Abstract Nitsche’s method is an effective framework for the solution of problems involving embedded domains. Weak enforcement of Dirichlet boundary and interface conditions engenders additional active degrees of freedom compared to the corresponding kinematically admissible formulation, and hence additional solutions in eigenvalue problems. The original and added eigenpairs are designated proper and complementary, respectively. The number of complementary pairs equals the number of degrees of freedom that would be constrained in the kinematically admissible formulation. We investigate the number of complementary pairs that arise in representative nonconforming configurations of bilinear quadrilaterals. Algebraic elimination of the added degrees of freedom from the Nitsche formulation yields a formulation with several advantageous features. Practical procedures for solving eigenvalue problems based on reduced methods are proposed.

中文翻译：

---

Nitsche 方法在不合格网格上的光谱方面

摘要 Nitsche 的方法是解决涉及嵌入式域问题的有效框架。与相应的运动学可接受公式相比，狄利克雷边界和界面条件的弱执行会产生额外的活动自由度，从而产生特征值问题的额外解决方案。原始的和添加的特征对分别被指定为适当的和互补的。互补对的数量等于在运动学允许公式中受到约束的自由度的数量。我们研究了在双线性四边形的代表性非一致配置中出现的互补对的数量。Nitsche 公式中增加的自由度的代数消除产生具有几个有利特征的公式。