# A note on $(\mathsf{2}\U0001d5aa+\mathsf{1})$-point conservative monotone schemes

Huazhong Tang; Gerald Warnecke

- Volume: 38, Issue: 2, page 345-357
- ISSN: 0764-583X

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topTang, Huazhong, and Warnecke, Gerald. "A note on $\sf (2K+1)$-point conservative monotone schemes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.2 (2004): 345-357. <http://eudml.org/doc/244919>.

@article{Tang2004,

abstract = {First–order accurate monotone conservative schemes have good convergence and stability properties, and thus play a very important role in designing modern high resolution shock-capturing schemes. Do the monotone difference approximations always give a good numerical solution in sense of monotonicity preservation or suppression of oscillations? This note will investigate this problem from a numerical point of view and show that a $(2K+1)$-point monotone scheme may give an oscillatory solution even though the approximate solution is total variation diminishing, and satisfies maximum principle as well as discrete entropy inequality.},

author = {Tang, Huazhong, Warnecke, Gerald},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {hyperbolic conservation laws; finite difference scheme; monotone scheme; convergence; oscillation; numerical examples; monotone conservative schemes; stability properties; shock-capturing schemes; monotonicity preservation; suppression of oscillations; oscillatory solution; total variation diminishing; satisfies maximum principle},

language = {eng},

number = {2},

pages = {345-357},

publisher = {EDP-Sciences},

title = {A note on $\sf (2K+1)$-point conservative monotone schemes},

url = {http://eudml.org/doc/244919},

volume = {38},

year = {2004},

}

TY - JOUR

AU - Tang, Huazhong

AU - Warnecke, Gerald

TI - A note on $\sf (2K+1)$-point conservative monotone schemes

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2004

PB - EDP-Sciences

VL - 38

IS - 2

SP - 345

EP - 357

AB - First–order accurate monotone conservative schemes have good convergence and stability properties, and thus play a very important role in designing modern high resolution shock-capturing schemes. Do the monotone difference approximations always give a good numerical solution in sense of monotonicity preservation or suppression of oscillations? This note will investigate this problem from a numerical point of view and show that a $(2K+1)$-point monotone scheme may give an oscillatory solution even though the approximate solution is total variation diminishing, and satisfies maximum principle as well as discrete entropy inequality.

LA - eng

KW - hyperbolic conservation laws; finite difference scheme; monotone scheme; convergence; oscillation; numerical examples; monotone conservative schemes; stability properties; shock-capturing schemes; monotonicity preservation; suppression of oscillations; oscillatory solution; total variation diminishing; satisfies maximum principle

UR - http://eudml.org/doc/244919

ER -

## References

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