A new Lagrange multiplier approach for constructing structure-preserving schemes, II. bound preserving

Qing Cheng; Jie Shen

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arXiv · 2109.12479

A new Lagrange multiplier approach for constructing structure-preserving schemes, II. bound preserving

Qing Cheng·Jie Shen

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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.

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Qing Cheng, Jie Shen. 2021-09-26. A new Lagrange multiplier approach for constructing structure-preserving schemes, II. bound preserving. https://arxiv.org/abs/2109.12479

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