A comparative study of certain finite-element and finite-difference methods in advection--diffusion simulations
R. Lee, P. Gresho, and R. Sani. Proc. Summer Computer Simulation Conference, page 37-42. Washington, D. C., (April 1976)
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.
%0 Conference Paper
%1 lee1976comparative
%A Lee, R. L.
%A Gresho, P. M.
%A Sani, R. L.
%B Proc. Summer Computer Simulation Conference
%C Washington, D. C.
%D 1976
%K 76m10-finite-element-methods-in-fluid-mechanics 76m20-finite-difference-methods-in-fluid-mechanics 76r05-forced-convection
%P 37-42
%T A comparative study of certain finite-element and finite-difference methods in advection--diffusion simulations
%U https://www.osti.gov/biblio/7184305
%X 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.
@inproceedings{lee1976comparative,
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.},
added-at = {2021-08-13T04:50:49.000+0200},
address = {Washington, D. C.},
author = {Lee, R. L. and Gresho, P. M. and Sani, R. L.},
biburl = {https://www.bibsonomy.org/bibtex/2e82fac23951446954b412903fbac79ad/gdmcbain},
booktitle = {Proc. Summer Computer Simulation Conference},
eventdate = {12 July 1976},
interhash = {054d2cc466f2434b722919ee306e54f2},
intrahash = {e82fac23951446954b412903fbac79ad},
keywords = {76m10-finite-element-methods-in-fluid-mechanics 76m20-finite-difference-methods-in-fluid-mechanics 76r05-forced-convection},
month = apr,
pages = {37-42},
timestamp = {2021-08-13T04:50:49.000+0200},
title = {A comparative study of certain finite-element and finite-difference methods in advection--diffusion simulations},
url = {https://www.osti.gov/biblio/7184305},
year = 1976
}