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Title: On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces
Authors: Bespalov, A
Heuer, N
Keywords: hp-version with quasi-uniform meshes;electric field integral equation;time-harmonic electro-magnetic scattering;boundary element method
Issue Date: 2008
Abstract: 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 $\bH(\div)$-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 $\tilde\bH^{-1/2}(\div)$-conforming p-interpolation operator that assumes only $\bH^r\cap\tilde\bH^{-1/2}(\div)$-regularity ($r>0$) and for which we show quasi-stability with respect to polynomial degrees.
Appears in Collections:Computer Science
Mathematical Sciences

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