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
Inria de Paris, INSMI - Institut National des Sciences Mathématiques et de leurs Interactions, LJLL - Laboratoire Jacques-Louis Lions
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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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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