An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems
| dc.contributor.author | Memon, Sajid | |
| dc.contributor.author | Nataraj, Neela | |
| dc.contributor.author | Pani, Amiya Kumar | |
| dc.date.accessioned | 2016-02-25T12:41:02Z | |
| dc.date.available | 2016-02-25T12:41:02Z | |
| dc.date.issued | 2012-01 | |
| dc.identifier.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. | |
| dc.identifier.issn | 0036-1429 | |
| dc.identifier.issn | 1095-7170 | |
| dc.identifier.doi | 10.1137/100782760 | |
| dc.identifier.uri | http://hdl.handle.net/10754/597504 | |
| dc.description.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. | |
| dc.description.sponsorship | 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. | |
| dc.publisher | Society for Industrial & Applied Mathematics (SIAM) | |
| dc.subject | A posteriori error estimates | |
| dc.subject | Adaptive algorithms | |
| dc.subject | Backward Euler | |
| dc.subject | Linear parabolic equation | |
| dc.subject | Mixed elliptic reconstructions | |
| dc.subject | Mixed finite element method | |
| dc.title | An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems | |
| dc.type | Article | |
| dc.identifier.journal | SIAM Journal on Numerical Analysis | |
| dc.contributor.institution | Indian Institute of Technology, Bombay, Mumbai, India | |
| kaust.grant.number | KUK-C1-013-04 |