OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA

Handle URI:
http://hdl.handle.net/10754/599092
Title:
OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA
Authors:
GOSWAMI, DEEPJYOTI; PANI, AMIYA K.; YADAV, SANGITA
Abstract:
AWe propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is based on energy arguments combined with repeated use of time integration, but without using parabolic-type duality techniques. An optimal L2-error estimate is derived for the semidiscrete approximation when the initial data is in L2. A superconvergence result is obtained and then used to prove a maximum norm estimate for parabolic integro-differential equations defined on a two-dimensional bounded domain. © 2014 Australian Mathematical Society.
Citation:
GOSWAMI D, PANI AK, YADAV S (2014) OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA. The ANZIAM Journal 55: 245–266. Available: http://dx.doi.org/10.1017/S1446181114000030.
Publisher:
Cambridge University Press (CUP)
Journal:
The ANZIAM Journal
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2014
DOI:
10.1017/S1446181114000030
Type:
Article
ISSN:
1446-1811; 1446-8735
Sponsors:
The first author would like to thank CSIR, Government of India, as well as INCTMat/CAPES (http://inctmat.impa.br) for financial support. The second author gratefully acknowledges the research support of the Department of Science and Technology, Government of India, under DST-CNPq Indo-Brazil Project-DST/INT/Brazil/RPO-05/2007 (Grant No. 490795/2007-2). The third author would like to acknowledge the financial support of MHRD, India. This publication is also based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorGOSWAMI, DEEPJYOTIen
dc.contributor.authorPANI, AMIYA K.en
dc.contributor.authorYADAV, SANGITAen
dc.date.accessioned2016-02-25T13:52:43Zen
dc.date.available2016-02-25T13:52:43Zen
dc.date.issued2014-01en
dc.identifier.citationGOSWAMI D, PANI AK, YADAV S (2014) OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA. The ANZIAM Journal 55: 245–266. Available: http://dx.doi.org/10.1017/S1446181114000030.en
dc.identifier.issn1446-1811en
dc.identifier.issn1446-8735en
dc.identifier.doi10.1017/S1446181114000030en
dc.identifier.urihttp://hdl.handle.net/10754/599092en
dc.description.abstractAWe propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is based on energy arguments combined with repeated use of time integration, but without using parabolic-type duality techniques. An optimal L2-error estimate is derived for the semidiscrete approximation when the initial data is in L2. A superconvergence result is obtained and then used to prove a maximum norm estimate for parabolic integro-differential equations defined on a two-dimensional bounded domain. © 2014 Australian Mathematical Society.en
dc.description.sponsorshipThe first author would like to thank CSIR, Government of India, as well as INCTMat/CAPES (http://inctmat.impa.br) for financial support. The second author gratefully acknowledges the research support of the Department of Science and Technology, Government of India, under DST-CNPq Indo-Brazil Project-DST/INT/Brazil/RPO-05/2007 (Grant No. 490795/2007-2). The third author would like to acknowledge the financial support of MHRD, India. This publication is also based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherCambridge University Press (CUP)en
dc.subjectenergy argumenten
dc.subjectfinite element methoden
dc.subjectmaximum norm estimateen
dc.subjectnonsmooth initial data,superconvergenceen
dc.subjectoptimal error estimateen
dc.subjectPhrases: parabolic integro-differential equationen
dc.subjectsemidiscrete solutionen
dc.titleOPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATAen
dc.typeArticleen
dc.identifier.journalThe ANZIAM Journalen
dc.contributor.institutionTezpur University, Tezpur, Indiaen
dc.contributor.institutionIndian Institute of Technology, Bombay, Mumbai, Indiaen
dc.contributor.institutionBirla Institute of Technology and Science Pilani, Pilani, Indiaen
kaust.grant.numberKUK-C1-013-04en
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