@Article{JCM-41-2,
author = {Liao, Hong-Lin and Tao, Tang and Zhou, Tao},
title = {Discrete Energy Analysis of the Third-Order Variable-Step BDF Time-Stepping for Diffusion Equations},
journal = {Journal of Computational Mathematics},
year = {2023},
volume = {41},
number = {2},
pages = {325--344},
abstract = {<p style="text-align: justify;">This is one of our series works on discrete energy analysis of the variable-step BDF schemes. In this part, we present stability and convergence analysis of the third-order BDF (BDF3) schemes with variable steps for linear diffusion equations, see, e.g., [SIAM J. Numer. Anal., 58:2294-2314] and [Math. Comp., 90: 1207-1226] for our previous works on the BDF2 scheme. To this aim, we first build up a discrete gradient structure of the variable-step BDF3 formula under the condition that the adjacent step ratios are less than 1.4877, by which we can establish a discrete energy dissipation law. Mesh-robust stability and convergence analysis in the $L^2$ norm are then obtained. Here the mesh robustness means that the solution errors are well controlled by the maximum time-step size but independent of the adjacent time-step ratios. We also present numerical tests to support our theoretical results.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2207-m2022-0020},
url = {https://global-sci.com/article/84119/discrete-energy-analysis-of-the-third-order-variable-step-bdf-time-stepping-for-diffusion-equations}
}