Necessary and sufficient condition for the validity of the discrete maximum principle

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Tomáš Vejchodský

Abstract

In this contribution we present a necessary and su±cient condition for the validity of the discrete maximum principle for one-dimensional elliptic diffusion-convection reaction problems discretized by the finite element method. The condition limits the size of individual mesh elements. This is an extraordinary result in this field, because similar mesh conditions known so far are sufficient only. 

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VEJCHODSKÝ, Tomáš. Necessary and sufficient condition for the validity of the discrete maximum principle. Proceedings of the Conference Algoritmy, [S.l.], p. 311-320, nov. 2015. Available at: <http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/342>. Date accessed: 23 oct. 2017.
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