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Title: Robust equilibration a posteriori error estimation for convection-diffusion-reaction problems
Authors: Eigel, MartinMerdon, Christian
Issue Date: 2013
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1822, ISSN 0946 – 8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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 (SDM), we derive robust and efficient error estimators based on the reconstruction of equilibrated fluxes in an admissible discrete subspace of H(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 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.
Keywords: Equilibration; adaptivity; a posteriori error analysis; convection dominated; reaction dominated; SUPG; SDM; stabilized FEM; inhomogeneous Dirichlet; Konvektions-Diffusionsgleichung; Numerisches Verfahren
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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