Numerical Examples

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


The aim of this chapter is to illustrate how previous theoretical results can be used for the numerical realization of several model examples. Our strategy is to transform the discrete hemivariational inequality to a problem of finding substationary points of the corresponding superpotential, and then to solve this by using nonsmooth and nonconvex optimization methods introduced in Chapter 5 (see Miettinen and Haslinger, 1995, Miettinen et al., 1995, Mäkelä et al., 1999 for some earlier numerical tests). The advantage of this strategy is that it is mathematically justified and is applicable to a large class of hemivariational inequalities. Other possibilities are: either to use some heuristic methods or to impose some additional restrictions on the nonconvexity (a difference of two convex functions, e.g.) and then to use some special methods (see Panagiotopoulos, 1993, Dem’yanov et al., 1996, Mistakidis and Stavroulakis, 1998).


Finite Element Method Variational Inequality Normal Displacement Numerical Realization Tangential Displacement 
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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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