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

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.