A Semianalytic Diagonalization Finite Element Method for the Spectral Fractional Laplacian

Abstract. We present a technique for approximating solutions to the spectral fractional Laplacian, which is based on the Caffarelli–Silvestre extension and diagonalization. Our scheme uses the analytic solution to the associated eigenvalue problem in the extended dimension. We show its relation to a quadrature scheme. Numerical examples demonstrate the performance of the method. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/shedsaw/Exact-Diagonalization-Tensor-FEM and in the supplementary materials ( Exact-Diagonalization-Tensor-FEM-main.zip [240KB]). [Formula: see text]