A Stabilized Characteristic Finite Element Method for the Viscoelastic Oldroyd Fluid Motion Problem

Abstract

In this article, a characteristic scheme is considered for the viscoelastic Oldroyd fluid flows based on the lowest equal-order finite element pair. The diffusion term in these equations is discretized by using finite element method, the temporal differentiation and advection terms are treated by characteristic scheme and the integral term is handled by applying right rectangle rule. Unconditionally stability and optimal error estimates for the velocity and pressure are derived. Finally, some numerical results are provided to verify the performance of the proposed method.