A Priori Error Estimates for Finite Volume Element Approximations to Second Order Linear Hyperbolic Integro-Differential Equations
Year: 2015
International Journal of Numerical Analysis and Modeling, Vol. 12 (2015), Iss. 3 : pp. 401–429
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 $L^∞(L^2)$ and $L^∞(H^1)$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2015-IJNAM-496
International Journal of Numerical Analysis and Modeling, Vol. 12 (2015), Iss. 3 : pp. 401–429
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Finite volume element hyperbolic integro-differential equation semidiscrete method numerical quadrature Ritz-Volterra projection completely discrete scheme optimal error estimates.