Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion

Handle URI:
http://hdl.handle.net/10754/598212
Title:
Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion
Authors:
Jin, B.; Lazarov, R.; Pasciak, J.; Zhou, Z.
Abstract:
© 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.
Citation:
Jin B, Lazarov R, Pasciak J, Zhou Z (2014) Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion. IMA Journal of Numerical Analysis 35: 561–582. Available: http://dx.doi.org/10.1093/imanum/dru018.
Publisher:
Oxford University Press (OUP)
Journal:
IMA Journal of Numerical Analysis
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
30-May-2014
DOI:
10.1093/imanum/dru018
Type:
Article
ISSN:
0272-4979; 1464-3642
Sponsors:
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).
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Full metadata record

DC FieldValue Language
dc.contributor.authorJin, B.en
dc.contributor.authorLazarov, R.en
dc.contributor.authorPasciak, J.en
dc.contributor.authorZhou, Z.en
dc.date.accessioned2016-02-25T13:14:48Zen
dc.date.available2016-02-25T13:14:48Zen
dc.date.issued2014-05-30en
dc.identifier.citationJin B, Lazarov R, Pasciak J, Zhou Z (2014) Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion. IMA Journal of Numerical Analysis 35: 561–582. Available: http://dx.doi.org/10.1093/imanum/dru018.en
dc.identifier.issn0272-4979en
dc.identifier.issn1464-3642en
dc.identifier.doi10.1093/imanum/dru018en
dc.identifier.urihttp://hdl.handle.net/10754/598212en
dc.description.abstract© 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.en
dc.description.sponsorshipThe 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).en
dc.publisherOxford University Press (OUP)en
dc.subjecterror estimateen
dc.subjectinhomogeneous problemen
dc.subjectlumped mass methoden
dc.subjectsemidiscrete Galerkin schemeen
dc.subjecttime-fractional diffusionen
dc.titleError analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusionen
dc.typeArticleen
dc.identifier.journalIMA Journal of Numerical Analysisen
dc.contributor.institutionUniversity of California, Riverside, Riverside, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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