A. Quarteroni and A.Valli, “Numerical Approximation of Partial Differential Equations,” Springer Series in Computational Mathematics, Springer, Berlin and Heidelberg, 2008. doi:10.1007/978-3-540-85268-1

has been cited by the following article:

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

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

  KEYWORDS: Finite Element; Stability Analysis; Pollution

  JOURNAL NAME: Applied Mathematics, Vol.4 No.3, March 21, 2013

  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.