论文标题
在任何维
Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions
论文作者
论文摘要
分段无差异的不合格的虚拟元素是为Stokes问题而设计的。在基于Stokes问题和稳定化引入局部能量投影仪之后，提出了用于Stokes问题的无差异的不合格虚拟元素方法。为离散方法提供了详细且严格的错误分析。分析中的一个重要特性是当地能源投影仪与Divergence运营商通勤。借助无差异插值操作员到广义的raviart-thomas元素空间上，通过简单地修改先前离散化的右侧，可以开发出压力稳定的不合格虚拟元素方法。还讨论了减少的虚拟元素方法。提供数值结果以验证理论收敛。
Piecewise divergence-free nonconforming virtual elements are designed for Stokes problem in any dimensions. After introducing a local energy projector based on the Stokes problem and the stabilization, a divergence-free nonconforming virtual element method is proposed for Stokes problem. A detailed and rigorous error analysis is presented for the discrete method. An important property in the analysis is that the local energy projector commutes with the divergence operator. With the help of a divergence-free interpolation operator onto a generalized Raviart-Thomas element space, a pressure-robust nonconforming virtual element method is developed by simply modifying the right hand side of the previous discretization. A reduced virtual element method is also discussed. Numerical results are provided to verify the theoretical convergence.
