominant diffusion and dominant convection. Numerical experiments confirm the theoretical results.

Ang Li, Hongtao Yang, Yulong Gao & Yonghai Li. (2024). A New Upwind Finite Volume Element Method for Convection-Diffusion-Reaction Problems on Quadrilateral Meshes. Communications in Computational Physics. 35 (1). 239-272. doi:10.4208/cicp.OA-2023-0189
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