高阶无发散有限元空间的基础

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics Pub Date : 2024-06-24 DOI:10.1016/j.rinam.2024.100469

A. Alonso Rodríguez , J. Camaño , E. De Los Santos , F. Rapetti

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引用次数: 0

摘要

在此，我们将一种在低多项式程度中用于构建无发散函数空间有限元基础的经典方法扩展到无拓扑限制的有界域的任意多项式程度。该方法使用与两个微分算子（梯度和发散）相关的图，并使用第一个图的生成树来选择基础。该方法可用于表达有限元微分形式的两个主要自由度系列--权值和矩值。

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Basis for high order divergence-free finite element spaces

A method classically used in the lower polynomial degree for the construction of a finite element basis of the space of divergence-free functions is here extended to any polynomial degree for a bounded domain without topological restrictions. The method uses graphs associated with two differential operators: the gradient and the divergence, and selects the basis using a spanning tree of the first graph. It can be applied for the two main families of degrees of freedom, weights and moments, used to express finite element differential forms.

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来源期刊

Results in Applied Mathematics Mathematics-Applied Mathematics

CiteScore

3.20

自引率

10.00%

发文量

审稿时长

23 days