TY - JOUR
T1 - A priori error estimates for finite volume element approximations to second order linear hyperbolic integro-differential equations
AU - Karaa, Samir
AU - Pani, Amiya K.
N1 - Publisher Copyright:
© 2015 Institute for Scientific Computing and Information.
PY - 2015
Y1 - 2015
N2 - 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 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.
AB - 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 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.
KW - Completely discrete scheme
KW - Finite volume element
KW - Hyperbolic integro-differential equation
KW - Numerical quadrature
KW - Optimal error estimates
KW - Ritz-Volterra projection
KW - Semidiscrete method
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M3 - Article
AN - SCOPUS:84929903856
SN - 1705-5105
VL - 12
SP - 401
EP - 429
JO - International Journal of Numerical Analysis and Modeling
JF - International Journal of Numerical Analysis and Modeling
IS - 3
ER -