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

Ito, K.; Kroller, M.; Kunisch, K.

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)

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