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Higher Order Galerkin Time Discretization for Nonstationary Incompressible Flow

  • S. HussainEmail author
  • F. Schieweck
  • S. Turek
Conference paper

Abstract

In this paper, we extend our work for the heat equation in (Hussain et al., J Numer Math 19(1):41–61, 2011) and for the Stokes equations in (Hussain et al., Open Numer Methods J 4:35–45, 2012) to the nonstationary Navier-Stokes equations in two dimensions. We examine continuous Galerkin-Petrov (cGP) time discretization schemes for nonstationary incompressible flow. In particular, we implement and analyze numerically the higher order cGP(2)-method. For the space discretization, we use the LBB-stable finite element pair \(Q_{2}/P_{1}^{\mathit{disc}}\). The discretized systems of nonlinear equations are treated by using the fixed-point as well as the Newton method and the associated linear subproblems are solved by using a monolithic multigrid solver with GMRES method as smoother. We perform nonstationary simulations for a benchmarking configuration to analyze the temporal accuracy and efficiency of the presented time discretization scheme.

Notes

Acknowledgements

The authors want to express their gratitude to the German Research Association (DFG) and the Higher Education Commission (HEC) of Pakistan for their financial support of the study; contract/grant number: SCHI 576/2-1, TU 102/35-1 and LC06052 by MSMT.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institut für Angewandte Mathematik, TU-DortmundDortmundGermany
  2. 2.Institut für Analysis und NumerikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

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