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Analysis of finite element schemes for convection‐type problems
Author(s) -
Comini Gianni,
Manzan Marco,
ino Carlo
Publication year - 1995
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.1650200603
Subject(s) - galerkin method , finite element method , mathematics , convection–diffusion equation , transient (computer programming) , equivalence (formal languages) , mathematical analysis , advection , truncation (statistics) , steady state (chemistry) , physics , computer science , statistics , discrete mathematics , thermodynamics , operating system , chemistry
Various finite element schemes of the Bubnov–Galerkin and Taylor–Galerkin types are analysed to obtain the expressions of truncation errors. This way, dispersion errors in the transient, and diffusion errors both in the transient and in the steady state, are identified. Then, with reference to the transient advection–diffusion equation, stability limits are determined by means of a general von Neumann procedure. Finally, the operational equivalence between Taylor–Galerkin methods, utilized for pseudo‐transient calculations, and Petrov–Galerkin methods, derived for the steady state forms of the advection–diffusion equation, is illustrated. Theoretical conclusions are supported by the results of numerical experiments.