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arXiv · 2212.11581

Analysis of a sinc-Galerkin Method for the Fractional Laplacian

Harbir Antil·Patrick Dondl·Ludwig Striet
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Abstract

We provide the convergence analysis for a sinc-Galerkin method to solve the fractional Dirichlet problem. This can be understood as a follow-up of an earlier article by the same authors, where the authors presented a sinc-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.

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Harbir Antil, Patrick Dondl, Ludwig Striet. 2022-12-22. Analysis of a sinc-Galerkin Method for the Fractional Laplacian. https://arxiv.org/abs/2212.11581

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