TY - JOUR
T1 - Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion
AU - Jin, B.
AU - Lazarov, R.
AU - Pasciak, J.
AU - Zhou, Z.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The research of B.J. was supported by NSF Grant DMS-1319052, that of R.L. and Z.Z. in part by US NSF Grant DMS-1016525 and that of J.P. by NSF Grant DMS-1216551. The work of all authors was also supported in part by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2014/5/30
Y1 - 2014/5/30
N2 - © 2014 Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We consider the initial-boundary value problem for an inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data and a nonsmooth right-hand side in a bounded convex polyhedral domain. We analyse two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right-hand side data f (x, t) ε L∞ (0, T; Hq(ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2(ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.
AB - © 2014 Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We consider the initial-boundary value problem for an inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data and a nonsmooth right-hand side in a bounded convex polyhedral domain. We analyse two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right-hand side data f (x, t) ε L∞ (0, T; Hq(ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2(ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.
UR - http://hdl.handle.net/10754/598212
UR - https://academic.oup.com/imajna/article-lookup/doi/10.1093/imanum/dru018
UR - http://www.scopus.com/inward/record.url?scp=84919894668&partnerID=8YFLogxK
U2 - 10.1093/imanum/dru018
DO - 10.1093/imanum/dru018
M3 - Article
SN - 0272-4979
VL - 35
SP - 561
EP - 582
JO - IMA Journal of Numerical Analysis
JF - IMA Journal of Numerical Analysis
IS - 2
ER -