A new Lagrange multiplier approach for constructing structure-preserving schemes, II. bound preserving
Numerical Analysis
2021-10-28 v2 Numerical Analysis
Abstract
In the second part of this series, we use the Lagrange multiplier approach proposed in the first part \cite{CheS21} to construct efficient and accurate bound and/or mass preserving schemes for a class of semi-linear and quasi-linear parabolic equations. We establish stability results under a general setting, and carry out an error analysis for a second-order bound preserving scheme with a hybrid spectral discretization in space. We apply our approach to several typical PDEs which preserve bound and/or mass, also present ample numerical results to validate our approach.
Keywords
Cite
@article{arxiv.2109.12479,
title = {A new Lagrange multiplier approach for constructing structure-preserving schemes, II. bound preserving},
author = {Qing Cheng and Jie Shen},
journal= {arXiv preprint arXiv:2109.12479},
year = {2021}
}