A Semi-Analytic Diagonalization FEM for the Spectral Fractional Laplacian
<|reference_start|>A Semi-Analytic Diagonalization FEM for the Spectral Fractional Laplacian: 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.<|reference_end|>
@article{salgado2024a,
    title={A Semi-Analytic Diagonalization FEM for the Spectral Fractional
  Laplacian},
    author={Abner J. Salgado and Shane E. Sawyer},
    journal={arXiv preprint arXiv:2409.17388},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.17388},
    primaryClass={math.NA cs.NA}
}