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The group velocity of some numerical schemes
Author(s) -
Cathers B.,
O'Connor B. A.
Publication year - 1985
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.1650050302
Subject(s) - finite element method , mathematics , quadratic equation , finite difference , numerical analysis , phase portrait , group (periodic table) , finite difference method , mathematical analysis , computer simulation , geometry , physics , bifurcation , nonlinear system , statistics , quantum mechanics , thermodynamics
Abstract The performances of various numerical schemes used to model hyperbolic/parabolic equations have been studied by the calculation of their numerical group velocities. Numerical experiments conducted with one dimensional linear and quadratic Lagrangian finite elements with a Crank‐Nicolson finite differencing in time confirm the results of the analysis. The group velocity analysis supplements the well‐known amplitude and phase portraits introduced by Leendertse 1 and helps explain the occurrence and behaviour of numerical oscillations in both finite difference and finite element schemes.