The multiscale approach to error estimation and adaptivity

A new explicit a-posteriori error estimator is investigated, which emanates from the variational multiscale theory. The error estimator uses an approximation of the Green’s function which propagates the error according to the dual problem. The technique predicts the error in the L2 norm from element residuals, both interior and inter-element jumps, therefore, leading to a very economical procedure. Finally, the methodology is applied to fluid flow transport, showing that for convection-dominated flows, the efficiency index is independent of the diffusion coefficient.