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IMA Journal of Numerical Analysis Advance Access first published online on August 25, 2009
This version published online on August 27, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drp020
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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.

On the stability of finite-element discretizations of convection–diffusion–reaction equations

Petr Knobloch{dagger}

Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Lutz Tobiska{ddagger}

Institute for Analysis and Computational Mathematics, Faculty of Mathematics, Otto von Guericke University Magdeburg, PF 4120, 39016 Magdeburg, Germany

{dagger} Email: knobloch{at}karlin.mff.cuni.cz

{ddagger} Corresponding author. Email: tobiska{at}mathematik.uni-magdeburg.de

Received on 13 June 2008. Revised on 22 April 2009.


  Abstract

A priori error estimates for the local projection (LP) stabilization applied to convection–diffusion–reaction equations are generally based on the coercivity of the underlying bilinear form with respect to the LP norm. We show that the bilinear form of the LP stabilization satisfies an inf–sup condition in a stronger norm that is equivalent to that of the streamline upwind/Petrov–Galerkin method. As a consequence, we get some insight into the stabilization mechanism of Galerkin discretizations of higher order.

Key Words: finite-element method; convection–diffusion–reaction equation; stability; inf–sup condition; stabilization; SUPG method; local projection

The surname of the author Lutz Tobiska was incorrect in the original version. This has been corrected in the updated version.


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