Abstract
In this article a mixed least-squares finite element method (LSFEM) for the time-dependent incompressible Navier-Stokes equations is proposed and investigated. The formulation is based on the incompressible Navier-Stokes equations consisting of the balance of momentum and the continuity equations. In order to obtain a first-order system the Cauchy stress tensor is introduced as an additional variable to the system of equations. From this stress-velocity-pressure approach a stress-velocity formulation is derived by adding a redundant residual to the functional without additional variables in order to strengthen specific physical relations, e.g. mass conservation. We account for implementation aspects of triangular mixed finite elements especially regarding the approximation used for H(div\() \times H^1\) and the discretization in time using the Newmark method. Finally, we present the flow past a cylinder benchmark problem in order to demonstrate the derived stress-velocity least-squares formulation.
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This work was supported by the German Research Foundation (DFG) under grant SCHW1355/3-1 and SCHR570/31-1.
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Schwarz, A., Nisters, C., Averweg, S., Schröder, J. (2018). Stress-Velocity Mixed Least-Squares FEMs for the Time-Dependent Incompressible Navier-Stokes Equations. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_14
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DOI: https://doi.org/10.1007/978-3-319-73441-5_14
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