Nonlinearity identification in divergence type elliptic boundary value problems

The identification of the nonlinearity a:Rd→Rd in the equation−diva(∇y)=finΩ,y=0on∂Ω, is done in terms of one observation y0∈L2(Ω)y0∈L2(Ω), in a least square sense, by minimizing∫Ω|y−y0|2dx. Here Ω   is a bounded domain in RdRd with smooth boundary ∂Ω  , f∈L2(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.