Advertisement

Approximations of Variational Inequalities

  • Anca Capatina
Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 31)

Abstract

This chapter is devoted to the discrete approximation of abstract elliptic and implicit evolutionary quasi-variational inequalities. Convergence results for internal approximations in space of elliptic quasi-variational inequalities together with a backward difference scheme in time of implicit evolutionary quasi-variational inequalities are proved. The results obtained in this chapter, representing generalizations of the approximations of variational inequalities of the first and second kinds, can be applied to a large variety of static and quasistatic contact problems, including unilateral and bilateral contact or normal compliance conditions with friction. In particular, static and quasistatic unilateral contact problems with nonlocal Coulomb friction in linear elasticity will be considered in last part of this book.

Keywords

Variational Inequality Nonempty Closed Convex Subset Discrete Approximation Closed Convex Cone Nonempty Convex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Capatina, A., Cocou, M., Raous, M.: A class of implicit variational inequalities and applications to frictional contact. Math. Meth. Appl. Sci. 32, 1804–1827 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Céa, J.: Approximation variationnelle des problèmes aux limites. Ann. Inst. Fourier (Grenoble) 14, 345–444 (1964)CrossRefzbMATHGoogle Scholar
  3. 3.
    Céa, J.: Optimisation, Théorie et Algorithmes. Dunod, Paris (1971)zbMATHGoogle Scholar
  4. 4.
    Falk, R.S.: Approximation of an elliptic boundary value problem with unilateral constraints. Math. Model. Numer. Anal. 9, 5–12 (1975)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Glowinski, R.: Numerical Methods for Nonlinear Variational Problems. Springer, Berlin/Heidelberg/New York (1984)CrossRefzbMATHGoogle Scholar
  6. 6.
    Glowinski, R., Lions, J.L., Trémolières, R.: Numerical Analysis of Variational Inequalities. North-Holland, Amsterdam (1981)zbMATHGoogle Scholar
  7. 7.
    Radoslovescu Capatina, A., Cocu, M.: Internal approximation of quasi-variational inequalities. Numer. Math. 59, 385–398 (1991)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Anca Capatina
    • 1
  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania

Personalised recommendations