Article ID Journal Published Year Pages File Type
4637896 Journal of Computational and Applied Mathematics 2016 24 Pages PDF
Abstract

In this paper, a finite element Galerkin method is applied to equations of motion arising in the Kelvin–Voigt viscoelastic fluid flow model, when the forcing function is in L∞(L2). Some a priori   estimates for the exact solution, which are valid uniformly in time as t↦∞t↦∞ and even uniformly in the retardation time κκ an κ↦0κ↦0 are derived. It is shown that the semidiscrete method admits a global attractor. Further, with the help of a priori   bounds and Sobolev–Stokes projection, optimal error estimates for the velocity in L∞(L2) and L∞(H1)-norms and for the pressure in L∞(L2)L∞(L2)-norm are established. Since the constants involved in error estimates have an exponential growth in time, therefore, in the last part of the article, under certain uniqueness condition, the error bounds are established which are valid uniformly in time. Finally, some numerical experiments are conducted which confirm our theoretical findings.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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