DOI: 10.1002/jcc.20200. Attaining exponential convergence for the flux error with second‐ and fourth‐order accurate finite‐difference equations. I. Presentation of the basic concept and application to a pure diffusion system

Attaining exponential convergence for the flux error with second‐ and fourth‐order accurate finite‐difference equations. I. Presentation of the basic concept and application to a pure diffusion system

10.1002/jcc.20200

Crossref journal-article

Wiley

Journal of Computational Chemistry (311)

Abstract

AbstractIt is a well‐known phenomenon called superconvergence in the mathematical literature that the error level of an integral quantity can be much smaller than the magnitude of the local errors involved in the computation of this quantity. When discretizing an integrated form of Fick's second law of diffusion the local errors reflect the accuracy of individual concentration points while the integral quantity has the physical meaning of the flux. This article demonstrates how an extraordinary fast exponential convergence towards zero can be achieved for the simulated flux error on the basis of finite–difference approximations that are only second‐order (Box 2 method) or fourth‐order (Box 4 method) accurate as far as the level of local errors is concerned. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 619–632, 2005

Bibliography

Rudolph, M. (2005). Attaining exponential convergence for the flux error with secondâ and fourthâorder accurate finiteâdifference equations. I. Presentation of the basic concept and application to a pure diffusion system. Journal of Computational Chemistry, 26(6), 619â632. Portico.

Authors 1

Manfred Rudolph (first)

References 28 Referenced 55

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Dates

Type	When
Created	20 years, 6 months ago (March 2, 2005, 10:48 a.m.)
Deposited	1 year, 10 months ago (Oct. 16, 2023, 11:52 p.m.)
Indexed	1 year, 3 months ago (June 2, 2024, 10:55 a.m.)
Issued	20 years, 6 months ago (March 2, 2005)
Published	20 years, 6 months ago (March 2, 2005)
Published Online	20 years, 6 months ago (March 2, 2005)
Published Print	20 years, 4 months ago (April 30, 2005)

Funders 0

None

BibTeX

@article{Rudolph_2005, title={Attaining exponential convergence for the flux error with second‐ and fourth‐order accurate finite‐difference equations. I. Presentation of the basic concept and application to a pure diffusion system}, volume={26}, ISSN={1096-987X}, url={http://dx.doi.org/10.1002/jcc.20200}, DOI={10.1002/jcc.20200}, number={6}, journal={Journal of Computational Chemistry}, publisher={Wiley}, author={Rudolph, Manfred}, year={2005}, month=mar, pages={619–632} }

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