An error analysis of a finite element method for a system of nonlinear advection–diffusion–reaction equations

In this paper we present an analysis of a finite element method for solving a system of nonlinear advection–diffusion–reaction equations. We prove the existence and uniqueness of the numerical solution, and obtain a prior error estimates optimal in H 1 norm. Numerical computations are carried out to test the order of accuracy in the error estimates. Blend function interpolations are applied in the calculation of numerical integrations over elements with a curved boundary.