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IMA Journal of Numerical Analysis Advance Access published online on July 6, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drp007
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Accurate approximations to time-dependent nonlinear convection–diffusion problems

Javier de Frutos{dagger}

Departamento de Matemática Aplicada, Universidad de Valladolid, 47011 Valladolid, Spain

Bosco García-Archilla{ddagger}

Departamento de Matemática Aplicada II, Universidad de Sevilla, 41002 Sevilla, Spain

Julia Novo§

Universidad Autónoma de Madrid, Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, 28049 Madrid, Spain

{dagger} Email: frutos{at}mac.uva.es

{ddagger} Email: bosco{at}esi.us.es

§ Corresponding author. Email: julia.novo{at}uam.es

Received on 20 June 2008. Revised on 15 January 2009.


  Abstract

A new technique to improve the accuracy of the spatial discretization of nonlinear convection–diffusion equations is introduced. Both h- and p-versions of the finite-element method are considered. The procedure amounts to solving a discrete stationary convection–diffusion problem with data based on the computed standard Galerkin approximation at any fixed time. We prove that the convergence rate is increased. Numerical experiments confirm the increase in the convergence rate and show that the procedure we propose annihilates the oscillations of the Galerkin approximation in the convection-dominated regime.

Key Words: convection–diffusion equations; finite element methods; stabilization; error estimates


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