Nonlinearity identification in divergence type elliptic boundary value problems

The identification of the nonlinearity a :Rd →Rd in the equation −div a(∇y) = f in Ω, y =0 on∂Ω, is done in terms of one observation y0 ∈ L2(Ω), in a least square sense, by minimizing Ω |y −y0|2 dx. Here Ω is a bounded domain in Rd with smooth boundary ∂Ω, f ∈ L2(Ω), and a is Lipschitz continuous and strongly elliptic. Numerical simulations and an algorithm based on a splitting method for the one-dimensional case are presented. © 2007 Elsevier Inc. All rights reserved