Approximation of the spectral fractional powers of the Laplace-Beltrami Operator
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We consider numerical approximation of spectral fractional Laplace-Beltrami problems on closed surfaces. The proposed numerical algorithms rely on their Balakrishnan integral representation and consists a sinc quadrature coupled with standard finite element methods for parametric surfaces. Possibly up to a log term, optimal rate of convergence is observed and derived analytically when the discrepancies between the exact solution and its numerical approximations are measured in L^2 and H^1.
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