Boundary Integral Operators in Countably Normed Spaces
Norbert Heuer, Ernst P. Stephan
Math. Nachr., 191 (1), 123-151, 1998.
Abstract
We show the mapping properties of several integral operators
acting on polygons within countably normed spaces.
The integral operators are the weakly singular single layer
potential operator for the Laplacian, the corresponding double
layer potential operator and the normal derivatives of these
operators. Our analysis of the boundary integral equations
in the countably normed spaces is based on
Mellin techniques and uses the Mellin symbols of the integral
operators.
Functions of these countably normed spaces can be approximated
very efficiently
by splines through the use of well adapted mesh-refinement and
polynomial degree distribution.
Therefore the hp-version of the boundary element method with
geometric mesh can be proved to converge exponentially fast for
the solutions to those integral equations.