Numerical methods for elliptic inverse problems

Abstract

Identifying physical parameters in elliptic boundary value problems is formulated as a constrained minimization problem using the output least squares method with the H ^l-regularization or the BV-regularization. The constrained minimization problem is then discretized by finite element methods and the discretization is shown to be convergent for both regularizations. The finite element minimization problem is proved to be equivalent to a sequence of unconstrained minimization problems and these unconstrained systems are solved by the Armijo-type algorithm. Numerical experiments are given which show that the algorithm is globally convergent and works well also for identifying highly discontinuous and oscillated parameters.

Keywords:

• Inverse BV problem
• unconstrained minimization problem
• finite element method
• Armijo algorithm

C.R. Categories::

• G.1.6
• G.1.8