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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 operator into a linear part which is treated implicitly and a regularized singular factor which is treated explicitly. It is shown that an unconditional energy stability property for this semi-implicit time stepping strategy holds. Related error estimates depend critically on a required regularization parameter. Numerical experiments reveal reduced experimental convergence rates for smaller regularization parameters and thereby confirm that this dependence cannot be avoided in general.

Unconditional Stability of Semi-Implicit Discretizations of Singular Flows