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Optimal error estimates of mixed FEMs for second order hyperbolic integro-differential equations with minimal smoothness on initial data

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Title Optimal error estimates of mixed FEMs for second order hyperbolic integro-differential equations with minimal smoothness on initial data
 
Creator KARAA, S
PANI, AK
 
Subject FINITE-ELEMENT APPROXIMATIONS
ACOUSTIC-WAVE EQUATION
POROUS-MEDIA
GALERKIN METHODS
QUADRATURE
SUPERCONVERGENCE
FLOWS
Hyperbolic integro-differential equation
Mixed finite element method
Semidiscrete Galerkin approximation
Completely discrete implicit method
Optimal error estimates
Minimal smoothness on initial data
 
Description In this article, mixed finite element methods are discussed for a class of hyperbolic integrodifferential equations (HIDEs). Based on a modification of the nonstandard energy formulation of Baker, both semidiscrete and completely discrete implicit schemes for an extended mixed method are analyzed and optimal L-infinity(L-2)-error estimates are derived under minimal smoothness assumptions on the initial data. Further, quasi-optimal estimates are shown to hold in L-infinity(L-infinity)-norm. Finally, the analysis is extended to the standard mixed method for HIDEs and optimal error estimates in L-infinity(L-2)-norm are derived again under minimal smoothness on initial data. (C) 2014 Elsevier B.V. All rights reserved.
 
Publisher ELSEVIER SCIENCE BV
 
Date 2016-01-14T13:09:54Z
2016-01-14T13:09:54Z
2015
 
Type Article
 
Identifier JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 275,113-134
0377-0427
1879-1778
http://dx.doi.org/10.1016/j.cam.2014.08.009
http://dspace.library.iitb.ac.in/jspui/handle/100/17579
 
Language en