Space–time adaptive finite elements for nonlocal parabolic variational inequalities

Heiko Gimperlein, Jakub Stocek

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)
90 Downloads (Pure)


This article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction, both in the domain and on the boundary. For a large class of parabolic variational inequalities associated to the fractional Laplacian we obtain a priori and a posteriori error estimates and study the resulting space–time adaptive mesh-refinement procedures. Particular emphasis is placed on mixed formulations, which include the contact forces as a Lagrange multiplier. Corresponding results are presented for elliptic problems. Our numerical experiments for 2-dimensional model problems confirm the theoretical results: They indicate the efficiency of the a posteriori error estimates and illustrate the convergence properties of space–time adaptive, as well as uniform and graded discretizations.

Original languageEnglish
Pages (from-to)137-171
Number of pages35
JournalComputer Methods in Applied Mechanics and Engineering
Early online date29 Apr 2019
Publication statusPublished - 1 Aug 2019


  • A posteriori error estimates
  • A priori error estimates
  • Dynamic contact
  • Fractional Laplacian
  • Space–time adaptivity
  • Variational inequality

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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