Panpenalty Finite Element Method

  • Yang Gao
  • Keh-chih Hwang
Conference paper


In the finite element analysis of variational problems with constraints, general hybrid/mixed models, based on the classical lagrange multiplier method, usually yield ill-conditioned discrete equations. As a result, the convergence can be assured only when LFB condition is satisfied, and the construction of the element is extremely limited. On the other hand, with penalty function method in the programming theory, convergence can always be assured, but, because of the inherent disadvantage of this method such as instability of numerical solution, slower convergence rate and lower numerical precision etc., pure penalty function method has incurred disrepute in nonlinear programming.


Variational Problem Constraint Function Rank Condition Programming Theory Complementary Energy 


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  1. [1]
    Gao Yang: On the complementary principles in elasto-plastic system and panpenalty finite element method. Ph. D. Thesis, Tsinghua University, Beijing, China, 1985.Google Scholar
  2. [2]
    Ekeland, I.; Temam, R.: Convex analysis and variational problems, North-Holland, 1976.MATHGoogle Scholar
  3. [3]
    Gao Yang; Hwang Keh-chih: On the complementary energy variational principle for Hencky plasticity. Proc. Int. Conf. Nonlinear Mechanics, ed. Chien Wei-zang, Science Press, 1985, pp.489–494.Google Scholar

Copyright information

© Springer Japan 1986

Authors and Affiliations

  • Yang Gao
    • 1
  • Keh-chih Hwang
    • 1
  1. 1.Department of Engineering MechanicsTsinghua UniversityBeijingChina

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