Superconvergent finite element solutions of Laplace and Poisson equation

The computation of local field quantities and forces is known to be one of the most serious problems in electromagnetic field computation. A novel technique for obtaining superconvergent derivatives of finite element solutions for Laplace and Poisson type equations is presented. This is achieved by analytical integration of Green's function over single triangles. Superconvergent derivatives of FEM potential solutions have an accuracy of higher order than predicted by the finite element theory. Compared to direct evaluation the number of significant digits doubles. The procedure is illustrated by application to several test examples. It is notable that no restrictive regularity assumptions on the mesh topology are made.