Convergence analysis of oversampled collocation boundary element methods in 2D

Collocation boundary element methods for integral equations are easier to implement than Galerkin because the elements of discretisation matrix given by lower-dimensional integrals. For that same reason, assembly also requires fewer computations. However, collocation typically yield slower convergence rates and less robustness, compared methods. We explore extent which oversampling can improve both robustness singular equations. show in some cases actually be higher corresponding method, although this at a faster linear rate. In most practical interest, least lowers error constant factor. This still substantial improvement: we analyse an example where factor J (leading rectangular system size JN × N) improves cubic rate J. Furthermore, oversampled method is much affected poor choice points, as how lead guaranteed convergence. Numerical experiments included two-dimensional Helmholtz equation.