An analysis of least-squares oversampled collocation methods for compactly perturbed boundary integral equations in two dimensions

In recent work (Maierhofer and Huybrechs, 2022, Adv. Comput. Math.), the authors showed that least-squares oversampling can improve convergence properties of collocation methods for boundary integral equations involving operators certain pseudo-differential form. The underlying principle is discrete method approximates a Bubnov–Galerkin in suitable sense. present work, we extend this analysis to case when operator perturbed by compact K which continuous as map on Sobolev spaces boundary, K:Hp→Hq all p,q∈R. This study complicated fact both test trial functions orthogonality conditions are modified over unperturbed setting. Our guarantees previous results concerning optimal rates sufficient preserved more general case. Indeed, first time, provides complete explanation advantages oversampled formulations Laplace equation arbitrary smooth Jordan curves 2D. theoretical shown be very good agreement with numerical experiments.