Variational multiscale a posteriori error estimation for systems: The Euler and Navier-Stokes equations

This paper extends explicit a posteriori error estimators based on the variational multiscale theory to systems of equations. In particular, the emphasis is placed on flow problems: the Euler and Navier-Stokes equations. Three error estimators are proposed: the standard, the naive and the upper bound. Numerical results show that with a very economical algorithm the attained global and local efficiencies for the naive approach are reasonably close to unity whereas the standard and upper bound approaches give, respectively, approximate lower and higher error estimates.