Error estimates and mesh adaption for a cell vertex finite volume scheme

Abstract

In this paper we investigate a posteriori error estimates for the cell vertex finite volume method and their applicability to adaptive mesh generation. We start from the cell vertex scheme reformulated as a Petrov-Galerkin finite element method and base the error estimate on the calculation of the finite element residual of the approximate solution. An analogy can be made between the residual in finite element methods and the truncation error of finite difference schemes. Numerical investigation of the performance of the error indicator for a model problem of two dimensional advection demonstrate its reliability and efficiency. The error indicator is then applied to a transonic Euler calculation where it is contrasted with an alternative procedure based on first and second differences of physical flow quantities which can be related to local interpolation error. Finally, we discuss the effective use of error estimates in adaptive mesh generation.