The Mathematical Institute, University of Oxford, Eprints Archive

Optimal error estimates of a mixed finite element method for
parabolic integro-differential equations with non smooth initial data

Goswami, D. and Pani, A. K. and Yadav, S (2010) Optimal error estimates of a mixed finite element method for
parabolic integro-differential equations with non smooth initial data.
Numer. Math. . (Submitted)

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Abstract

In this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to mixed methods for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments and without using parabolic type duality technique, optimal L2-error estimates are derived for semidiscrete approximations, when the initial data is in L2. Due to the presence of the integral term, it is, further, observed that estimate in dual of H(div)-space plays a role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof technique used for deriving optimal error estimates of 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, the proposed analysis can be easily extended to other mixed method for PIDE with rough initial data and provides an improved result.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1010
Deposited By:Peter Hudston
Deposited On:28 Oct 2010 14:38
Last Modified:09 Feb 2012 15:54

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