Dirichlet problems in polyhedral domains II: Approximation by FEM and BEM

The convergence of the classical finite element method (FEM) and boundary element method (BEM) is poor due to the edge and vertex singularities of the solution of the involved Dirichlet problem relative to an elliptic operator in a polyhedron. Using the global regularity results of Lubuma and Nicaise (1994), we analyse refined FEM and BEM with optimal rates of convergence.