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 R^N, 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:

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.

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