A local superconvergence analysis of the finite element method for the Stokes equations by local projections

作者：Li, Jian^*; He, Yinnian; Wu, Jianhua

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(17): 6499-6511.

DOI：10.1016/j.na.2011.06.033

• Stokes equation
• Local superconvergence
• Finite element method
• Local projection method

In this paper, we focus on a local superconvergence analysis of the finite element method for the Stokes equations by local projections. The local and global superconvergence results of finite element solutions are provided for the Stokes problem under some corresponding regularity assumptions. Conclusion can be drawn that the local superconvergence has advantages over the global superconvergence in two important aspects. On the one hand, it offsets theoretical limitation in practical applications. On the other hand, interior estimates are derived on the base of local properties of the domain without global smoothness for the exact solution and prior regularity of the problem globally over the whole domain.

• 出版日期2011-12
• 单位陕西师范大学; 西安交通大学; 宝鸡文理学院