Numerische Mathematik

, Volume 132, Issue 3, pp 519–539 | Cite as

The norm of a discretized gradient in \(\varvec{H({{\mathrm{div}}})^*}\) for a posteriori finite element error analysis

  • Carsten Carstensen
  • Daniel Peterseim
  • Andreas Schröder
Article

Abstract

This paper characterizes the norm of the residual of mixed schemes in their natural functional framework with fluxes or stresses in \(H({{\mathrm{div}}})\) and displacements in \(L^2\). Under some natural conditions on an associated Fortin interpolation operator, reliable and efficient error estimates are introduced that circumvent the duality technique and so do not suffer from reduced elliptic regularity for non-convex domains. For the Laplace, Stokes, and Lamé equations, this generalizes known estimators to non-convex domains and introduces new a posteriori error estimators.

Mathematics Subject Classification

65N30 65N15 65N12 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Carsten Carstensen
    • 1
  • Daniel Peterseim
    • 2
  • Andreas Schröder
    • 3
  1. 1.Institut für MathematikHumboldt Universität zu BerlinBerlinGermany
  2. 2.Institut für Numerische Simulation, Universität BonnBonnGermany
  3. 3.Fachbereich MathematikUniversität SalzburgSalzburgAustria

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