The authors consider the inverse problem for the boundary vlaue problem (BVP) \[ -\nabla(q\nabla u)= f \quad \text{in} \quad\Omega \subset \mathbb R^{d} \] with the Dirichlet and Neumann conditions, respectively, of the form \[ u= g_{2}\quad\text{on}\quad\Gamma:= \partial \Omega, \quad q\frac{\partial u}{\partial\nu}=g_{1}\quad\text{on}\quad\Gamma. \] The inverse problem consists in computing the coefficient \(q\), then the function \(f\) is given. This problem is nonlinear and ill-posed. Using the Tikhonov regularization principle and linear finite element method for the BVP \[ -\nabla(q^{+}\nabla u)= f \quad\text{in}\quad\Omega, \qquad q\frac{\partial u}{\partial\nu}=g_{1}\quad\text{on}\quad \Gamma, \int_{\Omega}udx=0, \] an iterative algorithm to determine the parameter \(q\) is constructed. Some numerical results are given to illustrate this method.