Variational Multiscale A Posteriori Error Estimation for Quantities of Interest

This paper applies the variational multiscale theory to develop an explicit a posteriori error estimator for quantities of interest and linear functionals of the solution. The method is an extension of a previous work on global and local error estimates for solutions computed with stabilized methods. The technique is based on approximating an exact representation of the error formulated as a function of the fine-scale Green function. Numerical examples for the multidimensional transport equation confirm that the method can provide good local error estimates of quantities of interest both in the diffusive and the advective limit. [DOI: 10.1115/1.3057403]