We investigate the convergence rates for Tikhonov regularization of the problem of identifying ( 1

We investigate the convergence rates for total variation regularization of the problem of identifying (i) the coefficient q in the Neumann problem for the elliptic equation − div(q∇u) = f in , q∂u/∂n = g on ∂ , and (ii) the coefficient a in the Neumann problem for the elliptic equationWe regularize these problems by correspondingly minimizing the convex functionalsandover the admissible sets, where U (q) (U (a)) is the solution of the first (second) Neumann boundary value problem; ρ > 0 is the regularization parameter.Taking the solutions of these optimization problems as the regularized solutions to the corresponding identification problems, we obtain the convergence rates of them to a total variation-minimizing solution in the sense of the Bregman distance under relatively simple source conditions without the smallness requirement on the source functions.

In this paper we investigate the problem of identifying the conductivity in electrical impedance tomography from one boundary measurement. A variational method with total variation regularization is here proposed to tackle this problem. We discretize the PDE as well as the conductivity with piecewise linear, continuous finite elements. We prove the stability and convergence of this technique. For the numerical solution we propose a projected Armijo algorithm. Finally, a numerical experiment is presented to illustrate our theoretical results.

We investigate the convergence rates for Tikhonov regularization of the problem of simultaneously estimating the coefficients q and a in the Neumann problem for the elliptic equation −div(q∇u) + au = f in , q∂u/∂n = g on the boundaryWe regularize this problem by minimizing the strictly convex functional of (q, a)over the admissible set K , where ρ > 0 is the regularization parameter and (q * , a * ) is an a priori estimate of the true pair (q, a) which is identified, and consider the unique solution of these minimization problem as the regularized one to that of the inverse problem. We obtain the convergence rate O( √ δ), as δ → 0 and ρ ∼ δ, for the regularized solutions under the simple and weak source condition there is a function w * ∈ V * such that U (q † , a † )

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