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. (C) 2010 Elsevier B.V. All rights reserved.