An adaptive variational multiscale method for convection–diffusion problems
Mats G. Larson, Axel Målqvist · Communications in Numerical Methods in Engineering · 2008
Abstract The adaptive variational multiscale method is an extension of the variational multiscale method where the fine‐scale part of the solution is approximated by a sum of numerically computed solutions to localized subgrid problems. Furthermore, the crucial discretization parameters are chosen automatically by an adaptive algorithm based on a posteriori error estimates. This method has been developed for diffusion‐dominated problems and applied to multiscale problems that arise in oil reservoir simulation. In this paper, we extend the method to convection–diffusion problems. We present a duality based a posteriori error representation formula and an adaptive algorithm that tunes the fine‐scale mesh size and the patch sizes of the local problems. Numerical results show rapid convergence of the adaptive algorithm. Copyright © 2008 John Wiley & Sons, Ltd.