The subject of the paper is the mesh independent convergence of the preconditioned conjugate gradient method for nonsymmetric elliptic problems. The approach of equivalent operators is involved, in which one uses the discretization of another suitable elliptic operator to construct a preconditioning matrix. By introducing the notion of compact-equivalent operators, it is proved that for a wide class of elliptic problems the superlinear convergence of the obtained PCGM is mesh independent under FEM discretizations, that is, the rate of superlinear convergence is given in the form of a sequence which is mesh independent and is determined only by the elliptic operators.
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