Alternating iteration and elliptic variational inequalities (Q1072351)

A free boundary problem is considered. Since the geometry of the domain is too complicated, the problem can not be formulated as a variational inequality. The method used to solve it is to consider two overlapping regions covering the domain and to formulate an ordinary boundary value problem on one region and a variational inequality for the ''free boundary part'' on the other region (which has ''good'' geometry). Hence an alternating iteration scheme is derived: the two problems are solved successively, their solutions being related on a common curve of the two regions. The sequence of iterates converges uniformly to a solution of the initial problem. An example is given which deals with a problem of filtration of a liquid through a porous medium that starts at a trapezoidal channel.