TY - JOUR
T1 - A Posteriori Error Estimates for Darcy-Forchheimer’s Problem Coupled with the Convection-Diffusion-Reaction Equation 
AU - Triki , Faouzi
AU - Sayah , Toni
AU - Semaan , Georges
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 65
EP - 103
PY - 2024
DA - 2024/01
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1003
UR - https://global-sci.org/intro/article_detail/ijnam/22329.html
KW - Darcy-Forchheimer problem, convection-diffusion-reaction equation, finite element method, a posteriori error estimates.
AB - <p style="text-align: justify;">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.</p>