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A popular and efficient discretization of evolutions involving the singular$p$-Laplace operator is based on a factorization of the differential operatorinto a linear part which is treated implicitly and a regularized singularfactor which is treated explicitly. It is shown that an unconditional energystability property for this semi-implicit time stepping strategy holds. Relatederror estimates depend critically on a required regularization parameter.Numerical experiments reveal reduced experimental convergence rates for smallerregularization parameters and thereby confirm that this dependence cannot beavoided in general.

Unconditional stability of semi-implicit discretizations of singular flows