A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation

This work concerns the use of the method of quasi-reversibility to solve the Cauchy problem for Laplace's equation. We describe a mixed formulation of the method and its relationship with a classical formulation. A discretized formulation using finite elements of class C⁰ is derived from the mixed formulation, and convergence of the solution of this discretized problem with noisy data to the exact solution is analysed. Finally, a simple numerical example is implemented in order to show the feasibility of the method.