Numerical method for solving a class of nonlinear elliptic inverse problems

This paper discusses a method to solve a family of nonlinear inverse problems with Cauchy conditions on a part of the boundary and no condition at all on another part. An iterative boundary element procedure is proposed. The scheme uses a dynamically estimated relaxation parameter on the under-specified boundary. Various types of convergence, boundary condition formulations and effects of added small perturbations into the input data are investigated. The numerical results show that the method produces a stable reasonably approximate solution.