The Galerkin finite element method for a multi-term time-fractional diffusion equation

Bangti Jin, Raytcho Lazarov, Yikan Liu, Zhi Zhou

Research output: Contribution to journalArticlepeer-review

242 Scopus citations

Abstract

© 2014 The Authors. We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates.
Original languageEnglish (US)
Pages (from-to)825-843
Number of pages19
JournalJournal of Computational Physics
Volume281
DOIs
StatePublished - Jan 2015
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The authors are grateful to the anonymous referees for their constructive comments. The research of B. Jin has been supported by NSF Grant DMS-1319052, R. Lazarov was supported in parts by NSF Grant DMS-1016525 and also by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), and Y. Liu was supported by the Program for Leading Graduate Schools, MEXT, Japan.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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