On the Accuracy of the Finite Volume Element Method for Diffusion Equations on Composite Grids

Abstract

This paper develops the finite volume element (FVE) method, which is similar to the so-called control volume finite element method but tailored to composite grid applications. FVE is described for the general two-dimensional diffusion equation in divergence form; $O(h^{{3 / 2}} )$ discretization error estimates are then developed for the case of triangular elements. These results are improved to $O(h^2 )$ using a special modification involving rectilinear elements at the grid interface.