An iterative scheme to compute numerical solutions to an over-determined boundary value problem

A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications

We propose a new iterative scheme to compute the numerical solution to an over-determined boundary value problem for a general quasilinear elliptic pde.The main idea is to repeatedly solve its linearization by using the quasi-reversibility method with a suitable carleman weight function.The convergence of the iteration is fast at an exponential rate without the need of an initial good guess.We apply this method to compute solutions to some general quasilinear elliptic equations and a large class of first-order first-order hamilton-jacobi equations.