瞬态Stokes模型亚网格多尺度稳定化有限元法的后验误差估计
Aposteriori error estimation of Subgrid multiscale stabilized finite element method for transient Stokes model
摘要：
在本研究中，我们提出一种新的稳定化有限元分析瞬态斯托克斯模型。代数次网格多尺度方法已被用来达到稳定的耦合变分公式。详细推导了稳定化形式，并对其全离散形式进行了稳定性分析。证明了压力稳定的离散$inf$ - $sup$条件。对于时间离散，采用了全隐格式。详细推导了稳定化亚网格多尺度有限元格式的后验误差估计。数值实验验证了理论建立的收敛阶。
英文摘要：
In this study, we present a novel stabilized finite element analysis for transient Stokes model. The algebraic subgrid multiscale approach has been employed to arrive at the stabilized coupled variational formulation. Derivation of the stabilized form as well as stability analysis of it's fully discrete formulation are presented elaborately. Discrete $inf$-$sup$ condition for pressure stabilization has been proven. For the time discretization the fully implicit schemes have been used. A detailed derivation of the aposteriori error estimate for the stabilized subgrid multiscale finite element scheme has been presented. Numerical experiment has been carried out to verify theoretically established order of convergence.
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