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

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 Some new a priori bounds are obtained for the exact solution when the forcing function is independent of time or belongs to 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 and -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.