| Abstract: | As a promising strategy to adjust the order in the variable-order BDF algorithm, 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. |
