On the stability of the collocation method for the double layer operator on polyhedral domains in R3
Olaf Hansen · PAMM · 2002
We develop a new method to give estimates for the double layer operator on cones in R3. Here we use weighted norms which are equivalent to the usual L∞-norm. This result includes the weighted norms which were constructed by Wendland and Kral for the case of rectangular cones. If all vertices in a polyhedral domain (resp. their corresponding cones) allow the construction of a weighted norm, such that the double layer operator has norm smaller than one half, we can prove the stability of the collocation method with piecewise constant trial functions.