| Issue |
ESAIM: M2AN
Volume 53, Number 6, November-December 2019
|
|
|---|---|---|
| Page(s) | 2121 - 2159 | |
| DOI | https://doi.org/10.1051/m2an/2019049 | |
| Published online | 12 December 2019 | |
A posteriori error estimates for Darcy’s problem coupled with the heat equation
1
Sorbonne Universités, Université Paris-Diderot SPC, CNRS, Laboratoire Jacques-Louis Lions, LJLL 75005 Paris, France
2
Laboratoire de Mathétiques et Applications, Unité de recherche Mathématiques et Modélisation, Faculté des Sciences, Université Saint-Joseph, B.P 11-514 Riad El Solh, 1107 2050 Beyrouth, Liban
* Corresponding author: toni.sayah@usj.edu.lb
Received:
14
December
2018
Accepted:
27
June
2019
This work derives a posteriori error estimates, in two and three dimensions, for the heat equation coupled with Darcy’s law by a nonlinear viscosity depending on the temperature. We introduce two variational formulations and discretize them by finite element methods. We prove optimal a posteriori errors with two types of computable error indicators. The first one is linked to the linearization and the second one to the discretization. Then we prove upper and lower error bounds under regularity assumptions on the solutions. Finally, numerical computations are performed to show the effectiveness of the error indicators.
Mathematics Subject Classification: 65N15 / 74S05
Key words: Nonlinear Darcy’s equations / heat equation / finite element method / error indicators / residual a posteriori error estimates
© EDP Sciences, SMAI 2019
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