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

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    Type
    Article
    Authors
    Jin, B.
    Lazarov, R.
    Pasciak, J.
    Zhou, Z.
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2014-05-30
    Online Publication Date
    2014-05-30
    Print Publication Date
    2015-04-01
    Permanent link to this record
    http://hdl.handle.net/10754/598212
    
    Metadata
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    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.
    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).
    Publisher
    Oxford University Press (OUP)
    Journal
    IMA Journal of Numerical Analysis
    DOI
    10.1093/imanum/dru018
    ae974a485f413a2113503eed53cd6c53
    10.1093/imanum/dru018
    Scopus Count
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