Multipole-accelerated iterative methods for potential problems will be developed to include automatic discretization error control, in particular, methods to include higher-order boundary elements and automatically refine low-and high- order elements. Two test problems with known analytical solutions specified by a mixture of Neuman and Dirichlet boundary conditions will be used to investigate the low-order approach and to give a direct numerical error calibration. Utilizing the above results several localized approached will be developed with different "Computational Cost" for the purpose of element refinements with specified error bounds.
