Compatible L2 norm convergence of variable-step L1 scheme for the time-fractional MBE model with slope selection

The convergence of variable-step L1 scheme is studied for the time-fractional molecular beam epitaxy (MBE) model with slope selection. A novel asymptotically compatible L2 norm error estimate established under a convergence-solvability-stability (CSS)-consistent time-step constraint. CSS-consistent condition means that maximum step-size limit required same order to solvability and stability (in certain norms) as small interface parameter ??0+. To best our knowledge, it first time establish such nonlinear subdiffusion problems. backward Euler classical MBE fractional ??1?. Just can maintain physical properties equation, also preserve corresponding model, including volume conservation, variational energy dissipation law boundedness. Numerical experiments are presented support theoretical results.