On the time discrete approximation of the Brinkman–Forchheimer equations |
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Authors: | J Djoko Kamdem |
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Institution: | Department of Mathematics and Applied Mathematics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0002, South Africa |
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Abstract: | 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. |
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Keywords: | Brinkman– Forchheimer discrete Gronwall lemma monotone implicit Euler scheme |
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