Unfitted finite element methods for the heat conduction in composite media with contact resistance

详细信息    查看全文

• 作者：Haifeng Ji ; Feng Wang and Jinru Chen
• 刊名：Numerical Methods for Partial Differential Equations
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：33
• 期：1
• 页码：354-380
• 全文大小：969K
• ISSN：1098-2426

文摘

This article is concerned with the heat conduction problem in composite media. In practical applications, the composite materials often do not contact well and there exist gaps between the contacting materials. This leads to the thermal contact resistance effect which results in a discontinuity of the temperature across the interface. In this article, an unfitted finite element method is proposed to solve the problem. Different from the traditional finite element method, the proposed method uses structured meshes that allow the interface to cut through. To avoid integrating on curved domains and interfaces, the interface is approximated by a broken line/plane corresponding to the triangulation. In addition, a ghost-penalty is added to recover the condition number of the stiffness matrix to O ( h − 2 ) with a hidden constant independent of the mesh-interface geometry. A rigorous analysis is provided. Finally, numerical tests are presented to verify the theoretical findings.