A goal oriented error estimator and mesh adaptivity for sea ice simulations

For the first time we introduce an error estimator for the numerical approximation of the equations describing the dynamics of sea ice. The idea of the estimator is to identify different error contributions coming from spatial and temporal discretization as well as from the splitting in time of the ice momentum equations from further parts of the coupled system. The novelty of the error estimator lies in the consideration of the splitting error, which turns out to be dominant with increasing mesh resolution. Errors are measured in user specified functional outputs like the total sea ice extent. The error estimator is based on the dual weighted residual method that asks for the solution of an additional dual problem for obtaining sensitivity information. Estimated errors can be used to validate the accuracy of the solution and, more relevant, to reduce the discretization error by guiding an adaptive algorithm that optimally balances the mesh size and the time step size to increase the efficiency of the simulation.