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

Abstract

It is still an open problem to prove a priori error 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 domain Omega in R-2 and we can prove such kind of an a priori error estimate.

In the part of the estimate, which refers to the discretization of the convective term, we gain h(1/2). Although the original problem is linear, the numerical problem becomes nonlinear, due to MUSCL type reconstruction/limiter technique.

Keywords

• linear convection dominated diffusion equation in 2D
• upwind finite volume scheme
• first and higher order finite volume schemes
• a priori error estimates
• MUSCL type reconstruction/limiter