Penalties, Lagrange multipliers and Nitsche mortaring
Christian Grossmann
Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 30 (2010), p. 205-220 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:271158 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1120,
     author = {Christian Grossmann},
     title = {Penalties, Lagrange multipliers and Nitsche mortaring},
     journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
     volume = {30},
     year = {2010},
     pages = {205-220},
     zbl = {1217.65122},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1120}
}

Christian Grossmann. Penalties, Lagrange multipliers and Nitsche mortaring. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 30 (2010) pp. 205-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1120/

[000] [1] R.A. Adams, Sobolev spaces (Academic Press, Inc., 1975).

[001] [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 | Zbl 1047.65099

[002] [3] P.G. Ciarlet, The finite element method for elliptic problems (North-Holland Publ. Co., Amsterdam 1978). | Zbl 0383.65058

[003] [4] L.C. Evans, Partial differential equations (AMS Publ. Providence, 1998).

[004] [5] C. Grossmann, Dualität und Strafmethoden bei elliptischen Differentialgleichungen, Z. Angew. Math. Mech. 64 (1984), 111-121. doi: 10.1002/zamm.19840640206 | Zbl 0537.49019

[005] [6] C. Grossmann and A. Kaplan, Strafmethoden und modifizierte Lagrange Funktionen in der nichtlinearen Optimierung (Teubner, 1979). | Zbl 0425.65035

[006] [7] C. Grossmann, H.-G. Roos and M. Stynes, Numerical treatment of partial differential equations (Springer, Berlin, 2007). | Zbl 1180.65147

[007] [8] K. Ito and K. Kunisch, Lagrange multiplier approach to variational problems and applications (SIAM Publ., 2008). doi: 10.1137/1.9780898718614 | Zbl 1156.49002

[008] [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). | Zbl 0804.49011

[009] [10] B. Riviére, Discontinuous Galerkin methods for solving elliptic and parabolic equations (SIAM Publ., 2008). doi: 10.1137/1.9780898717440 | Zbl 1153.65112

[010] [11] P. Le Tallec and T. Sassi, Domain decomposition with nonmatching grids: Augmented Lagrangian approach, Math. Comput. 64 (1995), 1367-1396. | Zbl 0849.65087

[011] [12] A. Toselli and O. Widlund, Domain decomposition methods - algorithms and theory (Springer, 2005). | Zbl 1069.65138

[012] [13] F. Tröltzsch, Optimale Steuerung partieller Differentialgleichungen. Theorie, Verfahren und Anwendungen (Vieweg, Wiesbaden, 2005).

[013] [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 | Zbl 0974.65105