Development and L2-analysis of a single-step characteristics finite difference scheme of second order in time for convection-diffusion problems

Hirofumi Notsu; Hongxing Rui; Masahisa Tabata

doi:10.1260/1748-3018.7.3.343

Development and L²-analysis of a single-step characteristics finite difference scheme of second order in time for convection-diffusion problems

Hirofumi Notsu, Hongxing Rui, Masahisa Tabata

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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	https://doi.org/10.1260/1748-3018.7.3.343
Publication status	Published - 2013 Sep 1

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

Access to Document

10.1260/1748-3018.7.3.343

Cite this

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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

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