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Křížek, Michal

On approximation of the Neumann problem by the penalty method. (English) Zbl 0795.65075

Appl. Math., Praha 38, No. 6, 459-469 (1993).
Author’s summary: We prove that penalization of constraints occurring 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.
Reviewer: J.D.P.Donnelly (Oxford)

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
78A25 Electromagnetic theory (general)
35Q60 PDEs in connection with optics and electromagnetic theory

Keywords:

linear elliptic Neumann problem; Lagrange’s multipliers; penalty method; magnetic field
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\textit{M. Křížek}, Appl. Math., Praha 38, No. 6, 459--469 (1993; Zbl 0795.65075)
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