Analysis and finite element simulations of a second-order fluid model in a bounded domain, submitted

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second-order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. Themethod is applied to the two-dimensional lid-driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic para-meters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals