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Convergence of adaptive FEM for elliptic obstacle problems
Author(s) -
Feischl Michael,
Page Marcus,
Praetorius Dirk
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110373
Subject(s) - affine transformation , estimator , convergence (economics) , obstacle problem , obstacle , residual , finite element method , mathematics , contraction (grammar) , generalization , mathematical analysis , algorithm , pure mathematics , physics , statistics , medicine , variational inequality , political science , law , economics , economic growth , thermodynamics
We treat the convergence of adaptive lowest‐order FEM for some elliptic obstacle problem with affine obstacle. For error estimation, we use a residual error estimator which is an extended version of the estimator from [2] and additionally controls the data oscillations. The main result states that an appropriately weighted sum of energy error, edge residuals, and data oscillations satisfies a contraction property that leads to convergence. In addition, we discuss the generalization to the case of inhomogeneous Dirichlet data and non‐affine obstacles χ ∈ H 2 (Ω) for which similar results are obtained. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)