Paper's Title:

Birkhoff-James orthogonality and Best Approximant in L₁(X)

Author(s):

Mecheri Hacene and Rebiai Belgacem

Department of Mathematics and Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
E-mail: mecherih2000@yahoo.fr

Department of Mathematics and Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
E-mail: brebiai@gmail.com

Abstract:

Let X  be a complex Banach space and let (X,ρ) be a positive measure space. The Birkhoff-James orthogonality is a generalization of Hilbert space orthogonality to Banach spaces. We use this notion of orthogonality to establish a new characterization of Birkhoff-James orthogonality of bounded linear operators in L₁(X,ρ) also implies best approximation has been proved.

Paper's Title:

A Posteriori Error Analysis for a Pollution Model in a Bounded Domain of the Atmosphere

Author(s):

Abdou Wahidi Bello, Jamal Adetola, Djibo Moustapha, Saley Bisso

Université d'Abomey-Calavi,
Département de Mathématiques, Abomey-Calavi,
Republic of Benin.
E-mail: wahidi.bello@fast.uac.bj

Université Nationale des Sciences Technologie,
Ingénierie et Mathématiques (UNSTIM),
Ecole Nationale Supérieure de Génie Mathématique et Modélisation (ENSGMM),
Republic of Benin.
E-mail: adetolajamal@unstim.bj

Département de Sciences Fondamentales,
 École Supérieure Des Sciences Du Numérique,
Université de Dosso, Dosso,
Niger.
E-mail: moustaphad530@gmail.com

Département de Mathématiques et Informatique,
Faculté des Sciences et Techniques,
Université Abdou Moumouni, Niamey,
Niger.
E-mail: bisso.saley@uam.edu.ne

Abstract:

This study conducts an a posteriori error analysis for a mathematical model of atmospheric pollution in a bounded domain. The finite element method is employed to approximate solutions to convection-diffusion-reaction equations, commonly used to model pollutant transport and transformation. The analysis focuses on deriving reliable and efficient error indicators for both temporal and spatial discretizations. Theoretical results establish upper and lower bounds for the discretization errors, ensuring optimal mesh refinement. Numerical simulations, supported by graphical representations, validate the theoretical findings by demonstrating the convergence of error indicators. These results confirm the effectiveness of the finite element method for solving atmospheric pollution models and highlight the importance of adaptive techniques for improving numerical accuracy.

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