On duality-based a posteriori error estimation in various norms and linear functionals for large eddy simulation

We derive a posteriori error estimates for the filtered velocity field in a large eddy simulation in various norms and linear functionals. The a posteriori error estimates take the form of an integral in space-time of a discretization residual and a modeling residual times a dual weight. The discretization residual is directly computable, and the modeling residual is estimated by a scale similarity model. We approximate the dual weight by solving an associated linearized dual problem numerically. Computational examples from transition to turbulence in Couette flow are presented.