Direct Discretization of Planar Div-Curl Problems

Abstract

A control volume method is proposed for planar div-curl systems. The method is independent of potential and least squares formulations, and works directly with the div-curl system. The novelty of the technique lies in its use of a single local vector field component and two control volumes rather than the other way round. A discrete vector field theory comes quite naturally from this idea and is developed in the paper. Error estimates are proved for the method, and other ramifications investigated.