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

• Main Authors: Samir Karaa, Amiya K. Pani
• Format: Journal
• Published: 2018
• Subjects: Agricultural and Biological Sciences
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84929903856&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/44750
• Institution: Chiang Mai University

© 2015 Institute for Scientific Computing and Information. 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 < sup > ∞ < /sup > (L < sup > 2 < /sup > ) and L < sup > ∞ < /sup > (H < sup > 1 < /sup > ) norms are shown to hold with minimal regularity assumptions on the initial data, whereas quasi-optimal estimate is derived in L < sup > ∞ < /sup > (L < sup > ∞ < /sup > ) 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.