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The Obstacle Problem

  • Sören BartelsEmail author
Chapter
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 47)

Abstract

The obstacle problem describes constrained deflection of a membrane and serves as a model problem for infinite-dimensional minimization problems with pointwise inequality constraint. Equivalent formulations of the problem including a variational inequality and a characterization with a Lagrange multiplier are derived. The well-posedness and convergence of lowest-order conforming finite element methods, together with a priori and a posteriori error estimates, are established. The application of the semismooth Newton method and a globally convergent primal-dual method together with their implementation conclude the chapter.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Abteilung für Angewandte MathematikAlbert-Ludwigs-Universität FreiburgFreiburgGermany

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