Stability and convergence of second order time discrete projection method for the linearized Oldroyd model

In this paper, we consider the second order time discrete projection method for the linearized Oldroyd model based on the time iterative discrete scheme. By the projection method, the original problem is decoupled into two linear subproblems, and each subproblem can be solved easily. Unconditional stability and the corresponding convergence results of the numerical solutions are derived. Our main results are that the convergence orders in time for the velocity in L2-norm is second order and for the pressure in H1-norm is first order. Finally, some numerical examples are provided to verify the performances of the developed numerical method.