TY - JOUR
T1 - The Galerkin finite element method for a multi-term time-fractional diffusion equation
AU - Jin, Bangti
AU - Lazarov, Raytcho
AU - Liu, Yikan
AU - Zhou, Zhi
N1 - 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.
PY - 2015/1
Y1 - 2015/1
N2 - © 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.
AB - © 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.
UR - http://hdl.handle.net/10754/599916
UR - https://linkinghub.elsevier.com/retrieve/pii/S0021999114007396
UR - http://www.scopus.com/inward/record.url?scp=84919915413&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2014.10.051
DO - 10.1016/j.jcp.2014.10.051
M3 - Article
SN - 0021-9991
VL - 281
SP - 825
EP - 843
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -