Overlapping solution finite element method – Higher order approximation and implementation

An hp-convergence result is established for an overlapping solution finite element method employed in exterior scattering problems. The method relies on the fundamental solution associated with the background medium. The results include the impact of approximating the fundamental solution. The method leads to, in part, nonlocal coupling of the degrees of freedom. Consequently, implementation via local matrices and static condensation of the interior degrees of freedom are illustrated. In addition, numerical examples are given to illustrate the theoretical results.