Hanging nodes and XFEM

Thomas Peter Fries*, Andreas Byfut, Alaskar Alizada, Kwok Wah Cheng, Andreas Schröder

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper investigates two approaches for the handling of hanging nodes in the framework of extended finite element methods (XFEM). Allowing for hanging nodes, locally refined meshes may be easily generated to improve the resolution of general, i.e. model-independent, steep gradients in the problem under consideration. Hence, a combination of these meshes with XFEM facilitates an appropriate modeling of jumps and kinks within elements that interact with steep gradients. Examples for such an interaction are, e.g. found in stress fields near crack fronts or in boundary layers near internal interfaces between two fluids. The two approaches for XFEM based on locally refined meshes with hanging nodes basically differ in whether (enriched) degrees of freedom are associated with the hanging nodes. Both approaches are applied to problems in linear elasticity and incompressible flows.

Original languageEnglish
Pages (from-to)404-430
Number of pages27
JournalInternational Journal for Numerical Methods in Engineering
Issue number4-5
Publication statusPublished - 29 Apr 2011


  • 1-irregular
  • Hanging nodes
  • Interface
  • Refinement
  • XFEM

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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