A Note on why Enforcing Discrete Maximum Principles by a simple a Posteriori Cutoff is a Good Idea

Abstract

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.

7 pages

References in corpus (2)

• The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and lubrication-type equations
• Convex Hull Property and Maximum Principle for Finite Element Minimisers of General Convex Functionals

Cited by in corpus (2)

• On enforcing maximum principles and achieving element-wise species balance for advection-diffusion-reaction equations under the finite element method
• On mesh restrictions to satisfy comparison principles, maximum principles, and the non-negative constraint: Recent developments and new results