A Nonlinear Galerkin/Petrov-Least Squares Mixed Element Method for the Stationary Navier-Stokes Equations
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摘要: 给出定常的Navier-Stokes方程的一种非线性Galerkin/Petrov最小二乘混合元法,该方法是将余量形式的Petrov最小二乘方法与非线性Galerkin混合元结合起来,使得速度和压力的混合元空间无需满足离散的Babu ka-Brezzi稳定性条件,从而使得它们的有限元空间可以任意选择。并证明该方法的解的存在唯一性和收敛性。
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关键词:
- Navier-Stokes方程 /
- 非线性Galerkin混合元法 /
- Petrov最小二乘法 /
- 误差估计
Abstract: A nonlinear Galerkin/Petrov-least squares mixed element (NGPLSME) method for the stationary Navier-Stokes equations is presented and analyzed. The scheme is that Petrov-least squares forms of residuals are added to the nonlinear Galerkin mixed element method so that it is stable for any combination of discrete velocity and pressure spaces without requiring the Babu韐a-Brezzi stability condition. The existence, uniqueness and convergence (at optimal rate) of the NGPLSME solution is. -
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