Variational method for multiple parameter identification in elliptic PDEs
This work addresses the challenging inverse problem of multiple parameter identification in elliptic PDEs, which is important for applications like medical imaging and geophysics, but the approach is incremental as it extends existing variational frameworks.
The paper proposes a variational method with Tikhonov regularization to simultaneously identify the diffusion matrix, source term, boundary condition, and state in an elliptic PDE from weaker measurement data, proving convergence and error bounds via finite element discretization.
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.