Approximation of Elliptic Hemivariational Inequalities

  • Jaroslav Haslinger
  • Markku Miettinen
  • Panagiotis D. Panagiotopoulos
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 35)


From the previous chapter we know that there exist many important problems in mechanics in which constitutive laws are expressed by means of nonmonotone, possibly multivalued relations (nonmonotone multivalued stress-strain or reaction-displacement relations,e.g). The resulting mathematical model leads to an inclusion type problem involving multivalued nonmonotone mappings or to a substationary type problem for a nonsmooth, nonconvex superpotential expressed in terms of calculus of variation. It is the aim of this chapter to give a detailed study of a discretization of such a type of problems including the convergence analysis. Here we follow closely Miettinen and Haslinger, 1995, Miettinen and Haslinger, 1997.


Finite Element Method Variational Inequality Bilinear Form Piecewise Constant Function Finite Element Space 
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  1. Chang, K. C. (1981). Variational methods for non-differentiable functionals and their applications to partial differential equations. J. Math. Anal. Appl., 80: 102–129.MathSciNetzbMATHCrossRefGoogle Scholar
  2. Ciarlet, P. G. (1978). The Finite Element Method for Elliptic Problems. North Holland, Amsterdam, New York, Oxford.Google Scholar
  3. Glowinski, R. (1984). Numerical Methods for Nonlinear Variational Problems. Springer-Verlag, New York.zbMATHGoogle Scholar
  4. Glowinski, R., Lions, J. L., and Trémoliéres, R. (1981). Numerical analysis of variational inequalities, volume 8 of Studies in Mathematics and its Applications. North Holland, Amsterdam, New York.Google Scholar
  5. Miettinen, M. and Haslinger, J. (1995). Approximation of nonmonotone multivalued differential inclusions. IMA J. Numer. Anal., 15: 475–503.MathSciNetzbMATHCrossRefGoogle Scholar
  6. Miettinen, M. and Haslinger, J. (1997). Finite element approximation of vectorvalued hemivariational problems. J. Global Optim., 10: 17–35.MathSciNetzbMATHCrossRefGoogle Scholar
  7. Naniewicz, Z. and Panagiotopoulos, P. D. (1995). Mathematical theory of hemivariational inequalities and applications. Marcel Dekker, New York.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Jaroslav Haslinger
    • 1
  • Markku Miettinen
    • 2
  • Panagiotis D. Panagiotopoulos
    • 3
  1. 1.Charles UniversityCzech Republic
  2. 2.University of JyväskyläFinland
  3. 3.Aristotle UniversityGreece

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