## Numerical Solution of Multicomponent Alloy Solidification by Multi-Grid Techniques.

Please always quote using this URN: urn:nbn:de:0297-zib-285
• The solidification of an $N$-component alloy is described by an initial boundary value problem for a system of degenerate parabolic equations modelling heat conduction and mass diffusion. Discretizing implicitly in time and by piecewise linear finite elements in the space variables, at each time step the solution of a system of quasivariational inequalities is required. For the numerical solution of that system, a multi-grid algorithm is developed by making use of game theoretic concepts and duality arguments from convex analysis. Finally, the efficiency of the algorithm is demonstrated by displaying numerical results for a ternary alloy.