Preconditioning Cell-centered finite difference equations on grids with local refinement} Ilya. D. Mishev Abstract We consider cell-centered finite difference discretizations with local refinement for nonsymmetric boundary value problems. Preconditioners with mesh independent convergence properties for corresponding matrices are constructed. %nonsymmetric boundary value discretized by finite difference schemes %on cell-centered grid with local refinement are constructed. The method is illustrated with numerical experiments.