Geodesic
On approximation of the Neumann problem by the penalty method
Applications of Mathematics, Tome 38 (1993) no. 6, pp. 459-469.

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We prove that penalization of constraints occuring in the linear elliptic Neumann problem yields directly the exact solution for an arbitrary set of penalty parameters. In this case there is a continuum of Lagrange's multipliers. The proposed penalty method is applied to calculate the magnetic field in the window of a transformer.
DOI : 10.21136/AM.1993.104568
Classification : 35J05, 35J25, 35J50, 35Q60, 65N30, 78-08, 78A25
Keywords: Neumann problem; penalty method; finite elements; magnetic field; linear elliptic Neumann problem; Lagrange’s multipliers 
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     author = {K\v{r}{\'\i}\v{z}ek, Michal},
     title = {On approximation of the {Neumann} problem by the penalty method},
     journal = {Applications of Mathematics},
     pages = {459--469},
     publisher = {mathdoc},
     volume = {38},
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     zbl = {0795.65075},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1993.104568/}
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Křížek, Michal. On approximation of the Neumann problem by the penalty method. Applications of Mathematics, Tome 38 (1993) no. 6, pp. 459-469. doi : 10.21136/AM.1993.104568. http://geodesic.mathdoc.fr/articles/10.21136/AM.1993.104568/

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