Workshop on Numerical Methods and Analysis in CFD - Abstract
Thiele, Jan Philipp
In this talk, we will present a space-time extension of the variational partition of unity (PU) approach [3] for localization of dual weighted residual (DWR) type error estimators [2]. This allows for estimation and control of both spatial and temporal errors w.r.t. a given quantity of interest. For CFD, typical quantities are drag and lift coefficients. The focus will be on application of the novel PU localization [4] to the global DWR estimator for adaptive refinement. Finally, we will discuss some numerical results based on the tensor-product space-time code introduced in [1] that substantiate our developments.
References:
[1] M. Bause, M.P. Bruchhaeuser and U. Koecher. Flexible goal-oriented adaptivity for higher-order space-time discretizations of transport problems with coupled flow. Computers & Mathematics with Applications, Vol. 91, pp. 17--35, 2021.
[2] R. Becker and R. Rannacher. An optimal control approach to a posteriori error estimation in finite element methods. Acta Numerica, Cambridge University Press, pp. 1--102, 2001.
[3] T. Richter and T. Wick, Variational localizations of the dual weighted residual estimator. Journal of Computational and Applied Mathematics, Vol. 279, pp. 192--208, 2015.
[4] J.P. Thiele and T. Wick, Variational localizations of space-time dual weighted residual estimators for parabolic problems. in preperation