Thin layers can lead to unfavorable meshes in a finite element (FE) analysis. Thin shell approximations (TSAs) avoid this issue by removing the need for a mesh of the thin layer while approximating the physics across the layer by an interface condition. Typically, a TSA requires the mesh of both sides of the TSA interface to be conforming. To alleviate this requirement, we propose to combine mortar methods and TSAs for solving the heat equation. The mortar TSA method's formulation is derived and enables an independent discretization of the subdomains on the two sides of the TSA depending on their accuracy requirements. The method is verified by comparison with a reference FE solution of a thermal model problem of a simplified superconducting accelerator magnet.

翻译：在有限元分析中，薄层可能导致不利的网格划分。薄壳近似法通过消除对薄层网格的需求，同时通过界面条件近似层间的物理行为，从而避免了这一问题。通常，薄壳近似法要求其界面两侧的网格必须协调一致。为了放宽这一要求，我们提出将砂浆法与薄壳近似法相结合来求解热传导方程。本文推导了砂浆薄壳近似法的公式，使得薄壳近似界面两侧的子域能够根据各自的精度要求进行独立的离散化。通过将本方法与一个简化的超导加速器磁体热模型问题的参考有限元解进行比较，验证了该方法的有效性。