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A note on why enforcing discrete maximum principles by a simple a posteriori cutoff is a good idea


Correspondence to: Christian Kreuzer, Faculty of Mathematics, Ruhr-Universität Bochum, Universitätsstrasse 150, D-44801 Bochum, Germany, (e-mail:


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. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 994–1002, 2014