Numerical approach of temperature distribution in a free boundary model for polythermal ice sheets

A numerical method for solving the thermal subproblem appearing in the mode lization of polythermal ice sheets is described. This thermal problem mainl y involves three nonlinearities: a reaction term due to the viscous dissipa tion, a Signorini boundary condition associated to the geothermic flux and an enthalpy term issued from the two phase Stefan formulation of the polyth ermal regime. The stationary temperature is obtained as the limit of an evo lutive problem which is discretized in time with an upwind characteristics scheme and in space with finite elements. The nonlinearities are solved eit her by Newton-Raphson method or by duality techniques applied to maximal mo notone operators. The application of the algorithms provides the dimensionl ess temperature distribution approximation and allows to identify the cold and temperate ice regions.