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Please use this identifier to cite or link to this item: http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/11398
Title: Optimal Error Estimates of Two Mixed Finite Element Methods for Parabolic Integro-Differential Equations with Nonsmooth Initial Data
Authors: Yadav, Sangita
Keywords: Mathematics
Differential equations
Parabolic integro-differential equations (PIDE)
Issue Date: May-2013
Publisher: Springer
Abstract: 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 L2-error estimates are derived for semidiscrete approximations, when the initial condition is in L2. 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 L2, which improves upon the results available in the literature.
URI: https://link.springer.com/article/10.1007/s10915-012-9666-8
http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/11398
Appears in Collections:Department of Mathematics

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