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Author: Linke, Alexander × Author: Wilson, Nicholas E. × End date: 2019 × Start date: 2010 × DDC: 510 × WGL Institute: WIAS ×

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Now showing 1 - 3 of 3
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    Improving efficiency of coupled schemes for Navier-Stokes equations by a connection to grad-div stabilitzed projection methods
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Linke, Alexander; Neilan, Michael; Rebholz, Leo G.; Wilson, Nicholas E.
    We prove that in finite element settings where the divergence-free subspace of the velocity space has optimal approximation properties, the solution of Chorin/Temam projection methods for Navier-Stokes equations equipped with grad-div stabilization with parameter , converge to the associated coupled method solution with rate gamma as gamma -> ?. We prove this first for backward Euler schemes, and then extend the results to BDF2 schemes, and finally to schemes with outflow boundary conditions. Several numerical experiments are given which verify the convergence rate, and show how using projection methods in this setting with large grad-div stabilization parameters can dramatically improve accuracy.
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    On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius solutions for incompressible flow problems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Linke, Alexander; Rebholz, Leo G.; Wilson, Nicholas E.
    It was recently proven that, under mild restrictions, grad-div stabilized Taylor-Hood solutions of Navier-Stokes problems converge to the Scott-Vogelius solution of that same problem. However, even though the analytical rate was only shown to be gamma^-frac12 (where gamma is the stabilization parameter), the computational results suggest the rate may be improvable gamma^-1. We prove herein the analytical rate is indeed gamma^-1, and extend the result to other incompressible flow problems including Leray-alpha and MHD. Numerical results are given that verify the theory.
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    Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Galvin, Keith J.; Linke, Alexander; Rebholz, Leo G.; Wilson, Nicholas E.
    We consider the problem of poor mass conservation in mixed finite element algorithms for flow problems with large rotation-free forcing in the momentum equation. We provide analysis that suggests for such problems, obtaining accurate solutions necessitates either the use of pointwise divergence-free finite elements (such as Scott-Vogelius), or heavy grad-div stabilization of weakly divergence-free elements. The theory is demonstrated in numerical experiments for a benchmark natural convection problem, where large irrotational forcing occurs with high Rayleigh numbers.