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Journal of Scientific Computing

Erschienen in:

01.10.2020

A Parareal Finite Volume Method for Variable-Order Time-Fractional Diffusion Equations

verfasst von: Huan Liu, Aijie Cheng, Hong Wang

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2020

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Abstract

In this paper, we investigate the well-posedness and solution regularity of a variable-order time-fractional diffusion equation, which is often used to model the solute transport in complex porous media where the micro-structure of the porous media may changes over time. We show that the variable-order time-fractional diffusion equations have flexible abilities to eliminate the nonphysical singularity of the solutions to their constant-order analogues. We also present a finite volume approximation and provide its stability and convergence analysis in a weighted discrete norm. Furthermore, we develop an efficient parallel-in-time procedure to improve the computational efficiency of the variable-order time-fractional diffusion equations. Numerical experiments are performed to confirm the theoretical results and to demonstrate the effectiveness and efficiency of the parallel-in-time method.

Vorheriger Artikel A New Method for Solving Variational Inequalities and Fixed Points Problems of Demi-Contractive Mappings in Hilbert Spaces

Nächster Artikel On Boundary-Value Problems for RANS Equations and Two-Equation Turbulence Models

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Titel: A Parareal Finite Volume Method for Variable-Order Time-Fractional Diffusion Equations
verfasst von: Huan Liu
Aijie Cheng
Hong Wang
Publikationsdatum: 01.10.2020
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2020
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01321-x

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