In this article,a level-set approach for solving nonlinear elliptic Cauchy problems with piecewise constant solutions is proposed,which allows the definition of a Tikhonov functional on a space of level-set functions....In this article,a level-set approach for solving nonlinear elliptic Cauchy problems with piecewise constant solutions is proposed,which allows the definition of a Tikhonov functional on a space of level-set functions.We provide convergence analysis for the Tikhonov approach,including stability and convergence results.Moreover,a numerical investigation of the proposed Tikhonov regularization method is presented.Newton-type methods are used for the solution of the optimality systems,which can be interpreted as stabilized versions of algorithms in a previous work and yield a substantial improvement in performance.The whole approach is focused on three dimensional models,better suited for real life applications.展开更多
文摘In this article,a level-set approach for solving nonlinear elliptic Cauchy problems with piecewise constant solutions is proposed,which allows the definition of a Tikhonov functional on a space of level-set functions.We provide convergence analysis for the Tikhonov approach,including stability and convergence results.Moreover,a numerical investigation of the proposed Tikhonov regularization method is presented.Newton-type methods are used for the solution of the optimality systems,which can be interpreted as stabilized versions of algorithms in a previous work and yield a substantial improvement in performance.The whole approach is focused on three dimensional models,better suited for real life applications.
