Abstract In this paper we introduce the semiregularity property for a family of decompositions of a polyhedron into a natural class of prisms. In such a family, prismatic elements are allowed to be very flat or very long compared to their triangular bases, and the edges of quadrilateral faces can be nonparallel. Moreover, the triangular faces of each element are either parallel or skew to each other. To estimate the error of the interpolation operator defined on the finite space whose basis functions are defined on the general prismatic elements, we consider quadratic polynomials as the basis functions for that space which are bilinear on the reference prism. We then prove that under this modification of the semiregularity criterion, the interpolation error is of order O ( h ) in the H 1 -norm.

中文翻译：

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估计半规则棱柱单元的插值误差

摘要 在本文中，我们介绍了多面体分解为自然棱柱类的一族分解的半正则性。在这样的族中，棱柱单元与其三角形底面相比可以非常平或非常长，四边形面的边缘可以不平行。此外，每个单元的三角形面相互平行或倾斜。为了估计在有限空间上定义的插值算子的误差，其基函数定义在一般棱柱元素上，我们将二次多项式视为该空间的基函数，它们在参考棱柱上是双线性的。然后我们证明，在半正则性准则的这种修改下，插值误差在 H 1 -范数中为 O ( h ) 阶。