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Finite element method for Darcy's problem coupled with the heat equation

Christine Bernardi 1 Séréna Dib 2, 1 Vivette Girault 1 Frédéric Hecht 3, 1 François Murat 1 Toni Sayah 2
3 ALPINES - Algorithms and parallel tools for integrated numerical simulations
LJLL - Laboratoire Jacques-Louis Lions, INSMI - Institut National des Sciences Mathématiques et de leurs Interactions, Inria de Paris
Abstract : In this article, we study theoretically and numerically the heat equation coupled with Darcy's law by a nonlinear viscosity depending on the temperature. We establish existence and uniqueness of the exact solution by using a Galerkin method. We propose and analyze two numerical schemes based on finite element methods. An optimal a priori error estimate is then derived for each numerical scheme. Numerical experiments are presented that confirm the theoretical accuracy of the discretization.
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Submitted on : Wednesday, December 14, 2016 - 3:26:29 PM
Last modification on : Friday, March 27, 2020 - 3:35:05 AM
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  • HAL Id : hal-01416505, version 1


Christine Bernardi, Séréna Dib, Vivette Girault, Frédéric Hecht, François Murat, et al.. Finite element method for Darcy's problem coupled with the heat equation. 2016. ⟨hal-01416505⟩



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