WIAS Preprint No. 1822, (2013)

Robust equilibration a posteriori error estimation for convection-diffusion-reaction problems


  • Eigel, Martin
    ORCID: 0000-0003-2687-4497
  • Merdon, Christian
    ORCID: 0000-0002-3390-2145

2010 Mathematics Subject Classification

  • 65N30 65N15 65J15 65N22 65J10


  • a posteriori, error analysis, finite element method, equilibrated, convection dominated, adaptivity, inhomogeneous Dirichlet, augmented norm




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 (SDM), we derive robust and efficient error estimators based on the reconstruction of equilibrated fluxes in an admissible discrete subspace of H (div, Ω). 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 some part of the differential operator, complete independence from the coefficients of the problem is achieved.

Numerical benchmarks illustrate the very good performance of the error estimators in the convection dominated and the singularly perturbed cases.

Appeared in

  • J. Sci. Comput., 67 (2016) pp. 747--768 under the title ``Equilibration a posteriori error estimation for convection-diffusion-reaction problems''

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