The hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: A priori error analysis

• Autores: Alexei Bespalov, Norbert Heuer
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 60, Nº. 7, 2010, págs. 705-718
• Idioma: inglés
• DOI: 10.1016/j.apnum.2010.03.012
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• Resumen

  • paper presents an a priori error analysis of the hp-version of the boundary element method for the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. We use H(div)-conforming discretisations with Raviart�Thomas elements on a sequence of quasi-uniform meshes of triangles and/or parallelograms. Assuming the regularity of the solution to the electric field integral equation in terms of Sobolev spaces of tangential vector fields, and based upon the known quasi-optimal convergence, we prove an a priori error estimate of the method in the energy norm. This estimate proves the expected rate of convergence with respect to the mesh parameter h and the polynomial degree p.