A general convergence theorem for finite volume approximation of variational problems

Du Pham

Indiana University


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.