On a second-order decoupled time-stepping scheme for solving a finite element problem for the approximation of Peterlin viscoelastic model

In the present paper, a decoupled second-order time-stepping scheme is proposed and analyzed for solving the evolutionary Peterlin viscoelastic model with finite element spatial discretization. To avoid solving a coupled fully discrete nonlinear system, a second-order extrapolation in time is employed to the nonlinear terms. It only requires sequentially solving the solution of the Navier-Stokes problem and one constitutive equation per time step, which needs smaller memory. Furthermore, optimal error estimates for the velocity, the pressure, and the conformation tensor are proved in suitable norms with using of the Stokes and Ritz projections. Finally, numerical experiments are conducted that confirm our theoretical results.