Ito, K.; Kroller, M.; Kunisch, K. A numerical study of an augmented Lagrangian method for the estimation of parameters in elliptic systems. (English) Zbl 0728.65100 SIAM J. Sci. Stat. Comput. 12, No. 4, 884-910 (1991). 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. Reviewer: R.Redlinger (Karlsruhe) Cited in 8 Documents MSC: 65Z05 Applications to the sciences 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35R30 Inverse problems for PDEs Keywords:parameter estimation; augmented Lagrangian method; inverse problem; equation-error technique; output least squares method; elliptic equation PDF BibTeX XML Cite \textit{K. Ito} et al., SIAM J. Sci. Stat. Comput. 12, No. 4, 884--910 (1991; Zbl 0728.65100) Full Text: DOI OpenURL