Improved accuracy in finite element methods using fundamental solutions

The present paper is about an improved accuracy approach to finite element calculations of local quantities of interest. Our approach is based on Betti's reciprocal theorem and an integral representation of the local quantity via Green's function. The idea is to split the unknown Green's function into a regular part and a fundamental solution so that only the regular part has to be approximated with finite elements. Further, an upper error bound of the quantity of interest will be obtained. Some numerical studies show highly accurate results.