Author(s)

A. Bermiidez, L. Carpintero, M.C. Muniz & P. Quintela

Abstract

b Invited Paper An inverse problem related to the three-dimensional modelling of aluminium electrolytic cells A. Bermiidez", L. Carpintero", M.C. Muniz P. Quintela" "Department of Applied Mathematics, University of Santiago de Compostela, 15706 Santiago, Spain Department of Applied Mathematics, University of Vigo, Campus Marcosende, 36200 Vigo, Spain In this paper we study an inverse problem for a system of partial dif- ferential equations modelling the thermoelectric behaviour of an aluminium electrolytic cell. In a first part, we consider the direct three-dimensional thermoelectric problem which is a free boundary problem. We solve it by a fixed domain method for a given heat flux through the surface of the ledge, which is the interface between the solid and the liquid phases. We use pentahedral finite elements of six degrees of freedom to discretize both temperature and electric potential fields. In a second part, we consider an

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