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A PRIORI ERROR ESTIMATES FOR FINITE VOLUME ELEMENT APPROXIMATIONS TO SECOND ORDER LINEAR HYPERBOLIC INTEGRO-DIFFERENTIAL EQUATIONS

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Title A PRIORI ERROR ESTIMATES FOR FINITE VOLUME ELEMENT APPROXIMATIONS TO SECOND ORDER LINEAR HYPERBOLIC INTEGRO-DIFFERENTIAL EQUATIONS
 
Creator KARAA, S
PANI, AK
 
Subject QUADRATURE
Finite volume element
hyperbolic integro-differential equation
semidiscrete method
numerical quadrature
Ritz-Volterra projection
completely discrete scheme
optimal error estimates
 
Description 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-infinity (L-2) and L-infinity(H-1) norms are shown to hold with minimal regularity assumptions on the initial data, whereas quasi-optimal estimate is derived in L-infinity(L-infinity) 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.
 
Publisher ISCI-INST SCIENTIFIC COMPUTING & INFORMATION
 
Date 2016-01-15T10:56:53Z
2016-01-15T10:56:53Z
2015
 
Type Article
 
Identifier INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 12(3)401-429
1705-5105
http://dspace.library.iitb.ac.in/jspui/handle/100/18403
 
Language en