A Galerkin finite element method for an optimal shape design semiconductor problem

An optimal shape design problem which appears in semiconductor device physics is transformed into an equivalent variational inequality one. The approximation is made by finite element methods. Optimal control methods are used to show the existence of a solution for the variational problem and for the approximate problem. For solving the discretized problem, an algorithm using Newtonʹs method for nonlinear algebraic systems is proposed. An example, together with experimental results, is presented.