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

Sinha, R. K. ; Pani, A. K. (1998) The effect of spatial quadrature on finite element galerkin approximations to hyperbolic integro-differential equations Numerical Functional Analysis and Optimization, 19 (9-0). pp. 1129-1153. ISSN 0163-0563

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/0163056...

Related URL: http://dx.doi.org/10.1080/01630569808816876

Abstract

The purpose of this paper is to study the effect of numerical quadrature on the finite element approximations to the solutions of hyperbolic intego-differential equations. Both semidiscrete and fully discrete schemes are analyzed and optimal estimates are derived in L(H1)L(L2) norms and quasi-optimal estimate in L(L) norm using energy arguments. Further, optimal L(L2)-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.

Item Type:Article
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Deposited On:09 Feb 2012 04:42
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