The optimal rate of convergence of the p-version of the
boundary element method in two dimensions
Benqi Guo and Norbert Heuer
Numer. Math. 98 (3), 499-538, 2004.
We introduce the Jacobi-weighted Besov and Sobolev spaces in the one-dimensional
setting. In the framework of these spaces, we analyze lower and upper
bounds for approximation errors in the p-version of the boundary element
method for hypersingular and weakly singular integral operators on polygons.
We prove the optimal rate of convergence for the p-version in the
energy norms of \tilde H1/2 and \tilde H-1/2, respectively.