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Numerical analysis of the motion of glass under external pressure

We give a mathematical model of the forming of a glass product in a mould under pressure. It turns out the the equations of motion are the Stokes equations. One part of the boundary is given, another part is free. The latter means that the velocity there comes from an external force, in particular from a piston that drives a moving part of the mould (the plunger) into the glass. This provides for an additional (kinematic) boundary condition. The complication here is that the movement of this piston on one hand and the counter force from the glass on the other are coupled. The equation of motion are the Stokes equations. The boundary condition couples these with the motion of the plunger, being an ordinary differential equation. It turns out that the resulting equation for the plunger velocity is stiff, so it should be solved by an implicit method. However, due to the afore mentioned coupling a straightforward implementation of such an implicit scheme is impossible. We give a solution to this problem.