{"title":"A Posteriori Error Estimates for Darcy-Forchheimer’s Problem Coupled with the Convection-Diffusion-Reaction Equation","authors":"Faouzi Triki,Toni Sayah, Georges Semaan","doi":"10.4208/ijnam2024-1003","DOIUrl":null,"url":null,"abstract":"In this work we derive a posteriori error estimates for the convection-diffusion-reaction\nequation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending\non the concentration of the fluid. We introduce the variational formulation associated to the\nproblem, and discretize it by using the finite element method. We prove optimal a posteriori\nerrors with two types of calculable error indicators. The first one is linked to the linearization and\nthe second one to the discretization. Then we find upper and lower error bounds under additional\nregularity assumptions on the exact solutions. Finally, numerical computations are performed to\nshow the effectiveness of the obtained error indicators.","PeriodicalId":50301,"journal":{"name":"International Journal of Numerical Analysis and Modeling","volume":"44 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Numerical Analysis and Modeling","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/ijnam2024-1003","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.
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