Unconditional convergence and superconvergence analysis for the transient Stokes equations with damping

Abstract

In this paper, the linearized backward Euler scheme for the transient Stokes equations with damping is presented, in which the velocity and pressure are approximated by the lowest-order Bernadi-Raugel rectangular element pair. Unconditional optimal error estimates of the velocity in the norms L∞(L2) and L∞(H1), and the pressure in the norm L∞(L2) are derived through the Stokes operator and the H−1-norm estimate. Moreover, the superclose properties and global superconvergent results are obtained by the interpolation post-processing technique. Finally, some numerical results are provided to confirm the theoretical analysis.