分数拉普拉斯方法的 sinc-Galerkin 方法分析

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Numerical Analysis Pub Date : 2023-12-06 DOI:10.1137/22m1542374

Harbir Antil, Patrick W. Dondl, Ludwig Striet

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引用次数: 0

摘要

SIAM 数值分析期刊》，第 61 卷，第 6 期，第 2967-2993 页，2023 年 12 月。摘要。我们提供了求解分数 Dirichlet 问题的 [math]-Galerkin 方法的收敛性分析。这可以理解为 [H. Antil, P. Dondl] 方法的后续。Antil, P. Dondl, and L. Striet, SIAM J. Sci. Comput., 43 (2021), pp.虽然最初的方法是作为配位法提出的，但我们证明，同样的方法可以解释为非顺应 Galerkin 方法，从而获得抽象误差估计。在不对解作任何不切实际的正则性假设的情况下，我们展示了最佳收敛阶次。

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Analysis of a sinc-Galerkin Method for the Fractional Laplacian

SIAM Journal on Numerical Analysis, Volume 61, Issue 6, Page 2967-2993, December 2023.
Abstract. We provide the convergence analysis for a [math]-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 [math]-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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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.