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

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

Year:    2023

Author:    Ying Zhao, Jiexin Wang, Hong-Lin Liao, Ying Zhao

Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 1 : pp. 165–181

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2022-0072

Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 1 : pp. 165–181

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    MBE model time filter energy dissipation law error estimate.

Author Details

Ying Zhao

Jiexin Wang

Hong-Lin Liao

Ying Zhao