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OPTIMAL L-2 ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA

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Title OPTIMAL L-2 ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA
 
Creator GOSWAMI, D
PANI, AK
YADAV, S
 
Subject parabolic integro-differential equation
finite element method
semidiscrete solution
energy argument
optimal error estimate
nonsmooth initial data
superconvergence
maximum norm estimate
FINITE-ELEMENT METHODS
EVOLVING SCALES
HETEROGENEITY
 
Description We 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 L-2-error estimate is derived for the semidiscrete approximation when the initial data is in L-2. 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.
 
Publisher CAMBRIDGE UNIV PRESS
 
Date 2014-12-28T11:58:31Z
2014-12-28T11:58:31Z
2014
 
Type Article
 
Identifier ANZIAM JOURNAL, 55(3)245-266
1446-1811
1446-8735
http://dx.doi.org/10.1017/S1446181114000030
http://dspace.library.iitb.ac.in/jspui/handle/100/16419
 
Language English