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Non-symmetric CG-like schems and the finite element solution of the advection-dispersion equation. (English) Zbl 0797.76043

Summary: Seven leading iterative methods for non-symmetric linear systems (GMRES, BCG, QMR, CGS, Bi-CGSTAB, TFQMR and CGNR) are compared in the specific context of solfing the advection-dispersion equation by a classic approach: The space derivatives are approximated by linear finite elements when an implicit scheme is used to integrate the time derivatives. Convergence formulae that predict the behaviour of the iterative methods as a function of the discretization parameters are developed and validated by experiments. It is shown that all methods converge nicely when the coefficient matrix of the linear system is close to normal and the finite element approximation of the advection- dispersion equation yields accurate results.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76R99 Diffusion and convection
65F10 Iterative numerical methods for linear systems

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