(untitled) (Communications in Computational Physics, 2024)
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.