TY - JOUR
T1 - A Priori Error Estimates for Finite Volume Element Approximations to Second Order Linear Hyperbolic Integro-Differential Equations
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 401
EP - 429
PY - 2015
DA - 2015/12
SN - 12
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/496.html
KW - Finite volume element, hyperbolic integro-differential equation, semidiscrete method, numerical quadrature, Ritz-Volterra projection, completely discrete scheme, optimal error estimates.
AB - <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>