Semidiscrete Galerkin method for equations of motion arising in Kelvin-Voigt model of viscoelastic fluid flow

Abstract

Finite element Galerkin method is applied to equations of motion arising in the Kelvin–Voigt model of viscoelastic fluids for spatial discretization. Some new a priori bounds which reflect the exponential decay property are obtained for the exact solution. For optimal L^∞(L²) estimate in the velocity, a new auxiliary operator which is based on a modification of the Stokes operator is introduced and analyzed. Finally, optimal error bounds for the velocity in L^∞(L²) as well as in L^∞(H¹₀)-norms and the pressure in L^∞(L²)-norm are derived which again preserves the exponential decay property.