Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation

Handle URI:
http://hdl.handle.net/10754/598210
Title:
Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation
Authors:
Jin, Bangti; Lazarov, Raytcho; Pasciak, Joseph; Zhou, Zhi
Abstract:
© 2014 Society for Industrial and Applied Mathematics We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann-Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and Hα/2 (D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.
Citation:
Jin B, Lazarov R, Pasciak J, Zhou Z (2014) Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation. SIAM J Numer Anal 52: 2272–2294. Available: http://dx.doi.org/10.1137/13093933X.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Numerical Analysis
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Jan-2014
DOI:
10.1137/13093933X
Type:
Article
ISSN:
0036-1429; 1095-7170
Sponsors:
This work was supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).This author's work was supported by NSF grant DMS-1319052.The second author's work was supported in part by NSF grant DMS-1016525, and the third author's work was supported by NSF grant DMS-1216551.
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Full metadata record

DC FieldValue Language
dc.contributor.authorJin, Bangtien
dc.contributor.authorLazarov, Raytchoen
dc.contributor.authorPasciak, Josephen
dc.contributor.authorZhou, Zhien
dc.date.accessioned2016-02-25T13:14:46Zen
dc.date.available2016-02-25T13:14:46Zen
dc.date.issued2014-01en
dc.identifier.citationJin B, Lazarov R, Pasciak J, Zhou Z (2014) Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation. SIAM J Numer Anal 52: 2272–2294. Available: http://dx.doi.org/10.1137/13093933X.en
dc.identifier.issn0036-1429en
dc.identifier.issn1095-7170en
dc.identifier.doi10.1137/13093933Xen
dc.identifier.urihttp://hdl.handle.net/10754/598210en
dc.description.abstract© 2014 Society for Industrial and Applied Mathematics We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann-Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and Hα/2 (D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.en
dc.description.sponsorshipThis work was supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).This author's work was supported by NSF grant DMS-1319052.The second author's work was supported in part by NSF grant DMS-1016525, and the third author's work was supported by NSF grant DMS-1216551.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectError estimateen
dc.subjectFinite element methoden
dc.subjectFully discrete schemeen
dc.subjectSemidiscrete schemeen
dc.subjectSpace fractional parabolic equationen
dc.titleError Analysis of a Finite Element Method for the Space-Fractional Parabolic Equationen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Numerical Analysisen
dc.contributor.institutionUCL, London, United Kingdomen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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