Convergence of adaptive FEM for elliptic obstacle problems | Zendy

Feischl Michael | Zendy; Page Marcus | Zendy; Praetorius Dirk | Zendy

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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)

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