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A modified nonlinear spectral Galerkin method for the equations of motion arising in the Kelvin-Voigt fluids
- Source :
- IndraStra Global.
- Publication Year :
- 2014
- Publisher :
- TAYLOR & FRANCIS LTD, 2014.
-
Abstract
- 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.
- Subjects :
- Applied Mathematics
Mathematical analysis
Viscoelastic Fluids
Equations of motion
Navier-Stokes Equations
Spectral Approximations
Finite-Element-Method
Nonlinear Galerkin Method
Time
Nonlinear system
Exact solutions in general relativity
Approximate Inertial Manifolds
Bounded function
Kelvin–Voigt material
Uniform Convergence In Time
Attractor
Kelvin-Voigt Model
A Priori Error Bound
Uniqueness
Galerkin method
Convergence
Analysis
Accuracy
Mathematics
Discretization
Subjects
Details
- Language :
- English
- ISSN :
- 23813652
- Database :
- OpenAIRE
- Journal :
- IndraStra Global
- Accession number :
- edsair.doi.dedup.....6f1d341760b837ff53fb0938b08b3be3