Journal of Computational Physics
A piecewise constant level set method for elliptic inverse problems
Applied Numerical Mathematics
Iterative regularization for elliptic inverse problems
Computers & Mathematics with Applications
On the inverse problem of identifying Lamé coefficients in linear elasticity
Computers & Mathematics with Applications
Evolutionary Algorithm for Identifying Discontinuous Parameters of Inverse Problems
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part IV: ICCS 2007
SIAM Journal on Scientific Computing
A Regularization Parameter for Nonsmooth Tikhonov Regularization
SIAM Journal on Scientific Computing
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The identification of discontinuous parameters in elliptic systems is formulated as a constrained minimization problem combining the output least squares and the equation error method. The minimization problem is then proved to be equivalent to the saddle-point problem of an augmented Lagrangian. The finite element method is used to discretize the saddle-point problem, and the convergence of the discretization is also proved. Finally, an Uzawa algorithm is suggested for solving the discrete saddle-point problem and is shown to be globally convergent.