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

0380465 - MÚ 2013 RIV SK eng C - Konferenční příspěvek (zahraniční konf.)
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]
Grant CEP: GA AV ČR(CZ) IAA100190803
Institucionální podpora: RVO:67985840
Klíčová slova: discrete maximum principle * finite element method * diffusion-convection-reaction problem
Kód oboru RIV: BA - Obecná matematika

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.
Trvalý link: http://hdl.handle.net/11104/0007471