GLS Stabilized Finite Element Methods For A Time-dependent Three-field Stokes Problem

Abstact: In this paper,we study two stabilized finite element approximations for solving the time-dependent three-field Stokes problem arising from the numerical study of viscoelastic flows.The approximate stress,velocity and pressure are respectively Pk continuous,Pk continuous,Pk continuous.The first method corresponds to the case of possible stabilization terms are added hi a least-squares fashion.In the second method,only a selected number of these terms are added.Stability and convergence results are established.