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 - <p style="text-align: justify;">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.</p>