On a Linearized Backward Euler Method for the Equations of Motion of Oldroyd Fluids of Order One

Abstract

In this paper, a linearized backward Euler method is discussed for the equations of motion arising in the Oldroyd model of viscoelastic fluids. Some new a priori bounds are obtained for the solution under realistically assumed conditions on the data. Further, the exponential decay properties for the exact as well as the discrete solutions are established. Finally, a priori error estimates in $\bH^1$ and $\bL^2$-norms are derived for the the discrete problem which are valid uniformly for all time $t>0$.