OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA
KAUST Grant NumberKUK-C1-013-04
Online Publication Date2014-06-05
Print Publication Date2014-01
Permanent link to this recordhttp://hdl.handle.net/10754/599092
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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.
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.
SponsorsThe 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).
PublisherCambridge University Press (CUP)
JournalThe ANZIAM Journal