Non‐symmetric CG‐like schemes and the finite element solution of the advection–dispersion equation
Alexander Peters · International Journal for Numerical Methods in Fluids · 1993
Abstract 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 solving the advection–dispersion equation by a classic approach: The space derivatives are approximated by linear finite elements while an implicit scheme is used to integrate the time derivatives. Convergence formulas 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 coefficent matrix of the linear system is close to normal and the finite element approximation of the advection–dispersion equation yields accurate results.