%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 }