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Volume 21, Issue 1
A Posteriori Error Estimates for Darcy-Forchheimer’s Problem Coupled with the Convection-Diffusion-Reaction Equation

Faouzi Triki, Toni Sayah & Georges Semaan

DOI: 10.4208/ijnam2024-1003

Int. J. Numer. Anal. Mod., 21 (2024), pp. 65-103.

Published online: 2024-01

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  • 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.

  • Keywords

Darcy-Forchheimer problem, convection-diffusion-reaction equation, finite element method, a posteriori error estimates.

  • AMS Subject Headings

35K05, 65N30, 65N15, 65M15, 65M50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-21-65, author = {Triki , FaouziSayah , Toni and Semaan , Georges}, title = {A Posteriori Error Estimates for Darcy-Forchheimer’s Problem Coupled with the Convection-Diffusion-Reaction Equation }, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {1}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1003}, url = {http://global-sci.org/intro/article_detail/ijnam/22329.html} }
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 -

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.

Triki , FaouziSayah , Toni and Semaan , Georges. (2024). A Posteriori Error Estimates for Darcy-Forchheimer’s Problem Coupled with the Convection-Diffusion-Reaction Equation . International Journal of Numerical Analysis and Modeling. 21 (1). 65-103. doi:10.4208/ijnam2024-1003
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