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2010 | 30 | 2 | 205-220
Tytuł artykułu

Penalties, Lagrange multipliers and Nitsche mortaring

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Języki publikacji
EN
Abstrakty
EN
Penalty methods, augmented Lagrangian methods and Nitsche mortaring are well known numerical methods among the specialists in the related areas optimization and finite elements, respectively, but common aspects are rarely available. The aim of the present paper is to describe these methods from a unifying optimization perspective and to highlight some common features of them.
Twórcy
  • Technische Universität Dresden, Institut für Numerische Mathematik, Germany
Bibliografia
  • [1] R.A. Adams, Sobolev spaces (Academic Press, Inc., 1975).
  • [2] R. Becker, P. Hansbo and R. Stenberg, A finite element method for domain decomposition with non-matching grids, Math. Model. Numer. Anal. 37 (2003), 209-225. doi: 10.1051/m2an:2003023
  • [3] P.G. Ciarlet, The finite element method for elliptic problems (North-Holland Publ. Co., Amsterdam 1978).
  • [4] L.C. Evans, Partial differential equations (AMS Publ. Providence, 1998).
  • [5] C. Grossmann, Dualität und Strafmethoden bei elliptischen Differentialgleichungen, Z. Angew. Math. Mech. 64 (1984), 111-121. doi: 10.1002/zamm.19840640206
  • [6] C. Grossmann and A. Kaplan, Strafmethoden und modifizierte Lagrange Funktionen in der nichtlinearen Optimierung (Teubner, 1979).
  • [7] C. Grossmann, H.-G. Roos and M. Stynes, Numerical treatment of partial differential equations (Springer, Berlin, 2007).
  • [8] K. Ito and K. Kunisch, Lagrange multiplier approach to variational problems and applications (SIAM Publ., 2008). doi: 10.1137/1.9780898718614
  • [9] A. Kaplan and R. Tichatschke, Stable methods for ill-posed variational problems: prox-regularization of elliptic variational inequalities and semi-infinite problems (Akademie Verlag, Berlin 1994).
  • [10] B. Riviére, Discontinuous Galerkin methods for solving elliptic and parabolic equations (SIAM Publ., 2008). doi: 10.1137/1.9780898717440
  • [11] P. Le Tallec and T. Sassi, Domain decomposition with nonmatching grids: Augmented Lagrangian approach, Math. Comput. 64 (1995), 1367-1396.
  • [12] A. Toselli and O. Widlund, Domain decomposition methods - algorithms and theory (Springer, 2005).
  • [13] F. Tröltzsch, Optimale Steuerung partieller Differentialgleichungen. Theorie, Verfahren und Anwendungen (Vieweg, Wiesbaden, 2005).
  • [14] B.I. Wohlmuth, A mortar finite element method using dual spaces for the Lagrange multiplier, SIAM J. Numer. Anal. 38 (2000), 989-1012. doi: 10.1137/S0036142999350929
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1120
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