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.
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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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Hussain, S., Schieweck, F., Turek, S. (2013). Higher Order Galerkin Time Discretization for Nonstationary Incompressible Flow. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_54
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DOI: https://doi.org/10.1007/978-3-642-33134-3_54
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