Stokes问题的杂交-混合有限元分析  

A HYBRID-MIXED FINITE ELEMENT METHOD FOR THE STOKES PROBLEM

作　　者：段火元[1] 梁国平[1] 马昌凤[1] 

机构地区：[1]中国科学院数学与系统科学研究院,北京100080

出　　处：《应用数学学报》2003年第3期551-565,共15页Acta Mathematicae Applicatae Sinica

摘　　要：本文发展Stokes问题的一个四变量杂交-混合变分方程:应力-速度-压力-拉格朗日乘子。然后发展其有限元方法:对应四变量分别用间断型Raviart-Thomas最低阶元,分片常数元,连续线性元和连续线性元的迹空间,我们获得了稳定性和最优误差界,通过后处理办法,我们得到一个适合于计算的速度-压力格式,该格式可视为“Mini”元方法的一个变形(本文格式中引入了局部投影算子),然而,本文格式关于压力具有“超收敛”结果;得到了压力关于H^1-范的误差界O(h)。A four-fields (stress-velocity-pressure-Lagrangian multiplier) hybrid-mixed vari-ational model is formulated for the Stokes problem. Finite element methods are analyzed, where the stress is approximated by the discontinuous Raviart-Thomas element of lowest-order, and the velocity by the piecewise constant element, and the pressure by the piecewise continuous linear element, and the Lagranian multiplier by the trace space of the piecewise continuous linear element. Using some postprocessing techniques to obtain a better approximation of the velocity, we obtain optimal error bounds O(h) in H 1-norm for both velocity and pressure, including O (ft2) error bound in L2-norm for the velocity.

关 键 词：STOKES问题 杂交-混合变分方程 稳定性 最优误差界 后处理 “Mini”有限元 投影有限元 分片常数元 

分 类 号：O241.82[理学—计算数学]