The k-th(k=3,4,5)order backward differential formula(BDFk)is applied to de-velop the high order energy stable schemes for the molecular beam epitaxial model with slope selection.The numerical schemes are established b...The k-th(k=3,4,5)order backward differential formula(BDFk)is applied to de-velop the high order energy stable schemes for the molecular beam epitaxial model with slope selection.The numerical schemes are established by combining the convex splitting technique with the k-th order accurate Douglas-Dupont stabilization term in the form of Sτ^(k−1)Δ_(h)(Ф^(n)−Ф^(n−1)).With the help of the new constructed discrete gradient structure of the k-th order explicit extrapolation formula,the stabilized BDFk scheme is proved to pre-serve energy dissipation law at the discrete levels and unconditionally stable in the energy norm.By using the discrete orthogonal convolution kernels and the associated convolution embedding inequalities,the L^(2) norm error estimate is established under a weak constraint of time-step size.Numerical simulations are presented to demonstrate the accuracy and efficiency of the proposed numerical schemes.展开更多
文摘The k-th(k=3,4,5)order backward differential formula(BDFk)is applied to de-velop the high order energy stable schemes for the molecular beam epitaxial model with slope selection.The numerical schemes are established by combining the convex splitting technique with the k-th order accurate Douglas-Dupont stabilization term in the form of Sτ^(k−1)Δ_(h)(Ф^(n)−Ф^(n−1)).With the help of the new constructed discrete gradient structure of the k-th order explicit extrapolation formula,the stabilized BDFk scheme is proved to pre-serve energy dissipation law at the discrete levels and unconditionally stable in the energy norm.By using the discrete orthogonal convolution kernels and the associated convolution embedding inequalities,the L^(2) norm error estimate is established under a weak constraint of time-step size.Numerical simulations are presented to demonstrate the accuracy and efficiency of the proposed numerical schemes.
