论文标题
分数laplacian的SINC-Galerkin方法的分析
Analysis of a sinc-Galerkin Method for the Fractional Laplacian
论文作者
论文摘要
我们为SINC-GALERKIL方法提供了收敛分析，以解决分数Dirichlet问题。这可以将其理解为同一作者对早期文章的后续行动，在该文章中，作者提出了一种基于SINC功能的方法来求解分数PDE。虽然原始方法是作为串联方法提出的，但我们表明，相同的方法可以解释为不合格的盖尔金方法，从而可以访问抽象错误估计。最佳的收敛顺序显示在解决方案上没有任何不切实际的规律性假设。
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.
