A modified nonlinear spectral Galerkin method for the equations of motion arising in the Kelvin-Voigt fluids
DSpace at IIT Bombay
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Title |
A modified nonlinear spectral Galerkin method for the equations of motion arising in the Kelvin-Voigt fluids
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Creator |
PANI, AK
PANY, AK DAMAZIO, P YUAN, JY |
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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 |
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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.
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Publisher |
TAYLOR & FRANCIS LTD
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Date |
2014-12-28T14:29:50Z
2014-12-28T14:29:50Z 2014 |
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Type |
Article
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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 |
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Language |
English
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