# Almost conserved

An almost conserved quantity is one whose derivative in time is not exactly zero, but is somehow small or low-order enough that the growth of the quantity can be controlled in time (perhaps by some variant of Gronwall's inequality).

A common way to create an almost conserved quantity is to start with a conservation law and insert a spatial or frequency weight.

The I-method relies heavily on the construction of an almost conserved quantity.

An important variant of an almost conserved quantity is a monotone quantity.