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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 2/2018

23.01.2018

Unconditionally Optimal Error Estimates of a Linearized Galerkin Method for Nonlinear Time Fractional Reaction–Subdiffusion Equations

verfasst von: Dongfang Li, Jiwei Zhang, Zhimin Zhang

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2018

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Abstract

This paper is concerned with unconditionally optimal error estimates of linearized Galerkin finite element methods to numerically solve some multi-dimensional fractional reaction–subdiffusion equations, while the classical analysis for numerical approximation of multi-dimensional nonlinear parabolic problems usually require a restriction on the time-step, which is dependent on the spatial grid size. To obtain the unconditionally optimal error estimates, the key point is to obtain the boundedness of numerical solutions in the \(L^\infty \)-norm. For this, we introduce a time-discrete elliptic equation, construct an energy function for the nonlocal problem, and handle the error summation properly. Compared with integer-order nonlinear problems, the nonlocal convolution in the time fractional derivative causes much difficulties in developing and analyzing numerical schemes. Numerical examples are given to validate our theoretical results.
Vorheriger Artikel High-Order Numerical Methods for 2D Parabolic Problems in Single and Composite Domains
Nächster Artikel High Order Algorithm for the Time-Tempered Fractional Feynman–Kac Equation

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Metadaten
Titel
Unconditionally Optimal Error Estimates of a Linearized Galerkin Method for Nonlinear Time Fractional Reaction–Subdiffusion Equations
verfasst von
Dongfang Li
Jiwei Zhang
Zhimin Zhang
Publikationsdatum
23.01.2018
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 2/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-018-0642-9

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