The Finite Element Approximation in Hyperbolic Equation and Its Application—The Pollution of the Water in the West of Algeria as an Example

Salah Boulaaras, Khaled Mahdi, Hamza Abderrahim, Ahmed Hamou, Sarah Kabli

Hydrometeorological Institute of Formation and Research, Seddikia, Oran, Algeria.
University of Mohamed Boudiaf USTO,El’ Monour Oran, Algeria.
University of Oran, Oran, Algeria.

DOI: 10.4236/am.2013.43068                

Abstract

Hyperbolic variational equations are discussed and their existence and uniqueness of weak solution is established over in the last six decades. In this paper the hyperbolic equations (strong formula) can be transformed into a Hyperbolic variational equations. In this research, we propose a time-space discretization to show the existence and uniqueness of the discrete solution and how we apply it in the transport problem. The proposed approach stands on a discrete L^∞-stability property with respect to the right-hand side and the boundary conditions of our problem which has been proposed. Furthermore the numerical example is given for the pollution in the smooth fluid as water and we have taken the pollution of the water in the west of Algeria as an example.

Keywords

Finite Element; Stability Analysis; Pollution

Conflicts of Interest

The authors declare no conflicts of interest.

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