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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
Residual-Based A Posteriori Error Estimates For A Conforming Mixed Finite Element Discretization of the Monge-Ampere Equation
Author(s):
J. Adetola, K. W. Houedanou and B. Ahounou
Institut de Mathematiques et de Sciences
Physiques (IMSP),
Universite d'Abomey-Calavi
E-mail: adetolajamal58@yahoo.com
Departement de Mathematiques,
Faculte des Sciences et Techniques (FAST),
Universite d'Abomey-Calavi
E-mail: khouedanou@yahoo.fr
Departement de Mathematiques,
Faculte des Sciences et Techniques (FAST),
Universite d'Abomey-Calavi
E-mail: bahounou@yahoo.fr
Abstract:
In this paper we develop a new a posteriori error analysis for the Monge-Ampere equation approximated by conforming finite element method on isotropic meshes in R2. The approach utilizes a slight variant of the mixed discretization proposed by Gerard Awanou and Hengguang Li in [4]. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.
Paper's Title:
Mass Transportation Approach For Parabolic P-Biharmonic Equations
Author(s):
A. Soglo, K. W. Houedanou, J. Adetola
Institut de Mathematiques et de Sciences
Physiques (IMSP)
Universite d'Abomey-Calavi,
Rep. of Benin
E-mail: ambroiso.soglo@gmail.com
Departement de Mathematiques
Faculte des Sciences et Techniques (FAST)
Universite d'Abomey-Calavi,
Rep. of Benin
E-mail: khouedanou@yahoo.fr
Universite Nationale des Sciences, Technologie, Ingenierie et
Mathematiques (UNSTIM,
Abomey,
Rep. of Benin
E-mail: adetolajamal58@yahoo.com
Abstract:
In this paper, we propose a mass transportation method to solving a parabolic p-biharmonic equations, which generalized the Cahn-Hilliard (CH) equations in RN, N∈N*. By using a time-step optimal approximation in the appropriate Wasserstein space, we define an approximate weak solution which converges to the exact solution of the problem. We also show that the solution under certain conditions may be unique. Therefore, we study the asymptotic behavior of the solution of the parabolic p-biharmonic problem.
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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