Optimal error bounds for two-grid schemes applied to the Navier-Stokes equations
Optimal error bounds for two-grid schemes applied to the Navier-Stokes equations
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DOI：
10.1016/j.amc.2011.12.051
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发表时间：
2010-11
期刊：
影响因子：
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通讯作者：
J. D. Frutos;B. García-Archilla;J. Novo
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文献类型：
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作者：
J. D. Frutos;B. García-Archilla;J. Novo
本文研究了不可压Navier-Stokes方程空间离散的两网格混合有限元格式。一个标准的混合有限元方法应用于粗网格近似的非线性Navier-Stokes方程，而线性演化问题是解决了细网格。先前计算的Galerkin近似的速度被用来线性化的对流项。对于分析，我们考虑到缺乏规律性的解决方案的Navier-Stokes方程在初始时间的非局部相容性条件的情况下的数据。最优误差界。
We consider two-grid mixed-finite element schemes for the spatial discretization of the incompressible Navier–Stokes equations. A standard mixed-finite element method is applied over the coarse grid to approximate the nonlinear Navier–Stokes equations while a linear evolutionary problem is solved over the fine grid. The previously computed Galerkin approximation to the velocity is used to linearize the convective term. For the analysis we take into account the lack of regularity of the solutions of the Navier–Stokes equations at the initial time in the absence of nonlocal compatibility conditions of the data. Optimal error bounds are obtained.