Analysis of a sinc-Galerkin Method for the Fractional Laplacian
Harbir Antil, Patrick Dondl, Ludwig Striet · SIAM Journal on Numerical Analysis · 2023
Abstract. We provide the convergence analysis for a [Formula: see text]-Galerkin method to solve the fractional Dirichlet problem. This can be understood as a follow-up of [H. Antil, P. Dondl, and L. Striet, SIAM J. Sci. Comput., 43 (2021), pp. A2897–A2922], where the authors presented a [Formula: see text]-function based method to solve fractional PDEs. While the original method was formulated as a collocation method, we show that the same method can be interpreted as a nonconforming Galerkin method, giving access to abstract error estimates. Optimal order of convergence is shown without any unrealistic regularity assumptions on the solution.