Implicit-explicit BDF $k$ SAV schemes for general dissipative systems and their error analysis
Numerical Analysis
2022-03-09 v1 Numerical Analysis
Abstract
We construct efficient implicit-explicit BDF scalar auxiliary variable (SAV) schemes for general dissipative systems. We show that these schemes are unconditionally stable, and lead to a uniform bound of the numerical solution in the norm based on the principal linear operator in the energy. Based on this uniform bound, we carry out a rigorous error analysis for the th-order SAV schemes in a unified form for a class of typical Allen-Cahn type and Cahn-Hilliard type equations. We also present numerical results confirming our theoretical convergence rates.
Cite
@article{arxiv.2103.06344,
title = {Implicit-explicit BDF $k$ SAV schemes for general dissipative systems and their error analysis},
author = {Fukeng Huang and Jie Shen},
journal= {arXiv preprint arXiv:2103.06344},
year = {2022}
}