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Systematic and generic construction of shape functions for p-adaptive meshes of multidimensional finite elements

机译:多维有限元的p自适应网格的形状函数的系统通用构建

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摘要

This paper presents a methodology for generating high-order shape functions for the complete family of finite elements. The geometric entities presented are the point, line, triangle, quadrilateral, tetrahedron, pyramid, prism, and hexahedron. The shape functions constructed are hierarchical and generate continuous approximation spaces. The order of interpolation of the shape function can be determined independently for each edge, face, and volume. The space of interpolation of order p for each element is complete. This definition allows for the construction of hybrid meshes with any combination of these elements, including elements of distinct dimension and/or interpolation order. The reader will observe that our systematic way of constructing shape functions can be extended to elements of higher-dimension.
机译:本文提出了一种用于为整个有限元族生成高阶形状函数的方法。显示的几何实体为点,线,三角形,四边形,四面体,金字塔,棱柱和六面体。构造的形状函数是分层的,并生成连续的近似空间。可以针对每个边缘,面和体积独立确定形状函数的插值顺序。每个元素的p阶插值空间已完成。该定义允许构造具有这些元素的任何组合的混合网格,包括不同尺寸和/或插值顺序的元素。读者将发现,我们构造形状函数的系统方法可以扩展到更高维度的元素。

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