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Error estimates for semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equation with nonsmooth data
DSpace at IIT Bombay
View Archive Info| Field | Value | |
| Title |
Error estimates for semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equation with nonsmooth data
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| Creator |
PANI, AK
SINHA, RK |
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| Subject |
finite-element methods
integrodifferential equations |
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| Description |
In this paper, an attempt has been made to carry over known results for the finite element Galerkin method for a time dependent parabolic equation with nonsmooth initial data to an integro-differential equation of parabolic type. More precisely, for the homogeneous problem a standard energy technique in conjunction with a duality argument is used to obtain an L-2-error estimate of order O ( h(2)/t) for the semidiscrete solution when the given initial function is only in L-2. Further, for the nonhomogeneous case with zero initial condition, an error estimate of order O (h(2) log (1/h)) uniformly in time is proved, provided that the nonhomogeneous term is in L-infinity(L-2). The present paper provides a complete answer to an open problem posed on p. 106 of the book Finite Element Methods for Integro-differential Equations by Chen and Shih.
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| Publisher |
SPRINGER-VERLAG
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| Date |
2011-08-30T11:24:24Z
2011-12-26T12:58:55Z 2011-12-27T05:49:37Z 2011-08-30T11:24:24Z 2011-12-26T12:58:55Z 2011-12-27T05:49:37Z 2000 |
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| Type |
Article
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| Identifier |
CALCOLO, 37(4), 181-205
0008-0624 http://dx.doi.org/10.1007/s100920070001 http://dspace.library.iitb.ac.in/xmlui/handle/10054/12296 http://hdl.handle.net/10054/12296 |
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| Language |
en
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