Convergence of the Natural hp-BEM for the Electric Field Integral Equation on Polyhedral Surfaces

2009/07/29 by Alex Bespalov, Bespalov, Alexei, Norbert Heuer +3 · 1 citation
Computer Science · Engineering · #65N12 #65N38 #78M15 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.0907.5231

openalex publication_date 2009/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the variational formulation of the electric field integral equation (EFIE) on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on div-conforming Raviart-Thomas boundary elements (BEM) of locally variable polynomial degree on shape-regular surface meshes. We establish asymptotic quasi-optimality of Galerkin solutions on sufficiently fine meshes or for sufficiently high polynomial degree.

Cited by

• A new H(div)-conforming p-interpolation operator in two dimensions

Related

• On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces
• The BEM with graded meshes for the electric field integral equation on polyhedral surfaces
• The hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: a priori error analysis
• Natural hp-BEM for the electric field integral equation with singular\n solutions
• A posteriori error estimates for the Electric Field Integral Equation on polyhedra