We explore the use of the non-symmetric Nitsche method for the weak imposition of boundary and coupling conditions along interfaces that intersect through a finite element mesh. In contrast to symmetric Nitsche methods, it does not require stabilization and therefore does not depend on the appropriate estimation of stabilization parameters. We first review the available mathematical background, recollecting relevant aspects of the method from a numerical analysis viewpoint. We then compare accuracy and convergence of symmetric and non-symmetric Nitsche methods for a Laplace problem, a Kirchhoff plate, and in 3D elasticity. Our numerical experiments confirm that the non-symmetric method leads to reduced accuracy in the L2 error, but exhibits superior accuracy and robustness for derivative quantities such as diffusive flux, bending moments or stress. Based on our numerical evidence, the non-symmetric Nitsche method is a viable alternative for problems with diffusion-type operators, in particular when the accuracy of derivative quantities is of primary interest.
|Original language||English (US)|
|Number of pages||28|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Sep 1 2016|
Bibliographical noteFunding Information:
This study is based on discussions that took place during the workshop “Advanced Computational Methods for Design, Analysis and Optimization” at Iowa State University in December 2015. We thank the organizers Ming-Chen Hsu and Adarsh Krishnamurthy and acknowledge the support of the Department of Mechanical Engineering at Iowa State University . The first author gratefully acknowledges support from the National Science Foundation ( ACI-1565997 ). The second author was supported by the Israel Science Foundation (Grant No. 1008/13 ) and the Diane and Arthur B. Belfer Chair in Mechanics and Biomechanics. The last author was supported by the “Excellence Initiative” of the German Federal and State Governments and the Graduate School of Computational Engineering at the Technical University of Darmstadt . We also acknowledge the Minnesota Supercomputing Institute (MSI) of the University of Minnesota for providing computing resources that have contributed to the research results reported within this paper ( https://www.msi.umn.edu/ ).
- Immersed finite element methods
- Non-symmetric Nitsche method
- Weak boundary and coupling conditions