Explicit trace inequalities for isogeometric analysis and parametric hexahedral finite elements
Explicit trace inequalities for isogeometric analysis and parametric hexahedral finite elements
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DOI：
10.1007/s00211-012-0484-6
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发表时间：
2013-02
影响因子：
2.1
通讯作者：
John A. Evans;T. Hughes
中科院分区：
文献类型：
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作者：
John A. Evans;T. Hughes
我们得到了NURBS映射域的新的迹不等式。除了Sobolev型不等式外，我们还导出了用于基于NURBS的等距分析的离散迹不等式。在我们的分析中，对形状、大小、多项式次数和NURBS加权函数的所有依赖关系都被精确地指定，并且为我们估计中出现的所有边界常数提供了显式的值。由于六面体有限元是NURBS的特例，我们的结果专门用于参数六面体有限元，我们的分析也推广到基于T-Spline的等距分析。我们将显式迹不等式中的边界常数与数值计算的最优边界常数进行了比较，并讨论了我们的结果在拉普拉斯问题中的应用。在这篇文章的最后，我们简要地探讨了等距分析中的所谓的逐块迹不等式。
We derive new trace inequalities for NURBS-mapped domains. In addition to Sobolev-type inequalities, we derive discrete trace inequalities for use in NURBS-based isogeometric analysis. All dependencies on shape, size, polynomial degree, and the NURBS weighting function are precisely specified in our analysis, and explicit values are provided for all bounding constants appearing in our estimates. As hexahedral finite elements are special cases of NURBS, our results specialize to parametric hexahedral finite elements, and our analysis also generalizes to T-spline-based isogeometric analysis. We compare the bounding constants appearing in our explicit trace inequalities with numerically computed optimal bounding constants, and we discuss application of our results to a Laplace problem. We finish this paper with a brief exploration of so-called patch-wise trace inequalities for isogeometric analysis.