On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces
Provides a theoretical convergence guarantee for hp-BEM applied to electromagnetic scattering on polyhedral surfaces, advancing numerical analysis for computational electromagnetics.
The paper proves quasi-optimal convergence of the hp-version boundary element method for the electric field integral equation on polyhedral surfaces using quasi-uniform meshes, establishing a new interpolation operator with quasi-stability.
In this paper the hp-version of the boundary element method is applied to the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. The underlying meshes are supposed to be quasi-uniform. We use H(div)-conforming discretisations with quadrilateral elements of Raviart-Thomas type and establish quasi-optimal convergence of hp-approximations. Main ingredient of our analysis is a new H^{-1/2}(div)-conforming p-interpolation operator that assumes only H^r \cap H^{-1/2}(div)-regularity (r > 0) and for which we show quasi-stability with respect to polynomial degrees.