A priori error estimates for finite volume element approximations to second order linear hyperbolic integro-differential equations

2014/01/21 by Samir Karaa, Karaa, Samir, Amiya K. Pani +1
Engineering · Computer Science · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1401.5139

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 integro- differential 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 in 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.

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