An exponentially convergent discretization for space-time fractional parabolic equations using hp-FEM

被引：0
|
作者：
Melenk, Jens Markus [1 ]
Rieder, Alexander [1 ]
机构：
[1] Tech Univ Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria
来源：
IMA JOURNAL OF NUMERICAL ANALYSIS | 2023年 / 43卷 / 04期
基金：
奥地利科学基金会;
关键词：
fractional diffusion; sinc quadrature; Mittag-Leffler; Riesz-Dunford; hp-FEM; APPROXIMATION; QUADRATURE; OPERATORS;
D O I：
10.1093/imanum/drac045
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a space-time fractional parabolic problem. Combining a sinc quadrature-based method for discretizing the Riesz-Dunford integral with hp-FEM in space yields an exponentially convergent scheme for the initial boundary value problem with homogeneous right-hand side. For the inhomogeneous problem, an hp-quadrature scheme is implemented. We rigorously prove exponential convergence with focus on small times t, proving robustness with respect to startup singularities due to data incompatibilities.
引用
收藏
页码：2352 / 2376
页数：25
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