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-...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 stepsize limit required for convergence is of the same order to that for solvability and stability(in certain norms)as the small interface parameterε→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.展开更多
基金Supported by NSFC(12171376,2020-JCJQ-ZD-029)Natural Science Foundation of Hubei Province(2019CFA007)the Fundamental Research Funds for the Central Universities(2042021kf0050)。
基金The work of H.-L.Liao is supported by NSF of China(Grant No.12071216)。
文摘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 stepsize limit required for convergence is of the same order to that for solvability and stability(in certain norms)as the small interface parameterε→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.
