Computational Experiments and Techniques for the Penalty Method With Extrapolation

In this note we present results of a computational investigation of the extrapolated penalty method for approximate solution of elliptic boundary value problems. We investigate the effects of extrapolation and present an iterative technique for solving the extra linear algebraic systems necessary to perform the process. We indicate how convergence of the iterative procedure may be accelerated when boundary weights are appropriately selected. We consider the Euclidean relative error in the iterative procedure and the effect of conditioning. We develop a bound for the difference between an extrapolate obtained assuming exact solution of all linear systems and the corresponding quantity computed by a terminated iterative procedure.