The optimal convergence of the h-p version of the boundary
element method with quasiuniform meshes for elliptic problems on
polygonal domains
Benqi Guo and Norbert Heuer
Adv. Comput. Math, 24 (1-4), 353-374, 2006.
In the framework of the Jacobi-weighted Besov spaces, we analyze the lower
and upper bounds of the errors in the h-p version of boundary
element method with quasiuniform meshes for elliptic problems on polygons.
Both, lower and upper bounds are optimal in h and p, and they
are of the same order. The optimal convergence of the h-p version
of boundary element method with quasiuniform meshes is proved, which includes
the optimal rates for h version with quasiuniform meshes and the p
version with quasiuniform degrees as two special cases.