Stokes问题的集中质量非协调有限元法

Lumped Mass Nonconforming Finite Element Methods for Stokes Problem

针对其平面有界凸区域上的一类非定常不可压 Stokes方程 ,提出了一种新的有限元方法 ,借助于所谓的速度 -压力混合型公式 ,讨论了非定常不可压 Stokes方程的质量集中非协调有限元逼近格式 (全离散情形 )。首先 ,给出了非定常不可压 Stokes方程的质量集中非协调 Galerkin有限元逼近的全离散格式 ,其次 ,对所讨论问题的解与其所给出的离散问题的解之间的误差进行了分析研究 ;最后 ,利用 Stokes投影算子的性质和离散的LBB条件 ,得到了非定常不可压 Stokes方程关于速度 L2 模和能量模及压力 L2 模方面的最优阶误差估计。

Lumped mass nonconforming finite element methods are presented for an initial-boundary va-lue problem of a non-stationary Stokes equation in two dimension bounded domain by using the velocity-pressure mixed formulation. Firstly, the discrete approximation scheme of the lumped mass nonconforming finite element methods are studied to discuss the problem-the nonstationary Stokes equation. Secondly, the error estimates for the solution of the problem and the solution of the discrete approximation scheme are considered. Finally, using the condition of the Stokes projection operator and the discrete LBB condition, optimal error estimates on L 2-norm, energy-norm of velocity and L 2-norm of the pressure are derived.