@Article{IJNAM-12-401,
author = {Samir Karaa and Amiya K. Pani},
title = {A Priori Error Estimates for Finite Volume Element Approximations to Second Order Linear Hyperbolic Integro-Differential Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2015},
volume = {12},
number = {3},
pages = {401--429},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/496.html}
}