Variational method for multiple parameter identification in elliptic PDEs

In the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix, source term and boundary condition as well as the state in the Neumann boundary value problem for an elliptic partial differential equation (PDE) from a measurement data, which is weaker than required of the exact state. A variational method based on energy functions with Tikhonov regularization is here proposed to treat the identification problem. We discretize the PDE with the finite element method and prove the convergence as well as analyse error bounds of this approach.