## A general convergence theorem for finite volume approximation of variational problems

## Du Pham

### Indiana University

Abstract:
We will first discretize a Dirichlet problem by finite volume
methods and discuss its weak consistency. Next, we prove strong
convergence results for general elliptic problems using the external
space approximation frame work of Lions and Cea. Due to the weak
consistency, the proof for convergence results is done by comparing
the well known convergence results in finite difference methods with
those in finite volume methods.