  In this paper we study the inverse problem of identifying the diffusion
matrix in an elliptic PDE from measurements. The convex energy functional
method with Tikhonov regularization is applied to tackle this problem. For the
discretization we use the variational discretization concept, where the PDE is
discretized with piecewise linear, continuous finite elements. We show the
convergence of approximations. Using a suitable source condition, we prove an
error bound for discrete solutions. For the numerical solution we propose a
gradient-projection algorithm and prove the strong convergence of its iterates
to a solution of the identification problem. Finally, we present a numerical
experiment which illustrates our theoretical results.
