Proper intrinsic scales for a-posteriori multiscale error estimation

Recently the multiscale a-posteriori error estimator has been introduced, showing excellent robustness for fluid mechanics problems. In this paper, a theoretical analysis for element edge exact solutions is conducted, in which case, the error constant is the norm of a Green's function or a residual-free bubble. This finds application when the solution is computed with a stabilized method. One of the features of the technique is that it gives the proper scales for a-posteriori error estimation in any norm of interest, such as the L-2, H-1, energy and L-infinity norms. For fluid transport problems it is shown that the constant for predicting the error in the H-1 seminorm is unbounded as the element Peclet number tends to infinity, making L-p norms more suitable for this type of problems. Furthermore, it is shown that the flow intrinsic time scale parameter represents the L-1 norm of the error as a function of the L-infinity norm of the residual. When these scales are employed for one-dimensional nodally-exact solutions, piecewise linear finite element spaces and piecewise constant residuals, the multiscale error estimator is shown to be exact. (c) 2005 Elsevier B.V. All rights reserved.