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

Authors:
Biyue Liu
Affiliations:
Department of Mathematics, Monmouth University, West Long Branch, NJ 07764-1898, United States
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

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.