Estimation of discontinuous parameters of elliptic partial differential equations by regularization for surface representations

In this paper we apply a new regularization method, regularization for surface representations to two-dimensional parameter estimation problems where the parameter is supposed to have jumps. This method is well-suited for ill-posed problems with discontinuous solutions. It is a generalization of the recently developed method, regularization for curve representations, which has been successfully applied to linear and nonlinear one-dimensional ill-posed problems. We prove convergence of the finite-dimensional Tikhonov regularized solutions and present some numerical results.