Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
Volume 70, Issue 9, Pages 1139-1166Publisher
WILEY
DOI: 10.1002/fld.2735
Keywords
nonstationary incompressible flow; space-time finite elements; goal-oriented adaptivity
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This paper presents a general strategy for designing adaptive spacetime finite element discretizations of the nonstationary NavierStokes equations. The underlying framework is that of the dual weighted residual method for goal-oriented a posteriori error estimation and automatic mesh adaptation. In this approach, the error in the approximation of certain quantities of physical interest, such as the drag coefficient, is estimated in terms of local residuals of the computed solution multiplied by sensitivity factors, which are obtained by numerically solving an associated dual problem. In the resulting local error indicators, the effects of spatial and temporal discretization are separated, which allows for the simultaneous adjustment of time step and spatial mesh size. The efficiency of the proposed method for the construction of economical meshes and the quantitative assessment of the error is illustrated by several test examples. Copyright (c) 2012 John Wiley & Sons, Ltd.
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