The author describes a framework for implementing the Schwarz alternating and iterative refinement method applied to elliptic boundary value problems. The structure of the resulting discretized equations is then considered in a similar way to the more standard block Jacobi and Gauss- Seidel methods. By exploiting any overlap between the blocks it is shown that if there is sufficient overlap between the domains convergence is proven independent of the local geometry and limited continuity of the coefficients.