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Journal of Scientific Computing

, Volume 67, Issue 2, pp 747–768 | Cite as

Equilibration a Posteriori Error Estimation for Convection–Diffusion–Reaction Problems

  • M. Eigel
  • C. MerdonEmail author
Article

Abstract

We study a posteriori error estimates for convection–diffusion–reaction problems with possibly dominating convection or reaction and inhomogeneous boundary conditions. For the conforming FEM discretisation with streamline diffusion stabilisation, we derive reliable and efficient error estimators based on the reconstruction of equilibrated fluxes in an admissible discrete subspace of \({H({{\mathrm{div}}},\Omega )}\). Error estimators of this type have become popular recently since they provide guaranteed error bounds without further unknown constants. The estimators can be improved significantly by some postprocessing and divergence correction technique. For an extension of the energy norm by a dual norm of the convection part of the differential operator, robustness of the error estimator with respect to the coefficients of the problem is achieved. Numerical benchmarks illustrate the good performance of the error estimators for singularly perturbed problems, in particular with dominating convection.

Keywords

A posteriori Error analysis Finite element method Equilibrated Convection dominated Adaptivity Inhomogeneous Dirichlet Augmented norm 

Mathematics Subject Classification

65N30 65N15 65J15 65N22 65J10 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Weierstrass Institute BerlinBerlinGermany

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