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Optimal Error Estimates of Two Mixed Finite Element Methods for Parabolic Integro-Differential Equations with Nonsmooth Initial Data

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Title Optimal Error Estimates of Two Mixed Finite Element Methods for Parabolic Integro-Differential Equations with Nonsmooth Initial Data
 
Creator GOSWAMI, D
PANI, AK
YADAV, S
 
Subject Parabolic integro-differential equation
Two mixed finite element methods
Semidiscrete Galerkin approximation
Optimal error estimates
Nonsmooth initial data
POROUS-MEDIA
ELLIPTIC PROBLEMS
EVOLVING SCALES
APPROXIMATIONS
FLOWS
SUPERCONVERGENCE
HETEROGENEITY
 
Description In the first part of this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to the standard mixed method for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments combined with a repeated use of an integral operator and without using parabolic type duality technique, optimal -error estimates are derived for semidiscrete approximations, when the initial condition is in . Due to the presence of the integral term, it is, further, observed that a negative norm estimate plays a crucial role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof techniques used in deriving optimal error estimates for finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, we extend the proposed analysis to the standard mixed method for PIDE with rough initial data and provide an optimal error estimate in which improves upon the results available in the literature.
 
Publisher SPRINGER/PLENUM PUBLISHERS
 
Date 2014-10-16T13:24:58Z
2014-10-16T13:24:58Z
2013
 
Type Article
 
Identifier JOURNAL OF SCIENTIFIC COMPUTING, 56(1)131-164
http://dx.doi.org/10.1007/s10915-012-9666-8
http://dspace.library.iitb.ac.in/jspui/handle/100/15659
 
Language en