Abstract: In this paper, a two-level method for resolving the nonlinearity in finite
element approximation of the stationary conduction-convection problems is presented. The two-level method involves solving
one small, nonlinear coarse mesh system, one Oseen problem on the fine mesh and one linear correction problem on the coarse mesh. Meanwhile, the existence and convergence of approximate solutions are shown.

Key words: Conduction-convection problems, Two-level method with backtracking,
Mixed element method, Error estimate