A Posteriori Error Estimators for the Stokes and Oseen Equations
A Posteriori Error Estimators for the Stokes and Oseen Equations
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DOI：
10.1137/s0036142994264092
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发表时间：
1997-02
影响因子：
2.9
通讯作者：
M. Ainsworth;J. Oden
中科院分区：
文献类型：
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作者：
M. Ainsworth;J. Oden
讨论了用有限元方法逼近带不可压缩约束问题时离散化误差的后验估计问题。给出了处理约束条件和相关动量方程(可能)非自伴的一般方法。给出了自适应h、p和h-p型有限元格式的后验误差估计。主要特点是局部误差残差问题不受不可压缩约束，从而避免了对特殊有限元格式的需要，并且分析基本上适用于任何离散化方案，包括连续和不连续的压力空间。估计器将以类似能量的范数测量的实际误差为界。
The problem of obtaining /posteriori/ estimates of the discretization error when one uses finite element methods to approximate problems with an incompressibility constraint is discussed. A general approach to the treatment of the constraint condition and to the (possible) non-self-adjointness of the associated momentum equations is presented. A posteriori error estimates are derived for adaptive h, p, and h-p type finite element schemes. Key features are that the local error residual problems are not subject to an incompressibility constraint thereby avoiding the need for special finite element schemes and that the analysis is valid for essentially any discretization scheme, including continuous and discontinuous pressure spaces. The estimator bounds the actual error measured in an energy-like norm.