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ON FULLY DISCRETE FINITE ELEMENT SCHEMES FOR EQUATIONS OF MOTION OF KELVIN-VOIGT FLUIDS

In this paper, we study two fully discrete schemes for the equations of motion arising in the Kelvin-Voigt model of viscoelastic fluids. Based on a backward Euler method in time and a finite element method in spatial direction, optimal error estimates which exhibit the exponential decay property in time are derived. In the later part of this article, a second order two step backward difference scheme is applied for temporal discretization and again exponential decay in time for the discrete solution is discussed. Finally, a priori error estimates are derived and results on numerical experiments conforming theoretical results are established.