The h-p version of the boundary element method for transmission
problems with piecewise analytic data
Benqi Guo, Norbert Heuer, Ernst P. Stephan
SIAM J. Numer. Anal., 33 (2), 789-808, 1996.
Abstract
This paper analyzes the rate of convergence of the h-p version of the
boundary element Galerkin method for transmission problems with
piecewise analytic data. Based on the regularity of solutions of
integral equations in terms of countably normed spaces, we design
the geometric mesh on the interface $\Gamma$ and the boundary element
subspace containing piecewise polynomials with varying degrees. We
prove that the boundary element Galerkin solution converges exponentially
fast to the solution of the integral equation in the
$H^{1/2}(\Gamma) \times H^{-1/2}(\Gamma)$-norm.