A stabilized formulation for discrete gradient method | Zendy

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A stabilized formulation for discrete gradient method

Author(s) -

Qian Jing,

Lu Jia

Publication year - 2011

Publication title -

international journal for numerical methods in biomedical engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.741

H-Index - 63

eISSN - 2040-7947

pISSN - 2040-7939

DOI - 10.1002/cnm.1337

Subject(s) - polygon (computer graphics) , spurious relationship , polygon mesh , extension (predicate logic) , finite element method , energy (signal processing) , mathematics , strain energy , scheme (mathematics) , zero (linguistics) , algorithm , mathematical optimization , mathematical analysis , computer science , geometry , structural engineering , engineering , statistics , telecommunications , linguistics , philosophy , frame (networking) , programming language

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. Copyright © 2009 John Wiley & Sons, Ltd.

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