Space-Time NURBS-Enhanced Finite Elements for Solving the Compressible Navier–Stokes Equations

  • Michel MakeEmail author
  • Norbert Hosters
  • Marek Behr
  • Stefanie Elgeti
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 132)


This article considers the NURBS-Enhanced Finite Element Method (NEFEM) applied to the compressible Navier–Stokes equations. NEFEM, in contrast to conventional finite element formulations, utilizes a NURBS-based computational domain representation. Such representations are typically available from Computer-Aided-Design tools. Within the NEFEM, the NURBS boundary definition is utilized only for elements that are touching the domain boundaries. The remaining interior of the domain is discretized using standard finite elements. Contrary to isogeometric analysis, no volume splines are necessary.

The key technical features of NEFEM will be discussed in detail, followed by a set of numerical examples that are used to compare NEFEM against conventional finite element methods with the focus on compressible flow.


Spline-based methods NURBS-enhanced finite elements Stabilized space-time finite elements Compressible Navier–Stokes equations 


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Michel Make
    • 1
    Email author
  • Norbert Hosters
    • 1
  • Marek Behr
    • 1
  • Stefanie Elgeti
    • 1
  1. 1.RWTH-Aachen UniversityAachenGermany

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