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2. A posteriori error estimates for the time-dependent convection-diffusion-reaction equation coupled with the Darcy system

Author

Nancy Chalhoub, Rebecca El Zahlaniyeh, Toni Sayah, Pascal Omnes, Université Saint-Joseph de Beyrouth (USJ), Service de Thermo-hydraulique et de Mécanique des Fluides (STMF), Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Laboratoire Analyse, Géométrie et Applications (LAGA), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord

Subjects
a posteriori error estimates, Discretization, Applied Mathematics, Numerical analysis, finite element method, Space (mathematics), Backward Euler method, convection-diffusion-reaction equation, Finite element method, Darcy–Weisbach equation, A priori and a posteriori, Applied mathematics, Darcy's equations, adaptive methods, Convection–diffusion equation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

International audience; In this article, we consider the time dependent convection-diffusion-reaction equation coupled with the Darcy equation. We propose a numerical scheme based on finite element methods for the discretization in space and the implicit Euler method for the discretization in time. We establish optimal a posteriori error estimates with two types of computable error indicators, the first one linked to the time discretization and the second one to the space discretization. Finally, numerical investigations are performed and presented.

Published
2021
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