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dc.contributor.authorJin, Bangti
dc.contributor.authorLazarov, Raytcho
dc.contributor.authorZhou, Zhi
dc.date.accessioned2016-02-25T13:16:59Z
dc.date.available2016-02-25T13:16:59Z
dc.date.issued2013-01
dc.identifier.citationJin B, Lazarov R, Zhou Z (2013) Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations. SIAM J Numer Anal 51: 445–466. Available: http://dx.doi.org/10.1137/120873984.
dc.identifier.issn0036-1429
dc.identifier.issn1095-7170
dc.identifier.doi10.1137/120873984
dc.identifier.urihttp://hdl.handle.net/10754/597967
dc.description.abstractWe consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition ν(x) and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain Ω. We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., ν ∈ H2(Ω) ∩ H0 1(Ω) and ν ∈ L2(Ω). For the lumped mass method, the optimal L2-norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study. © 2013 Society for Industrial and Applied Mathematics.
dc.description.sponsorshipThe research of R. Lazarov and Z. Zhou was supported in part by US NSF grant DMS-1016525. The work of all authors has been supported also by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subjectFinite element method
dc.subjectFractional diffusion
dc.subjectLumped mass method
dc.subjectOptimal error estimates
dc.subjectSemidiscrete Gelerkin method
dc.titleError Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations
dc.typeArticle
dc.identifier.journalSIAM Journal on Numerical Analysis
dc.contributor.institutionTexas A and M University, College Station, United States
kaust.grant.numberKUS-C1-016-04


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