High order convergence for collocation of second kind boundary integral equations on polygons
The paper deals with the double layer potential \(Ku\) (\(u\) being the density), defined as the surface integral over the connected polygonal boundary of a bounded domain in \(\mathbb{R}^2\). Theorem 1 claims that \(K\) is an isomorphism between some spaces of Sobolev type. For solving the equation \(Ku= f\) approximately a system of collocation equations is proposed and estimates of the error are given in Theorems 2, 3. The proofs of the theorems are based on some properties of the Mellin transform, which is studied thoroughly in the paper and on a suitable extension of Cea's lemma. Numerical experiments are also presented.
scientific article; zbMATH DE number 1145974