A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving

Abstract

In the second part of this series, we use the Lagrange multiplier approach proposed in the first part [Comput. Methods Appl. Mech. Engr., 391 (2022), 114585] to construct efficient and accurate bound and/or mass preserving schemes for a class of semilinear 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 and also present ample numerical results to validate our approach.