A note on (2K+1)-point conservative monotone schemes
LMAM, School of Mathematical Sciences, Peking University,
Beijing 100871, PR China,
2 Institüt für Analysis und Numerik, Otto–von–Guericke Universität Magdeburg, 39106 Magdeburg, Germany, Gerald.Warnecke@mathematik.uni-magdeburg.de.
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.
Mathematics Subject Classification: 35L65 / 65M06 / 65M10
Key words: Hyperbolic conservation laws / finite difference scheme / monotone scheme / convergence / oscillation.
© EDP Sciences, SMAI, 2004