Volume 12, Issue 3
A Priori Error Estimates for Finite Volume Element Approximations to Second order Linear Hyperbolic Integro-Differential Equations

Samir Karaa and Amiya K. Pani

Int. J. Numer. Anal. Mod., 12 (2015), pp. 401-429

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  • Abstract

In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integrodifferential equations in a two-dimensional convex polygonal domain. The effect of numerical quadrature is also examined. In the semidiscrete case, optimal error estimates in L∞(L²) and L∞(H¹) norms are shown to hold with minimal regularity assumptions on the initial data, whereas quasi-optimal estimate is derived in L∞(L∞) norm under higher regularity on the data. Based on a second order explicit method in time, a completely discrete scheme is examined and optimal error estimates are established with a mild condition on the space and time discretizing parameters. Finally, some numerical experiments are conducted which confirm the theoretical order of convergence.

  • History

Published online: 2015-12

  • AMS Subject Headings

65N30, 65N15

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