Discretization error estimation of a chemical reaction-diffusion equations system approximate solution

Abstract

This paper describes a result of the discretization error estimation in the approximate solution of a system of a nonlinear of diffusion-reaction equations modelling a one step, binary, exothermic, irreversible chemical reaction, that occurs in an incompressible fluid , with Newmann boundary conditions and no negative initial conditions. For this, the continuous problem is formulated as a problem in the finite elements space. To estimate the error between the exact solution of the approximate problem and its approximate solution the first order implicit Euler method is used assuming some hypotheses on the operator in the finite element space .As a result, the discretization error is the order O(hπ)+O(τ1+) for h small in the norm of the Hilbert space L2.