A unified framework for a posteriori error estimation for the Stokes problem
A unified framework for a posteriori error estimation for the Stokes problem
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DOI：
10.1007/s00211-012-0472-x
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发表时间：
2012-12
影响因子：
2.1
通讯作者：
A. Hannukainen;R. Stenberg;M. Vohralík
中科院分区：
文献类型：
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作者：
A. Hannukainen;R. Stenberg;M. Vohralík
在本文中，一个统一的框架后验误差估计的斯托克斯问题。它是基于一致的速度重建和一致的，局部保守的通量（应力）重建。它给出了保证，完全可计算的全球上界以及当地的能量误差的下界。为了将该框架应用于给定的数值方法，需要检查两个简单的条件。我们将展示如何做到这一点，各种符合和符合稳定的有限元方法，不连续Galerkin方法，Crouzeix-RaviartTM有限元方法，混合有限元方法，和一般类的有限体积法。开发和使用的工具包括一个新的简单的平衡对偶网格和解决方案的局部泊松型诺依曼问题的混合有限元法。数值实验说明了理论的发展。
In this paper, a unified framework for a posteriori error estimation for the Stokes problem is developed. It is based on-conforming velocity reconstruction and-conforming, locally conservative flux (stress) reconstruction. It gives guaranteed, fully computable global upper bounds as well as local lower bounds on the energy error. In order to apply this framework to a given numerical method, two simple conditions need to be checked. We show how to do this for various conforming and conforming stabilized finite element methods, the discontinuous Galerkin method, the Crouzeix–Raviart nonconforming finite element method, the mixed finite element method, and a general class of finite volume methods. The tools developed and used include a new simple equilibration on dual meshes and the solution of local Poisson-type Neumann problems by the mixed finite element method. Numerical experiments illustrate the theoretical developments.