@article{e30a402535114b058175ca3be41b1141,
title = "OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA",
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. {\textcopyright} 2014 Australian Mathematical Society.",
author = "DEEPJYOTI GOSWAMI and PANI, {AMIYA K.} and SANGITA YADAV",
note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",
year = "2014",
month = jun,
day = "5",
doi = "10.1017/S1446181114000030",
language = "English (US)",
volume = "55",
pages = "245--266",
journal = "The ANZIAM Journal",
issn = "1446-1811",
publisher = "Cambridge University Press",
number = "3",
}