On a certain class of one step temporal integration methods for standard dissipative continua

A class of isothermal dissipative continua being often referred to as “standard dissipative” is considered. The initial boundary value problem describing the behavior of these continua can be conveniently formulated in terms of a Helmholtz free energy functional, a dissipation functional, a power functional, and, possibly, a Lagrangian multiplier functional. In order to obtain (approximate) solutions for the initial boundary value problem, temporal and spatial discretization are necessary in most cases. In the present contribution, certain approaches for temporal discretization are discussed. In particular, different straightforward to apply first and second order accurate one step schemes are investigated; and the properties of these schemes are demonstrated by applying them to a diffusion problem.