Many PDEs (for example the Swift–Hohenberg equation and the the KdV equation) have a
variational structure. As a direct consequence of this structure we can deduce the existence of
properties such as dissipation and conservation laws, as well as the existence of (for example)
soliton solutions. A discrete variational derivative method exploits this variational structure when
discretising the PDE. In this talk I will use a modified equation analysis to show that the discrete
solution of such a method can be considered to be samples of a function which also satisfies a
modified variational principle. It is then possible to derive a series of novel conservation or
dissipation laws for this new function which mimic those of the original. I will show how these new
laws can be constructed and the various consequences of them. This will include the existence of
discrete soliton solutions of the KdV equation