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Least‐squares characteristics and finite elements for advection–dispersion simulation
Author(s) -
Li C. W.
Publication year - 1990
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620290615
Subject(s) - advection , mathematics , finite element method , basis function , instability , numerical analysis , quadrature (astronomy) , mathematical analysis , basis (linear algebra) , physics , geometry , mechanics , optics , thermodynamics
Abstract The method of characteristics is combined with the method of least‐squares to solve the advection equation within the finite element framework. Fourier mode analysis shows that the numerical scheme is stable and accurate even when a linear basis function is used. However, in practical application, the involvement of using numerical quadrature in this method can produce numerical instability, depending on the value of the Courant number used. It is found that using C 1 continuous Hermitian cubic basis functions in the scheme reduces the degree of instability significantly and produces high accuracy. When being used in a split‐operator approach, this method combines naturally with the standard finite element method and results in a highly accurate scheme for advection–dispersion simulation.