$V$-cycle multi-grid method of viscoelastic fluid flow obeying an Oldroyd-B-type constitutive law

For the time-dependent viscoelastic fluid flow obeying an Oldroyd B type constitutive law in three dimensional domains, we put forward a $V$-cycle multi-grid method. At the same time, we discuss existence, uniqueness and error estimates of the approximate solution. The approximate stress, velocity and pressure are, respectively, $\sigma_k$ discontinuous, $u_k$ continuous, $p_k$ continuous.