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Galerkin boundary element methods for the solution of novel first kind Steklov–Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in two-and three-dimensional Lipschitz domains with nonlinear boundary conditions. For the numerical solution of the resulting Newton… (More)

We study a subspace of bivariate trigonometric polynomials for interpolating functions on the sphere. We give an explicit construction for a system of interpolation nodes, and the corresponding basis for this space, that allows a (discrete) fast Fourier transform–type formula for the interpolant. We prove that the uniform norm of our interpolation operator… (More)

In this work, we describe, analyze, and implement a pseudospec-tral quadrature method for a global computer modeling of the incompressible surface Navier-Stokes equations on the rotating unit sphere. Our spectrally accurate numerical error analysis is based on the Gevrey regularity of the solutions of the Navier-Stokes equations on the sphere. The scheme is… (More)