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

Abstract

This 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.