On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces

Details On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces

2008-10-20

arxiv.org/abs/0810.3590v1

Mathematics

Numerical Analysis

Scientific paper

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.

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