Numerical approximation of free boundary problem by variational inequalities - Application to semiconductor devices

In this paper we treat problem arasing in sermiconductor theory from a mathematical and numerical point of view, in particular we consider a boundary value problem with unknown interfaces arising by the determination of the depletion layer in the most basic semiconductor device namely the p-n junction diode. We present the numerical approximation of free boundary problem with double obstacle treated with quasi-variational inequalities. We deal with the L-infinity convergence of the standard finite element approximation of the system of quasi-variational inequalities.