On the essential norm of the double layer potential on polyhedral domains and the stability of the collocation method
The author studies the double layer operator on a polyhedral domain \(D\) in \({\mathbb R}^{3}\) and constructs weighted norms for a class of nonconvex cones, such that the double layer operator has a norm smaller than \(1/2\) with respect to this weighted norm. This allows to prove the stability for the collocation method with piecewise polynomial trial functions of arbitrary degree if some modifications near the vertices are introduced and if the grid respects the weighted norm in some given sense.
scientific article; zbMATH DE number 1779484
scientific article