PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Some remarks on nonuniqueness of minimizers for discrete minimization problems

Autorzy
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate the issue of uniqueness and nonuniqueness of minimizers for the approximation of variational problems. We show that when the continuous problem does not admit a minimizer its approximation by finite elements may lead to several discrete minimizers.
Wydawca
Rocznik
Strony
191--208
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
  • Institut für Mathematik Universität Zürich Winterthurerstr. 190 CH-8057 Zürich, Switzerland
autor
  • Institut für Mathematik Universität Zürich Winterthurerstr. 190 CH-8057 Zürich, Switzerland
Bibliografia
  • [1] Brighi, B., Sur quelques problèmes de calcul des variations et l’approximation de leur fonctionnelles relaxées, Thesis, University of Metz, 1991.
  • [2] Brighi, B. and Chipot, M., Approximated convex envelope of a function, SIAM J. Numer. Anal. 31(1) (1994), 128-148.
  • [3] Chipot, M., Numerical analysis of oscillations in nonconvex problems, Numer. Math. 59 (1991), 747-767.
  • [4] Chipot, M., The appearence of microstructures in problems with incompatible wells and their numerical approach, Numer. Math. 83(3) (1999), 325-352.
  • [5] Chipot, M. and Collins, C., Numerical approximation in variational problems with potential wells, SIAM J. Numer. Anal. 29(4) (1993), 473-487.
  • [6] Chipot, M., Collins, C. and Kinderlehrer, D., Numerical analysis of oscillations in multiple well problems, Numer. Math. 70 (1995), 259-282.
  • [7] Chipot, M. and Elfanni, A., On the numerical analysis of some variational problems with nonhomogeneous boundary conditions, Japan J. Indust. Appl. Math. 15 (1998), 345-361.
  • [8] Chipot, M. and Kinderlehrer, D., Equilibrium configurations of crystals, Arch. Rational Mech. Anal. 103 (1988), 237-277.
  • [9] Chipot, M. and Müller, S., Sharp energy estimates for finite element approximations of non-convex problems, IUTAM Symposium on Variations of Domain and Free Boundary Problems in Solid Mechanics (P. Argoul, M. Frémond, Q. S. Nguyen, eds), Kluwer, Dordrecht, 1999, 317-325.
  • [10] Dacorogna, B., Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin, 1989.
  • [11] Elfanni, A., Sur quelques questions d’analyse numérique relatives à des problèmes non convexes, Thesis, University of Metz. 1996.
  • [12] Friesecke, G., A necessary and sufficient condition for nonattainment and formation of micro structure almost everywhere in scalar variational problems. Proc. Roy. Soc. Edinburgh Sect. A 124 (1994), 437-471.
  • [13] Kohn, R. V. and Müller, S., Branching of twins near an austenite/twinned martensite interface, Philos. Mag. Ser. A 66 (1992), 697-715.
  • [14] Raviart, P. A., Thomas, J. M., Introduction à l’Analyse Numérique des Équations aux Dérivées Partielles, Masson, Paris, 1988.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0013-0030
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.