# TVD scheme

(Difference between revisions)
 Revision as of 04:05, 30 September 2005 (view source)Praveen (Talk | contribs)← Older edit Revision as of 04:41, 30 September 2005 (view source)Zxaar (Talk | contribs) Newer edit → Line 13: Line 13: 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]] $\Longrightarrow$ [[TVD scheme]] $\Longrightarrow$ [[Monotonicity preserving scheme]] + : [[Monotone scheme]] $\Longrightarrow$ [[TVD scheme]] $\Longrightarrow$ [[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.,

$TV(u^{n+1}) \le TV(u^n)$

The total variation of a grid function is defined as

$TV(u) = \sum_j | u_{j+1} - u_j|$

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 $\Longrightarrow$ TVD scheme $\Longrightarrow$ Monotonicity preserving scheme