hp-adaptive two-level methods for boundary integral equations on curves

We consider the p- and hp-versions of the Galerkin boundary element method for hypersingular and weakly singular integral equations of the first kind on curves. We derive a-posteriori error estimates that are based on stable two-level decompositions of enriched ansatz spaces, The Galerkin errors are estimated by inverting local projection operators that are defined on small subspaces of the second level. A p-adaptive and two hp-adaptive algorithms are defined and numerical experiments confirm their efficiency.