Superlinearly convergent CG methods via equivalent preconditioning for nonsymmetric elliptic operators

Summary. The convergence of the conjugate gradient method is studied for preconditioned linear operator equations with nonsymmetric normal operators, with focus on elliptic convection-diffusion operators in Sobolev space. Superlinear convergence is proved first for equations whose preconditioned form is a compact perturbation of the identity in a Hilbert space. Then the same convergence result is verified for elliptic convection-diffusion equations using different preconditioning operators. The convergence factor involves the eigenvalues of the corresponding operators, for which an estimate is also given. The above results enable us to verify the mesh independence of the superlinear convergence estimates for suitable finite element discretizations of the convection-diffusion problems.Mathematics Subject Classification (2000): 65J10, 65F10, 65N15The second author was supported by the Hungarian Research Grant OTKA No. T. 043765.Dedicated to David M. Young on the occasion of his 80th birthday.