A note on (2K+1)-point conservative monotone schemes
Huazhong Tang, Gerald Warnecke (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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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. This note will investigate this problem from a numerical point of view and show that a -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. ...