Radial basis functions for the solution of
hypersingular operators on open surfaces
Norbert Heuer and Thanh Tran
Comput. Math. Appl. 63 (11), 1504-1518, 2012.
We analyze the approximation by radial basis functions
of a hypersingular integral equation on an open surface.
In order to accommodate the homogeneous essential
boundary condition along the surface boundary, scaled radial
basis functions on an extended surface and Lagrangian multipliers
on the extension are used.
We prove that our method converges quasi-optimally.
Approximation results for scaled radial basis functions indicate
that, for highly regular radial basis functions, the achieved
convergence rates are close to the one of low-order conforming
boundary element schemes. Numerical experiments confirm our conclusions.