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IMA Journal of Numerical Analysis Advance Access originally published online on March 20, 2008
IMA Journal of Numerical Analysis 2009 29(2):284-314; doi:10.1093/imanum/drn001
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Weighted error estimates of the continuous interior penalty method for singularly perturbed problems

Erik Burman{dagger}

Department of Mathematics, University of Sussex, Brighton, BN1 9RF, UK

Johnny Guzmán{ddagger}

School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

Dmitriy Leykekhman§

Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA

{dagger} Email: e.n.burman{at}sussex.ac.uk

{ddagger} Corresponding author. Email: guzma033{at}umn.edu

§ Email: leykekhman{at}math.uconn.edu

Received on 7 February 2007. Revised on 20 December 2007.


  Abstract

In this paper, we analyse local properties of the continuous interior penalty (CIP) method for a model convection-dominated singularly perturbed convection–diffusion problem. We show weighted a priori error estimates, where the weight function exponentially decays outside the subdomain of interest. This result shows thats locally, the CIP method is comparable to the streamline-diffusion or the discontinuous Galerkin methods.

Key Words: singularly perturbed; convection–diffusion; local error analysis; continuous interior penalty method


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