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Analysis of some dispersion corrected numerical schemes for solution of the transport equation
Author(s) -
Van Genuchten Martinus T H.,
Gray William G.
Publication year - 1978
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.1620120302
Subject(s) - finite element method , mathematics , galerkin method , finite difference , basis function , convection–diffusion equation , dispersion (optics) , mathematical analysis , derivative (finance) , mixed finite element method , physics , financial economics , optics , economics , thermodynamics
In the last decade or so finite element techniques have been applied with increased frequency to contaminant transport problems. Whereas most of the attention has focused on finite element approximations of spatial derivatives, standard finite difference techniques are generally used for approximation of the time derivative. Such an approach yields a scheme which is at best second order correct in time. In this study several higher order approximations of the time derivative are developed and analyzed using a finite difference approximation, and Galerkin‐type finite element approximations in conjunction with several sets of basis functions. Results obtained with the different schemes exhibit significant improvements in the numerical solution of the convective‐dispersive equation.