论文标题
简单的正交规则，用于非参数不合格的四边形元素
Simple quadrature rules for a nonparametric nonconforming quadrilateral element
论文作者
论文摘要
我们为具有四个自由度的非参数不合格的四边形元素介绍了简单的正交规则。我们的正交规则是由Meng {\ it等} \ cite {meng2018new}的工作激发的。首先，我们介绍了MVP的家族（平均值属性） - 在Meng {\ it等人}引入的中间参考域上提供四个不合格元素。然后，我们在中间参考域设计了两点和三点正交规则。在相等的正交权重的假设下，两个点和三个点规则的偏离高斯点点的偏差假定相同的二次多项式，并修改了常数术语。因此，两点规则和三点规则是在一个行程中构建的。正交规则在渐近上是最佳的，因为网格尺寸足够小。进行了几个数值实验，这些实验显示了新的正交规则的效率和收敛性。
We introduce simple quadrature rules for the family of nonparametric nonconforming quadrilateral element with four degrees of freedom. Our quadrature rules are motivated by the work of Meng {\it et al.} \cite{meng2018new}. First, we introduce a family of MVP (Mean Value Property)-preserving four DOFs nonconforming elements on the intermediate reference domain introduced by Meng {\it et al.}. Then we design two--points and three--points quadrature rules on the intermediate reference domain. Under the assumption on equal quadrature weights, the deviation from the quadrilateral center of the Gauss points for the two points and three points rules assumes the same quadratic polynomials with constant terms modified. Thus, the two--points rule and three--points rule are constructed at one stroke. The quadrature rules are asymptotically optimal as the mesh size is sufficiently small. Several numerical experiments are carried out, which show efficiency and convergence properties of the new quadrature rules.
