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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MR Zbl
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.
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 
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
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