Discrete energy analysis of the third-order variable-step BDF time-stepping for diffusion equations
Abstract
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 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.
Keywords
Cite
@article{arxiv.2204.12742,
title = {Discrete energy analysis of the third-order variable-step BDF time-stepping for diffusion equations},
author = {Hong-lin Liao and Tao Tang and Tao Zhou},
journal= {arXiv preprint arXiv:2204.12742},
year = {2024}
}
Comments
21 pages, 5 tables