Error estimates for higher-order finite volume schemes for convection–diffusion problems

Abstract

AbstractIt is still an open problem to provea priorierror estimates for finite volume schemes of higher order MUSCL type, including limiters, on unstructured meshes, which show some improvement compared to first order schemes. In this paper we use these higher order schemes for the discretization of convection dominated elliptic problems in a convex bounded domainΩin ℝ2and we can prove such kind of ana priorierror estimate. In the part of the estimate, which refers to the discretization of the convective term, we gainh1/2. Although the original problem is linear, the numerical problem becomes nonlinear, due to MUSCL type reconstruction/limiter technique.