An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems
KAUST Grant NumberKUK-C1-013-04
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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.
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.
SponsorsReceived 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.