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Computable Error Estimators and Adaptive Techniques for Fluid Flow Problems

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Book cover Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 25))

Abstract

The present paper reviews several methods for a posteriori error estimation of finite element approximations. The first part (Section 1) is concerned with global error estimators which provide for estimates and bounds in global norms (so-called energy norms). In particular, explicit and implicit residual methods are described in detail. The second part of the paper (Section 2) deals with a more recent technique, in which the numerical error in finite element approximations of general problems are estimated in terms of quantities of interest. The concept of goal-oriented adaptivity which embodies mesh adaptation procedures designed to control error in specific quantities is also described. Both global and goal-oriented error estimation methods are illustrated on model problems based on the Poisson, convection-diffusion, Stokes and steady-state Navier-Stokes equations. The third part of the paper (Section 3) presents preliminary work on a posteriori error estimation for time-dependent problems, namely the parabolic heat equation and the incompressible Navier-Stokes equations. The methods deal with estimating the approximation errors due to the discretization in space using either explicit or implicit error estimators.

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Authors and Affiliations

  1. Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, Austin, Texas, 78712, USA

    Serge Prudhomme & J. Tinsley Oden

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  1. Serge Prudhomme
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  2. J. Tinsley Oden
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Editors and Affiliations

  1. NAS Division, NASA Ames Research Center, Moffett Field, CA, 94035, USA

    Timothy J. Barth

  2. Karman Institute for Fluid Dynamics, Waterloosesteenweg, 72, 1640, Sint-Genesius-Rode, Belgium

    Herman Deconinck

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Prudhomme, S., Oden, J.T. (2003). Computable Error Estimators and Adaptive Techniques for Fluid Flow Problems. In: Barth, T.J., Deconinck, H. (eds) Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics. Lecture Notes in Computational Science and Engineering, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05189-4_5

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  • DOI: https://doi.org/10.1007/978-3-662-05189-4_5

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  • Print ISBN: 978-3-642-07841-5

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