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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. 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 -point monotone scheme may give an oscillatory solution even though...
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.
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