A stabilized formulation for discrete gradient method

作者：Qian Jing; Lu Jia^*

来源：International Journal for Numerical Methods in Biomedical Engineering, 2011, 27(6): 860-873.

DOI：10.1002/cnm.1337

• Average strain
• Discrete gradient method
• Discrete method
• Dispersion analysis
• Low energies
• Low-order finite elements
• Nodal integration
• Polygon meshes
• Spurious modes
• Stabilization effects
• Stabilized formulation

This paper presents a stabilization scheme for the discrete gradient method proposed by the authors (Int. J. Numer. Methods Eng. 2009; 78:505-527). The discrete method is an extension of the nodal average strain triangle element to arbitrary polygon meshes. The method outperforms the low-order finite elements in many aspects; however, it is susceptible to spurious zero-energy or low-energy modes arising from cancelation of strains during strain averaging. In this paper, stabilization is achieved by a penalty scheme that penalizes the difference between the nodal strain and the subcell strains. Several examples, including an analytical dispersion analysis, are presented to demonstrate the stabilization effect.

• 出版日期2011
• 单位The University of Iowa