In this paper we will discuss different coupling methods {suitable for usein} the framework of the recently introduced CutFEM paradigm, cf. Burman, Erik;Claus, Susanne; Hansbo, Peter; Larson, Mats G.; Massing, Andr\'e . CutFEM:discretizing geometry and partial differential equations. Internat. J. Numer.Methods Engrg. 104 (2015), no. 7, 472-501. In particular we will considermortaring using Lagrange multipliers on the one hand and Nitsche's method onthe other. For simplicity we will first discuss these method in the setting ofuncut meshes, and end with some comments on the extension to CutFEM. We will,for comparison, discuss some different types of problems such as high contrastproblems and problems with stiff coupling or adhesive contact. We will reviewsome of the existing methods for these problems and propose some alternativemethods resulting from crossovers from the Lagrange multiplier framework toNitsche's method and vice versa.
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机译:在本文中,我们将讨论不同的耦合方法{适用于}最近引入的CutFEM范例框架cf。埃里克(Erik)布尔曼;苏珊(Susanne)克劳斯(Claus);汉斯伯,彼得; Larson,Mats G .; Massing,安德烈。 CutFEM:离散几何和偏微分方程。国际交流。 J.纽默方法工程。 104(2015),第。 7,472-501。特别是,我们将一方面考虑使用Lagrange乘法器,另一方面考虑使用Nitsche的方法。为简单起见,我们将首先在未切割网格的设置中讨论这些方法,最后以对CutFEM扩展的一些注释结束。为了进行比较,我们将讨论一些不同类型的问题,例如高对比度问题以及刚性耦合或粘合剂接触问题。我们将回顾一些针对这些问题的现有方法,并提出从拉格朗日乘数框架与尼采方法(反之亦然)交叉产生的替代方法。
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