The hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: a priori error analysis
This work offers a theoretical foundation for practitioners using hp-BEM on polyhedral surfaces, but it is an incremental extension of existing analysis frameworks.
The paper provides an a priori error analysis for the hp-version boundary element method applied to the electric field integral equation on polyhedral surfaces, proving error estimates that confirm expected convergence rates in mesh size and polynomial degree.
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, 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.