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Mathematical modelling of an electrolysis process. (English) Zbl 0704.35021
The paper is devoted to the mathematical and numerical study of a problem arising in the investigation of the electrolytical production of aluminium. The electrolytic process is described by the Poisson equation for the stream function to which we add nonlinear Newton boundary and transmission conditions representing turbulent flows in the boundary and anodes layers. The solvability is proved by the use of the monotone operator theory. The problem is discretized by conforming linear triangular elements and the solvability of the discrete problem and the convergence of approximate solutions to the exact solution is studied.
Reviewer: M.Feistauer

MSC:
35D05 Existence of generalized solutions of PDE (MSC2000)
35J65 Nonlinear boundary value problems for linear elliptic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76D99 Incompressible viscous fluids
76W05 Magnetohydrodynamics and electrohydrodynamics
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