The elliptic property and local truncation error for the full finite volume method of the convection-diffusion problem

Abstract EN

In this paper, a full finite volume method is studied for the two-dimensional linear convection- diffusion problem.

A linear convection term is approximated by the upwind finite element method considered over a mesh to the triangular grid, whereas the linear diffusion term is approximated by using divergence theorem and approximate the direction derivative by difference quotient.

The elliptic property, the discrete conservation law and local truncation error of this method are proved under some assumption on the numerical fluxes.