a stabilized p1-p0-p1 finite element method for the approximation of linearized viscoelastic fluid flow problems

In this article, we present a stabilized finite element (fe) method for the linearized viscoelastic fluid flow problems by discontinuous galerkin (dg) method. the fe spaces for the unknown variables are chosen as p1−p0−p1, where the fluid velocity and the pressure are discretized by the lowest-order lagrange elements and the stress tensor is discretized by piecewise p1 polynomial. in order to get a stable scheme, we added a stabilization term in the discretized weak formulation. this method has some prominent features: parameter-free, avoiding calculation of higher-order derivatives and its behaviour towards pressure is totally local. we obtained optimal error estimates and presented several numerical experiments to verify the proposed scheme.