An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems

Handle URI:
http://hdl.handle.net/10754/597504
Title:
An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems
Authors:
Memon, Sajid; Nataraj, Neela; Pani, Amiya Kumar
Abstract:
In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.
Citation:
Memon S, Nataraj N, Pani AK (2012) An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems. SIAM J Numer Anal 50: 1367–1393. Available: http://dx.doi.org/10.1137/100782760.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Numerical Analysis
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2012
DOI:
10.1137/100782760
Type:
Article
ISSN:
0036-1429; 1095-7170
Sponsors:
Received by the editors January 15, 2010; accepted for publication (in revised form) January 3, 2012; published electronically May 31, 2012. This work was supported by the DST-CNPq Indo-Brazil Project DST/INT/Brazil/RPO-05/2007 (grant 490795/2007-2) and award KUK-C1-013-04 made by KAUST.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMemon, Sajiden
dc.contributor.authorNataraj, Neelaen
dc.contributor.authorPani, Amiya Kumaren
dc.date.accessioned2016-02-25T12:41:02Zen
dc.date.available2016-02-25T12:41:02Zen
dc.date.issued2012-01en
dc.identifier.citationMemon S, Nataraj N, Pani AK (2012) An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems. SIAM J Numer Anal 50: 1367–1393. Available: http://dx.doi.org/10.1137/100782760.en
dc.identifier.issn0036-1429en
dc.identifier.issn1095-7170en
dc.identifier.doi10.1137/100782760en
dc.identifier.urihttp://hdl.handle.net/10754/597504en
dc.description.abstractIn this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipReceived by the editors January 15, 2010; accepted for publication (in revised form) January 3, 2012; published electronically May 31, 2012. This work was supported by the DST-CNPq Indo-Brazil Project DST/INT/Brazil/RPO-05/2007 (grant 490795/2007-2) and award KUK-C1-013-04 made by KAUST.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectA posteriori error estimatesen
dc.subjectAdaptive algorithmsen
dc.subjectBackward Euleren
dc.subjectLinear parabolic equationen
dc.subjectMixed elliptic reconstructionsen
dc.subjectMixed finite element methoden
dc.titleAn A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problemsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Numerical Analysisen
dc.contributor.institutionIndian Institute of Technology, Bombay, Mumbai, Indiaen
kaust.grant.numberKUK-C1-013-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.