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.
翻译:在本系列的第二部分,我们使用第一部分中提议的拉格朗梯乘数法,为一类半线性和准线性抛物线性方程制定高效和准确的约束和/或大规模保护计划。我们在一般情况下建立稳定结果,并对带有多光谱分解于空间的第二等级分解保护计划进行误差分析。我们采用一些典型的保有约束和/或质量的PDE方法,同时也为验证我们的方法提供了充分的数字结果。