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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Local Projection Stabilized Galerkin Approximations For The Generalized Stokes Problem
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Local Projection Stabilized Galerkin Approximations For The Generalized Stokes Problem

机译：广义Stokes问题的局部投影稳定Galerkin逼近

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摘要

We analyze pressure stabilized finite element methods for the solution of the generalized Stokes problem and investigate their stability and convergence properties. An important feature of the method is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations. Although stability of the method has been established, for the homogeneous Stokes equations, the proof given here is based on the existence of a special interpolant with additional orthogonal property with respect to the projection space. This, makes it a lot simpler and more attractive. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations.
机译：我们分析了压力稳定有限元方法来求解广义Stokes问题，并研究了它们的稳定性和收敛性。该方法的一个重要特征是可以局部消除压力梯度未知数，从而导致方程组解耦。尽管已经确定了该方法的稳定性，但是对于齐次Stokes方程，此处给出的证明是基于存在一个特殊的插值，该插值相对于投影空间具有附加的正交性。这使它变得更加简单和吸引人。结果表明，所得的稳定化方法可导致速度和压力近似值的最佳收敛速度。

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