等几何接合方法
Isogeometric mortar methods
AI总结：
研究等几何分析框架下接合方法的理论与数值应用，探讨了拉格朗日乘子的两种稳定空间选择，展示了不同阶数的样条空间，并验证了无交叉点修改的稳定性。
摘要：
在等几何分析框架内，研究了接合方法的理论和数值应用。对于拉格朗日乘子，提出了两种均匀稳定的空问选择，这两种空问都是样条空间但阶数不同。在一种情况下，需要基于局部阶数降低的交叉点修改。在另一种情况下，对偶空间的阶数比原空间低两阶。这种配对被证明在没有必要交叉点修改的情况下是inf-sup稳定的。几个数值例子验证了理论结果并展示了额外的方面。关键词：等几何分析，接合方法，inf-sup稳定性，交叉点修改。
英文摘要：
The application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically. For the Lagrange multiplier two choices of uniformly stable spaces are presented, both of them are spline spaces but of a different degree. In one case, we consider an equal order pairing for which a cross point modification based on a local degree reduction is required. In the other case, the degree of the dual space is reduced by two compared to the primal. This pairing is proven to be inf-sup stable without any necessary cross point modification. Several numerical examples confirm the theoretical results and illustrate additional aspects. Keywords: isogeometric analysis, mortar methods, inf-sup stability, cross point modification.
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