TVD scheme
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Note that a TVD scheme may not satisfy the entropy condition and hence can give incorrect solution. We have the following relationship between monotone, TVD and monotonicity preserving schemes, | Note that a TVD scheme may not satisfy the entropy condition and hence can give incorrect solution. We have the following relationship between monotone, TVD and monotonicity preserving schemes, | ||
| - | + | : [[Monotone scheme]] <math>\Longrightarrow</math> [[TVD scheme]] <math>\Longrightarrow</math> [[Monotonicity preserving scheme]] | |
==TVD condition: Incremental form== | ==TVD condition: Incremental form== | ||
==TVD condition: Viscosity form== | ==TVD condition: Viscosity form== | ||
Revision as of 04:41, 30 September 2005
A scheme is said to be TVD or Total Variation Diminishing if it does not increase the total variation of the solution, i.e.,
The total variation of a grid function is defined as
Note that a TVD scheme may not satisfy the entropy condition and hence can give incorrect solution. We have the following relationship between monotone, TVD and monotonicity preserving schemes,
- Monotone scheme
TVD scheme Monotonicity preserving scheme
