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On Taylor weak statement finite element methods for computational fluid dynamics
Author(s) -
Chaffin D. J.,
Baker A. J.
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.1650210402
Subject(s) - finite element method , taylor series , mathematics , mixed finite element method , galerkin method , finite volume method , extended finite element method , mathematical analysis , smoothed finite element method , boundary knot method , physics , mechanics , boundary element method , thermodynamics
A Taylor series augmentation of a weak statement (a ‘Taylor weak statement’ or ‘Taylor‐Galerkin’ method) is used to systematically reduce the dispersion error in a finite element approximation of the one‐dimensional transient advection equation. A frequency analysis is applied to determine the phase velocity of semi‐implicit linear, quadratic and cubic basis one‐dimensional finite element methods and of several comparative finite difference/finite volume algorithms. The finite element methods analysed include both Galerkin and Taylor weak statements. The frequency analysis is used to obtain an improved linear basis Taylor weak statement finite element algorithm. Solutions are reported for verification problems in one and two dimensions and are compared with finite volume solutions. The improved finite element algorithms have sufficient phase accuracy to achieve highly accurate linear transient solutions with little or no artificial diffusion.