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On the time discrete approximation of the Brinkman–Forchheimer equations
Author(s) -
Kamdem J. Djoko
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1458
Subject(s) - mathematics , discretization , lemma (botany) , a priori and a posteriori , backward euler method , stability (learning theory) , gronwall's inequality , scheme (mathematics) , discrete time and continuous time , mathematical analysis , computer science , ecology , philosophy , statistics , poaceae , epistemology , machine learning , inequality , biology
In this work, we study the structural stability of the fully implicit Euler scheme for the Brinkman‐Forchheimer equations. More precisely, we consider the time discretization scheme of the unsteady Brinkman–Forchheimer equations, and we prove the existence of solutions. Moreover, we derive somebia priori estimates of the discrete in time solutions. Next, with the aid of the discrete Gronwall lemma, we show that the numerical solutions depend continuously on the Brinkman and the Forchheimer coefficient. Copyright © 2011 John Wiley & Sons, Ltd.