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Abstract

Subject of this paper is the development of an a posteriori error estimator for nonstationary incompressible flow problems. The error estimator is computable and able to assess the temporal and spatial discretization errors separately. Thereby, the error is measured in an arbitrary quantity of interest because measuring errors in global norms is often of minor importance in practical applications. The basis for this is a finite element discretization in time and space. The techniques presented here also provide local error indicators which are used to adaptively refine the temporal and spatial discretization. A key ingredient in setting up an efficient discretization method is balancing the error contributions due to temporal and spatial discretization. To this end, a quantitative assessment of the individual discretization errors is required. The described method is validated by an established Navier-Stokes benchmark.