Computational Investigations of Least-Squares Type Methods for the Approximate Solution of Boundary Value Problems

Several Galerkin schemes for approximate solution of linear elliptic boundary value problems are studied for such computational aspects as obtainable accuracy, sensitivity to parameters and conditioning of linear systems. Methods studied involve computing subspaces (e.g., splines) whose elements need not satisfy boundary conditions. A Poisson problem study on the square produces computed error reflective of theoretical L2 estimates and Lœ behavior optimal for smooth data but loss according to Sobolev's lemma for nonsmooth data. Insensitivity to parameters is evidenced. Analogous one-dimensional methods enhance the conditioning study. Studies are included for parallelogram and ¿-shaped domains.