Output-based error estimation and mesh adaptation for variational multiscale methods

Duality-based approaches to estimate errors for functional output quantities require the solution of an auxiliary dual problem. This dual solution must be approximated in a richer function space than the one used for the original problem of interest. A novel strategy for dual enrichment is proposed based on variational multiscale (VMS) methods and an error representation for output quantities for VMS methods is derived. An implicit error estimate based on the derived error representation is compared to a recently developed explicit error estimate for VMS methods. It is shown that while both estimates are identical with respect to calculating the total output error, the newly derived estimate provides superior local indicators for use in driving mesh adaptivity.