New connections between finite element formulations of the Navier-Stokes equations

Bowers A.L.; Cousins B.R.; Linke A.; Rebholz L.G.

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New connections between finite element formulations of the Navier-Stokes equations

机译：Navier-Stokes方程的有限元公式之间的新连接

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We show the velocity solutions to the convective, skew-symmetric, and rotational Galerkin finite element formulations of the Navier-Stokes equations are identical if Scott-Vogelius elements are used, and thus all three formulations will be the same pointwise divergence free solution velocity. A connection is then established between the formulations for grad-div stabilized Taylor-Hood elements: under mild restrictions, the formulations' velocity solutions converge to each other (and to the Scott-Vogelius solution) as the stabilization parameter tends to infinity. Thus the benefits of using Scott-Vogelius elements can be obtained with the less expensive Taylor-Hood elements, and moreover the benefits of all the formulations can be retained if the rotational formulation is used. Numerical examples are provided that confirm the theory.

机译：我们显示了如果使用Scott-Vogelius元素，则Navier-Stokes方程的对流，倾斜对称和旋转Galerkin有限元公式的速度解是相同的，因此所有这三个公式将具有相同的点向散度自由解速度。然后在grad-div稳定的Taylor-Hood元素的配方之间建立联系：在轻微的限制下，由于稳定参数趋于无穷大，因此配方的速度解彼此收敛（并且收敛于Scott-Vogelius解）。因此，可以使用较便宜的泰勒-霍德元件来获得使用斯科特-沃格利乌斯元件的益处，此外，如果使用旋转制剂，则可以保留所有制剂的益处。数值例子证实了这一理论。

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《Journal of Computational Physics》 |2010年第24期|共6页
作者
Bowers A.L.; Cousins B.R.; Linke A.; Rebholz L.G.;
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正文语种 eng
中图分类数学物理方法;
关键词
Navier-Stokes equations; Rotational form; Scott-Vogelius; Strong mass conservation;

机译：Navier-Stokes方程;旋转形式;Scott-Vogelius;强质量守恒;

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1. New connections between finite element formulations of the Navier-Stokes equations [J] . Bowers A.L., Cousins B.R., Linke A., Journal of Computational Physics . 2010,第24期

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2. Efficient a priori pivoting schemes for a sparse direct Gaussian equation solver for the mixed finite element formulation of the Navier-Stokes equations [J] . S.O. Wille, O. Staff, A.F.D. Loula Applied Mathematical Modelling . 2004,第7期

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4. Boundary element-finite element method for velocity-vorticity formulation of Navier-Stokes equations [C] . Z. Zunic, L. Skerget, M. Hribersek, International Conference on Computational Methods and Experimental Measurements(CMEM XII); 2005; Malta(MT) . 2005

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7. Two Level Finite Element Technique for Pressure Recovery from Stream Function Formulation of The Navier-Stokes Equations [O] . Faisal Fairag 2015

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8. Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation [R] . Glaisner, F., Tezduyar, T. E. 1987

机译：原始变量公式和涡量流函数公式中Navier-stokes方程的有限元技术

New connections between finite element formulations of the Navier-Stokes equations

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