Numerical investigation of effectivity indices of space-time error indicators for Navier–Stokes equations

In this paper we propose two error indicators aimed at estimating the space discretization error and the time discretization error for the unsteady Navier–Stokes equations. We define a space error indicator for evaluating the quality of the mesh and a time error indicator for evaluating the time discretization error. Moreover, we verify the reliability of the estimations through numerical experiments and we propose an effective space-time adaptive strategy for the unsteady Navier–Stokes equations. Such technique is based on two residual-based error indicators that suitably drive the mesh and the timestep-length modifications. Adaptive simulations show that the presented strategy allows to obtain accurate solutions in efficient way.