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|Title:||The effect of spatial quadrature on finite element Galerkin approximations to hyperbolic integro-differential equations|
|Publisher:||MARCEL DEKKER INC|
|Citation:||NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 19(9-10), 1129-1153|
|Abstract:||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.|
|Appears in Collections:||Article|
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