Abstract
The utility of the finite-element Galerkin technique in advection-diffusion flow problems is examined by comparison with several finite-difference schemes in one dimension. The calculations show that for relatively coarse grids, finite-element solutions are either comparable to or significantly better than those obtained from the finite-difference schemes considered. For advection-dominated flows, the superiority of the finite-element technique is attributed to spatial coupling of time-derivative terms inherent in the Galerkin discretization. This procedure, absent from conventional finite-difference schemes, leads to very accurate phase properties for the approximate solution even when coarse grids are used. A two-dimensional analogue of the advection-diffusion problem further illustrates the advantages and accuracy of the finite-element method in conjunction with the use of isoparametric elements.
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