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The exponential decay of the relative entropy associated to a fully discreteporous-medium equation in one space dimension is shown by means of a discreteBakry-Emery approach. The first ingredient of the proof is an abstract discreteBakry-Emery method, which states conditions on a sequence under which theexponential decay of the discrete entropy follows. The second ingredient is anew nonlinear summation-by-parts formula which is inspired by systematicintegration by parts developed by Matthes and the first author. Numericalsimulations illustrate the exponential decay of the entropy for various timeand space step sizes.

A discrete Bakry-Emery method and its application to the porous-medium equation