The hp-BEM with quasi-uniform meshes for the electric field
integral equation on polyhedral surfaces: a priori error analysis
Alexei Bespalov and Norbert Heuer
Appl. Numer. Math. 60 (7), 705-718, 2010.
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.