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Non‐symmetric CG‐like schemes and the finite element solution of the advection–dispersion equation
Author(s) -
Peters Alexander
Publication year - 1993
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650171104
Subject(s) - mathematics , discretization , finite element method , advection , convergence (economics) , iterative method , linear system , mathematical analysis , generalized minimal residual method , dispersion (optics) , context (archaeology) , mathematical optimization , physics , paleontology , optics , biology , economics , thermodynamics , economic growth
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.