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.
Highlights
IntroductionThe construction of a numerical model consists of two distinct stages: the first is to establish a system of equations and strongly coupled nonlinear governing the behavior of continuous phenomena
The construction of a numerical model consists of two distinct stages: the first is to establish a system of equations and strongly coupled nonlinear governing the behavior of continuous phenomena.In the late 40’s methods of grid points were used to model the universally large-scale atmospheric flow
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
Summary
The construction of a numerical model consists of two distinct stages: the first is to establish a system of equations and strongly coupled nonlinear governing the behavior of continuous phenomena. We present the main tools for implementations of the method more generally belong to family of Galerkin methods These are commonly used instead of the finite difference method (considered too simplistic) to treat horizontal and vertical fields in the models. The finite element method is one of the tools of applied mathematics It is put in place, using principles inherited from the variational formulation or weak formulation, a discrete mathematical algorithm for finding an approximate solution of a free boundary problem (see [3,4,5,6,7]). The finite element method is different than the spectral method because it is not comprehensive, but rather determined by local values It is distinct approximations the function is defined over the entire region and not just the discrete points (see [2]).
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