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A modified nonlinear spectral Galerkin method for the equations of motion arising in the Kelvin-Voigt fluids

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Title A modified nonlinear spectral Galerkin method for the equations of motion arising in the Kelvin-Voigt fluids
 
Creator PANI, AK
PANY, AK
DAMAZIO, P
YUAN, JY
 
Subject viscoelastic fluids
Kelvin-Voigt model
nonlinear Galerkin method
spectral approximations
a priori error bound
uniform convergence in time
NAVIER-STOKES EQUATIONS
APPROXIMATE INERTIAL MANIFOLDS
FINITE-ELEMENT-METHOD
TIME
DISCRETIZATION
CONVERGENCE
ACCURACY
 
Description In this paper, a variant of nonlinear Galerkin method is proposed and analysed for equations of motions arising in a Kelvin-Voigt model of viscoelastic fluids in a bounded spatial domain in IRd (d = 2, 3). Some new a priori bounds are obtained for the exact solution when the forcing function is independent of time or belongs to L-infinity in time. As a consequence, existence of a global attractor is shown. For the spectral Galerkin scheme, existence of a unique discrete solution to the semidiscrete scheme is proved and again existence of a discrete global attractor is established. Further, optimal error estimate in L-infinity(L-2) and L-infinity(H-0(1))-norms are proved. Finally, a modified nonlinear Galerkin method is developed and optimal error bounds are derived. It is, further, shown that error estimates for both schemes are valid uniformly in time under uniqueness condition.
 
Publisher TAYLOR & FRANCIS LTD
 
Date 2014-12-28T14:29:50Z
2014-12-28T14:29:50Z
2014
 
Type Article
 
Identifier APPLICABLE ANALYSIS, 93(8)1587-1610
0003-6811
1563-504X
http://dx.doi.org/10.1080/00036811.2013.841143
http://dspace.library.iitb.ac.in/jspui/handle/100/16756
 
Language English