Discontinuous Galerkin hp-BEM with quasi-uniform meshes
For researchers in computational boundary element methods, this work provides a rigorous analysis of a discontinuous hp-version, though it is an incremental extension of existing hp-BEM theory.
The paper presents a discontinuous Galerkin hp-boundary element method for hypersingular integral operators on polyhedral surfaces, proving quasi-optimal error estimates with quasi-uniform meshes. Numerical results confirm the theoretical convergence rates.
We present and analyze a discontinuous variant of the hp-version of the boundary element Galerkin method with quasi-uniform meshes. The model problem is that of the hypersingular integral operator on an (open or closed) polyhedral surface. We prove a quasi-optimal error estimate and conclude convergence orders which are quasi-optimal for the h-version with arbitrary degree and almost quasi-optimal for the p-version. Numerical results underline the theory.