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IMA Journal of Numerical Analysis Advance Access published online on July 28, 2007
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drm009
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A posteriori error analysis of hp-version discontinuous Galerkin finite-element methods for second-order quasi-linear elliptic PDEs

Paul Houston{dagger}

School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

Endre Süli{ddagger}

Computing Laboratory, University of Oxford, Parks Road, Oxford OX1 3QD, UK

Thomas P. Wihler§

Department of Mathematics and Statistics, McGill University, 805 Sherbrooke West, Montréal, Québec H3A 2K6, Canada

{dagger} Email: paul.houston{at}nottingham.ac.uk

{ddagger} Email: endre.suli{at}comlab.ox.ac.uk

§ Email: wihler{at}math.mcgill.ca

Received on 2 November 2006. Revised on 5 April 2007.


  Abstract

We develop the a posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite-element methods for a class of second-order quasi-linear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh dependent) energy norm. The bounds are explicit in the local mesh size and the local polynomial degree of the approximating finite element function. The performance of the proposed error indicators within an automatic hp-adaptive refinement procedure is studied through numerical experiments.

Key Words: hp-adaptivity; a posteriori error analysis; discontinuous Galerkin finite-element methods; quasi-linear elliptic PDEs


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