A numerical study of an augmented Lagrangian method for the estimation of parameters in elliptic systems. (English) Zbl 0728.65100

The authors present an augmented Lagrangian formulation of the output least squares method for estimating numerically an unknown coefficient function q, appearing in a partial differential equation, from measurements of the solution u. Theoretical as well as implementation aspects of the proposed approach are discussed. To illustrate the method, the elliptic equation \(-div(q(x)\text{grad} u)=f\) in D, \(u=0\) on \(\partial D\), with f a given function and D the unit interval in 1 or 2 dimensions is treated in detail.


65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35R30 Inverse problems for PDEs
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