- Journal Home
- Volume 43 - 2025
- Volume 42 - 2024
- Volume 41 - 2023
- Volume 40 - 2022
- Volume 39 - 2021
- Volume 38 - 2020
- Volume 37 - 2019
- Volume 36 - 2018
- Volume 35 - 2017
- Volume 34 - 2016
- Volume 33 - 2015
- Volume 32 - 2014
- Volume 31 - 2013
- Volume 30 - 2012
- Volume 29 - 2011
- Volume 28 - 2010
- Volume 27 - 2009
- Volume 26 - 2008
- Volume 25 - 2007
- Volume 24 - 2006
- Volume 23 - 2005
- Volume 22 - 2004
- Volume 21 - 2003
- Volume 20 - 2002
- Volume 19 - 2001
- Volume 18 - 2000
- Volume 17 - 1999
- Volume 16 - 1998
- Volume 15 - 1997
- Volume 14 - 1996
- Volume 13 - 1995
- Volume 12 - 1994
- Volume 11 - 1993
- Volume 10 - 1992
- Volume 9 - 1991
- Volume 8 - 1990
- Volume 7 - 1989
- Volume 6 - 1988
- Volume 5 - 1987
- Volume 4 - 1986
- Volume 3 - 1985
- Volume 2 - 1984
- Volume 1 - 1983
Cited by
- BibTex
- RIS
- TXT
This paper provides an analysis on the effects of exact and inexact integrations on stability, convergence, numerical diffusion, and numerical oscillations for the Eulerian-Lagrangian method (ELM). In the finite element ELM, when more accurate integrations are used for the right-hand-side, less numerical diffusion is introduced and better approximation is obtained. When linear interpolation is used for numerical integrations, the resulting ELM is shown to be unconditionally stable and of first-order accuracy. When Gauss quadrature is used, conditional stability and second-order accuracy are established under some mild constraints for the convection-diffusion problems. Finally, numerical experiments demonstrate that more accurate integrations lead to better approximation, and spatial adaptivity can substantially reduce numerical oscillations and smearing that often occur in the ELM when inexact numerical integrations are used.
}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1012-m3397}, url = {http://global-sci.org/intro/article_detail/jcm/8484.html} }This paper provides an analysis on the effects of exact and inexact integrations on stability, convergence, numerical diffusion, and numerical oscillations for the Eulerian-Lagrangian method (ELM). In the finite element ELM, when more accurate integrations are used for the right-hand-side, less numerical diffusion is introduced and better approximation is obtained. When linear interpolation is used for numerical integrations, the resulting ELM is shown to be unconditionally stable and of first-order accuracy. When Gauss quadrature is used, conditional stability and second-order accuracy are established under some mild constraints for the convection-diffusion problems. Finally, numerical experiments demonstrate that more accurate integrations lead to better approximation, and spatial adaptivity can substantially reduce numerical oscillations and smearing that often occur in the ELM when inexact numerical integrations are used.