论文标题
$ P_1 $ - 具有周期性边界条件的不合格的四边形有限元元素空间：第一部分。
$P_1$--Nonconforming Quadrilateral Finite Element Space with Periodic Boundary Conditions: Part I. Fundamental results on dimensions, bases, solvers, and error analysis
论文作者
论文摘要
$ p_1 $ - 研究了具有周期性边界条件的不合格四边形有限元元素空间。该空间的维度和基础的特征是最小基本离散边界条件的概念。我们表明，根据坐标的离散数量的均衡，情况完全不同。基于对空间的分析，我们提出了几个数值方案，以解决具有周期性边界条件的椭圆问题。这些数值方案中的一些与求解由不可变基矩阵组成的线性方程有关。由Drazin逆的礼貌，保证了相应的数值解决方案的存在。得出了数值解之间的理论关系，并通过数值结果证实。最后，提供了三维的扩展。
The $P_1$--nonconforming quadrilateral finite element space with periodic boundary condition is investigated. The dimension and basis for the space are characterized with the concept of minimally essential discrete boundary conditions. We show that the situation is totally different based on the parity of the number of discretization on coordinates. Based on the analysis on the space, we propose several numerical schemes for elliptic problems with periodic boundary condition. Some of these numerical schemes are related with solving a linear equation consisting of a non-invertible matrix. By courtesy of the Drazin inverse, the existence of corresponding numerical solutions is guaranteed. The theoretical relation between the numerical solutions is derived, and it is confirmed by numerical results. Finally, the extension to the three dimensional is provided.
