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

0380465 - MÚ 2013 RIV SK eng C - Conference Paper (international conference)
Vejchodský, Tomáš
Necessary and sufficient condition for the validity of the discrete maximum principle.
Algoritmy 2012. Bratislava: Slovak University of Technology and Comenius University, 2012 - (Handlovičová, A.; Mnarechová, Z.; Ševčovič, D.), s. 311-320. ISBN 978-80-227-3742-5.
[Algoritmy 2012. Vysoké Tatry - Podbanske (SK), 09.09.2012-14.09.2012]
R&D Projects: GA AV ČR(CZ) IAA100190803
Institutional support: RVO:67985840
Keywords : discrete maximum principle * finite element method * diffusion-convection-reaction problem
Subject RIV: BA - General Mathematics

In this contribution we present a necessary and sufficient 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.
Permanent Link: http://hdl.handle.net/11104/0007471