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The effect of spatial quadrature on finite element Galerkin approximations to hyperbolic integro-differential equations

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Title The effect of spatial quadrature on finite element Galerkin approximations to hyperbolic integro-differential equations
 
Creator SINHA, RK
PANI, AK
 
Subject convergence
 
Description The purpose of this paper is to study the effect of numerical quadrature on the finite element approximations to the solutions of hyperbolic integro-differential equations. Both semidiscrete and fully discrete schemes are analyzed and optimal estimates are derived in L-infinity(H-1), L-infinity(L-2) norms and quasi-optimal estimate in L-infinity(L-infinity) norm using energy arguments. Further, optimal L-infinity(L-2)-estimates are shown to hold with minimal smoothness assumptions on the initial functions. The analysis in the present paper not only improves upon the earlier results of Baker and Dougalis [SIAM J. Numer. Anal. 13 (1976), pp. 577-598] but also confirms the minimum smoothness assumptions of Rauch [SIAM J. Numer. Anal. 22 (1985), pp. 245-249] for purely second order hyperbolic equation with quadrature.
 
Publisher MARCEL DEKKER INC
 
Date 2011-08-18T13:35:14Z
2011-12-26T12:55:46Z
2011-12-27T05:42:25Z
2011-08-18T13:35:14Z
2011-12-26T12:55:46Z
2011-12-27T05:42:25Z
1998
 
Type Article
 
Identifier NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 19(9-10), 1129-1153
0163-0563
http://dx.doi.org/10.1080/01630569808816876
http://dspace.library.iitb.ac.in/xmlui/handle/10054/10034
http://hdl.handle.net/10054/10034
 
Language en