A Posteriori Error Estimates for Darcy-Forchheimer’s Problem Coupled with the Convection-Diffusion-Reaction Equation
Year: 2024
Author: Faouzi Triki, Toni Sayah, Georges Semaan
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 1 : pp. 65–103
Abstract
In this work we derive a posteriori error estimates for the convection-diffusion-reaction equation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending on the concentration of the fluid. We introduce the variational formulation associated to the problem, and discretize it by using the finite element method. We prove optimal a posteriori errors with two types of calculable error indicators. The first one is linked to the linearization and the second one to the discretization. Then we find upper and lower error bounds under additional regularity assumptions on the exact solutions. Finally, numerical computations are performed to show the effectiveness of the obtained error indicators.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1003
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 1 : pp. 65–103
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 39
Keywords: Darcy-Forchheimer problem convection-diffusion-reaction equation finite element method a posteriori error estimates.
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