An Energy Stable Filtered Backward Euler Scheme for the MBE Equation with Slope Selection

. As a promising strategy to adjust the order in the variable-order BDF algo-rithm, a time filtered backward Euler scheme is investigated for the molecular beam epitaxial equation with slope selection. The temporal second-order convergence in the L 2 norm is established under a convergence-solvability-stability (CSS)-consistent time-step constraint. The CSS-consistent condition means that the maximum step-size limit required for convergence is of the same order to that for solvability and stability (in certain norms) as the small interface parameter ε → 0 + . Similar to the backward Euler scheme, the time filtered backward Euler scheme preserves some physical properties of the original problem at the discrete levels, including the volume conservation, the energy dissipation law and L 2 norm boundedness. Numerical tests are included to support the theoretical results.