A high-order finite difference discretization strategy based on extrapolation for convection diffusion equations

Haiwei Sun, Jun Zhang

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

Abstract

We propose a new high-order finite difference discretization strategy, which is based on the Richardson extrapolation technique and an operator interpolation scheme, to solve convection diffusion equations. For a particular implementation, we solve a fine grid equation and a coarse grid equation by using a fourth-order compact difference scheme. Then we combine the two approximate solutions and use the Richardson extrapolation to compute a sixth-order accuracy coarse grid solution. A sixth-order accuracy fine grid solution is obtained by interpolating the sixth-order coarse grid solution using an operator interpolation scheme. Numerical results are presented to demonstrate the accuracy and efficacy of the proposed finite difference discretization strategy, compared to the sixth-order combined compact difference (CCD) scheme, and the standard fourth-order compact difference (FOC) scheme.

Original languageEnglish
Pages (from-to)18-32
Number of pages15
JournalNumerical Methods for Partial Differential Equations
Volume20
Issue number1
DOIs
StatePublished - Jan 2004

Keywords

  • CCD scheme
  • Compact difference scheme
  • Convection diffusion equation
  • Richardson extrapolation

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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