Penalties, Lagrange multipliers and Nitsche mortaring

Christian Grossmann

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2010)

  • Volume: 30, Issue: 2, page 205-220
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Christian Grossmann. "Penalties, Lagrange multipliers and Nitsche mortaring." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 30.2 (2010): 205-220. <http://eudml.org/doc/271158>.

@article{ChristianGrossmann2010,
abstract = {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.},
author = {Christian Grossmann},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {augmented Lagrangian; penalty method; domain decomposition; Nitsche mortaring; finite elements},
language = {eng},
number = {2},
pages = {205-220},
title = {Penalties, Lagrange multipliers and Nitsche mortaring},
url = {http://eudml.org/doc/271158},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Christian Grossmann
TI - Penalties, Lagrange multipliers and Nitsche mortaring
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2010
VL - 30
IS - 2
SP - 205
EP - 220
AB - 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.
LA - eng
KW - augmented Lagrangian; penalty method; domain decomposition; Nitsche mortaring; finite elements
UR - http://eudml.org/doc/271158
ER -

References

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  9. [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). Zbl0804.49011
  10. [10] B. Riviére, Discontinuous Galerkin methods for solving elliptic and parabolic equations (SIAM Publ., 2008). doi: 10.1137/1.9780898717440 Zbl1153.65112
  11. [11] P. Le Tallec and T. Sassi, Domain decomposition with nonmatching grids: Augmented Lagrangian approach, Math. Comput. 64 (1995), 1367-1396. Zbl0849.65087
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  14. [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 Zbl0974.65105

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