  We design and analyze an iterative two-grid algorithm for the finite element
discretizations of strongly nonlinear elliptic boundary value problems in this
paper. We propose an iterative two-grid algorithm, in which a nonlinear problem
is first solved on the coarse space, and then a symmetric positive definite
problem is solved on the fine space. The innovation of this paper lies in the
establishment of a first convergence analysis, which requires simultaneous
estimation of four interconnected error estimates. We also present some
numerical experiments to confirm the efficiency of the proposed algorithm.
