= Total variation diminishing scheme
{title2=$\operatorname{TV}(TU)\leq\operatorname{TV}(U)$}
= TVD scheme
{c}
{synonym}
A translation-invariant conservative monotone update decreases discrete <total variation>. If $S$ is the one-cell shift, $TS=ST$, and <L1 contraction of a monotone conservative scheme> applied to $U,SU$ gives $\sum_j|(TU)_{j+1}-(TU)_j|\leq\sum_j|U_{j+1}-U_j|$. This prevents creation of new total variation, though it does not make every discontinuity sharply resolved.
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