On modified Gordon-Wixom interpolation schemes and their applications to nonlinear and exterior domain problems
Alexander G. Belyaev, Pierre‐Alain Fayolle · Numerical Algorithms · 2017
We introduce and study extensions and modifications of the Gordon-Wixom transfinite barycentric interpolation scheme (Gordon and Wixom, SIAM J. Numer. Anal. 11 (5), 909–933, 1974 ). We demonstrate that the modified Gordon-Wixom scheme proposed in Belyaev and Fayolle (Comput. Graph. 51 , 74–80, 2015 ) reproduces harmonic quadratic polynomials in convex domains. We adapt the scheme for dealing with the exterior of a bounded domain and for the exterior of a disk, where we demonstrate that our interpolation formula reproduces harmonic functions. Finally, we show how to adapt the Gordon-Wixom approach for approximating p -harmonic functions and to derive computationally efficient approximations of the solutions to boundary value problems involving the p -Laplacian.