ON THE NUMERICAL-SOLUTION OF SEMILINEAR PARABOLIC PROBLEMS IN MULTICOMPONENT STRUCTURES WITH VOLTERRA OPERATORS IN THE TRANSMISSION CONDITIONS AND IN THE BOUNDARY-CONDITIONS

This paper deals with a Rothe Galerkin finite element method for a class of parabolic problems in composite media. At the internal boundaries both the conormal derivative (heat flux) and the unknown function (temperature) may be discontinuous. Fairly general jumps are allowed, viz. being expressed in terms of Volterra operators acting on the unknown from both sides of the interfaces. Both the conductivity matrices and the source terms may be dependent on the unknown. Finally also the natural boundary conditions may include Volterra operators. Such imperfect (thermal) contact problems arise e.g. when modelling some heat transfer problems in buildings, see for instance [5] and [10].