A POSTERIORI ERROR ESTIMATES FOR DARCY-FORCHHEIMER'S PROBLEM COUPLED WITH THE CONVECTION-DIFFUSION-REACTION EQUATION

被引：1
|
作者：
Triki, Faouzi [1 ]
Sayah, Toni [2 ]
Semaan, Georges [2 ]
机构：
[1] Univ Grenoble Alpes, CNRS, UMR 5224, Lab Jean Kuntzmann, 700 Ave Cent, F-38401 St Martin Dheres, France
[2] Univ St Joseph Beyrouth, Unite Rech Math & Modelisat, CAR, Fac Sci, BP 11-514 Riad El Solh, Beirut 11072050, Lebanon
来源：
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING | 2024年 / 21卷 / 01期
关键词：
Darcy-Forchheimer problem; convection-diffusion-reaction equation; finite element method; a posteriori error estimates; ADAPTIVE MESH-REFINEMENT; THEORETICAL DERIVATION; DISCRETIZATION; INTERPOLATION; OPERATOR; FLOW;
D O I：
10.4208/ijnam2024-1003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：65 / 103
页数：39
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