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On the time discrete approximation of the Brinkman–Forchheimer equations

✍ Scribed by J. Djoko Kamdem

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
195 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by J. Banasiak

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 some a 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.

📜 SIMILAR VOLUMES

Existence of global attractors for the t
Existence of global attractors for the three-dimensional Brinkman–Forchheimer equation
✍ Bixiang Wang; Siyu Lin 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 132 KB

## Abstract In this paper, we investigate the asymptotic behavior of solutions of the three‐dimensional Brinkman–Forchheimer equation. We first prove the existence and uniqueness of solutions of the equation in __L__^2^, and then show that the equation has a global attractor in __H__^2^ when the ex