The effect of spatial quadrature on finite element galerkin approximations to hyperbolic integro-differential equations
作者:
R. K. Sinha,
A. K. Pani,
期刊:
Numerical Functional Analysis and Optimization
(Taylor Available online 1998)
卷期:
Volume 19,
issue 9-10
页码: 1129-1153
ISSN:0163-0563
年代: 1998
DOI:10.1080/01630569808816876
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
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 inL∞(H1)L∞(L2) norms and quasi-optimal estimate inL∞(L∞) norm using energy arguments. Further, optimalL(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.
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