Discrete gradient methods have an energy conservation law
Robert I. McLachlan G. R. W. Quispel
Discrete & Continuous Dynamical Systems - A 2014, 34(3): 1099-1104 doi: 10.3934/dcds.2014.34.1099
We show for a variety of classes of conservative PDEs that discrete gradient methods designed to have a conserved quantity (here called energy) also have a time-discrete conservation law. The discrete conservation law has the same conserved density as the continuous conservation law, while its flux is found by replacing all derivatives of the conserved density appearing in the continuous flux by discrete gradients.
keywords: Discrete conservation laws energy method. discrete gradient methods

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