关于为何通过简单后验截断强制执行离散最大值原理是一个好主意的注释
A Note on why Enforcing Discrete Maximum Principles by a simple a Posteriori Cutoff is a Good Idea
AI总结：
本文提出通过简单后验截断强制执行离散最大值原理，并证明该方法能在自然能量范数下改善逼近精度，适用于多种逼近方法且无几何限制。
摘要：
在偏微分方程逼近中，离散最大值原理对于保持物理模型的定性性质至关重要。本文通过执行简单截断来强制执行离散最大值原理。我们证明，对于许多问题，这种后验过程甚至能改善自然能量范数下的逼近。结果适用于多种不同类型的逼近，包括协调高阶和$hp$-有限元。此外，在有限元逼近的情况下，对域的分割没有几何限制。
英文摘要：
Discrete maximum principles in the approximation of partial differential equations are crucial for the preservation of qualitative properties of physical models. In this work we enforce the discrete maximum principle by performing a simple cutoff. We show that for many problems this a posteriori procedure even improves the approximation in the natural energy norm. The results apply to many different kinds of approximations including conforming higher order and $hp$-finite elements. Moreover in the case of finite element approximations there is no geometrical restriction on the partition of the domain.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
