Abstract
A new finite difference scheme based on the method of characteristics is presented for convection-diffusion problems. The scheme is of single-step and second order in time, and the matrix of the derived system of linear equations is symmetric. Since it is a finite difference scheme, we can get rid of numerical integration which may cause some instability in the characteristics finite element method. An optimal error estimate is proved in the framework of the discrete L2-theory. Numerical results are shown to recognize the convergence order and advantages of the scheme.
| Original language | English |
|---|---|
| Pages (from-to) | 343-380 |
| Number of pages | 38 |
| Journal | Journal of Algorithms and Computational Technology |
| Volume | 7 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2013 Sep 1 |
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Keywords
- Discrete L-Analysis
- Finite difference method
- Second order in time
- The method of characteristics
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics
Cite this
Development and L2-analysis of a single-step characteristics finite difference scheme of second order in time for convection-diffusion problems. / Notsu, Hirofumi; Rui, Hongxing; Tabata, Masahisa.
In: Journal of Algorithms and Computational Technology, Vol. 7, No. 3, 01.09.2013, p. 343-380.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Development and L2-analysis of a single-step characteristics finite difference scheme of second order in time for convection-diffusion problems
AU - Notsu, Hirofumi
AU - Rui, Hongxing
AU - Tabata, Masahisa
PY - 2013/9/1
Y1 - 2013/9/1
N2 - A new finite difference scheme based on the method of characteristics is presented for convection-diffusion problems. The scheme is of single-step and second order in time, and the matrix of the derived system of linear equations is symmetric. Since it is a finite difference scheme, we can get rid of numerical integration which may cause some instability in the characteristics finite element method. An optimal error estimate is proved in the framework of the discrete L2-theory. Numerical results are shown to recognize the convergence order and advantages of the scheme.
AB - A new finite difference scheme based on the method of characteristics is presented for convection-diffusion problems. The scheme is of single-step and second order in time, and the matrix of the derived system of linear equations is symmetric. Since it is a finite difference scheme, we can get rid of numerical integration which may cause some instability in the characteristics finite element method. An optimal error estimate is proved in the framework of the discrete L2-theory. Numerical results are shown to recognize the convergence order and advantages of the scheme.
KW - Discrete L-Analysis
KW - Finite difference method
KW - Second order in time
KW - The method of characteristics
UR - http://www.scopus.com/inward/record.url?scp=84883196833&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84883196833&partnerID=8YFLogxK
U2 - 10.1260/1748-3018.7.3.343
DO - 10.1260/1748-3018.7.3.343
M3 - Article
AN - SCOPUS:84883196833
VL - 7
SP - 343
EP - 380
JO - Journal of Algorithms and Computational Technology
JF - Journal of Algorithms and Computational Technology
SN - 1748-3018
IS - 3
ER -