OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA

GOSWAMI, DEEPJYOTI; PANI, AMIYA K.; YADAV, SANGITA

Type

Article

Authors

GOSWAMI, DEEPJYOTI
PANI, AMIYA K.
YADAV, SANGITA

KAUST Grant Number

KUK-C1-013-04

Date

2014-06-05

Online Publication Date

2014-06-05

Print Publication Date

2014-01

Permanent link to this record

http://hdl.handle.net/10754/599092

Metadata

Show full item record

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. © 2014 Australian Mathematical Society.

Citation

GOSWAMI 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.

Sponsors

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).