Numerische Mathematik

, Volume 130, Issue 1, pp 151–197 | Cite as

An efficient and reliable residual-type a posteriori error estimator for the Signorini problem

  • Rolf Krause
  • Andreas Veeser
  • Mirjam WallothEmail author


We derive a new a posteriori error estimator for the Signorini problem. It generalizes the standard residual-type estimators for unconstrained problems in linear elasticity by additional terms at the contact boundary addressing the non-linearity. Remarkably these additional contact-related terms vanish in the case of so-called full-contact. We prove reliability and efficiency for two- and three-dimensional simplicial meshes. Moreover, we address the case of non-discrete gap functions. Numerical tests for different obstacles and starting grids illustrate the good performance of the a posteriori error estimator in the two- and three-dimensional case, for simplicial as well as for unstructured mixed meshes.

Mathematics Subject Classification

65N15 65N30 74G15 74S05 35J86 



One of the authors (M.W.) would like to thank the Bonn International Graduate School for financial support. Moreover this project was also supported by FORD, university research program, “Advanced numerical algorithms to improve high nonlinear crash simulation with multi-body contacts and friction” and by the BMBF-project ASIL (advanced solvers integrated library).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute of Computational ScienceUniversity of LuganoLuganoSwitzerland
  2. 2.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanItaly
  3. 3.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany

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