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Development of a two‐dimensional finite element model for pure advective equation
Author(s) -
Sheu Tony W. H.,
Lee P. H.
Publication year - 2004
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10091
Subject(s) - discontinuity (linguistics) , mathematics , classification of discontinuities , finite element method , monotone polygon , mathematical analysis , galerkin method , partial differential equation , convection–diffusion equation , advection , matrix (chemical analysis) , geometry , physics , materials science , composite material , thermodynamics
This article deals with a six‐parameter flux corrected transport (FCT) Taylor Galerkin finite element model for solving the pure convection equation that admits discontinuities. Modified equation analysis is conducted to optimize the scheme accuracy in the smooth flow. In the presence of discontinuity, the introduced free parameters are further controlled to yield a slower group velocity ahead of the discontinuity using the group velocity theory. In contrast, free parameters that result in a faster group velocity than the analytic phase velocity are chosen to reduce postdiscontinuity oscillations. The success in employing the FCT technique of Zalesak is to obtain a monotone solution and we apply the M‐matrix theory to achieve the goal. To validate the proposed finite element model, analytic tests, which are amenable to smooth as well as sharply varying solutions, are conducted. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 302–326, 2004