Energy estimate for Oldroyd-B model under Tresca boundary condition: scheme preserving properties

Abstract

This paper is concerned with the design of a numerical scheme that preserves; the symmetry, positive definiteness, and a priori estimate for the Oldroyd-B model with Tresca boundary condition. Such a scheme is important for its numerical stability, and for investigation of long time behaviour of macro-macro models. The theoretical findings are validated with simulations for lid driven cavity