Polygonal finite elements for incompressible fluid flow

Cameron Talischi, Anderson Pereira, Glaucio H. Paulino, Ivan F.M. Menezes, Márcio S. Carvalho

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66 Scopus citations


We discuss the use of polygonal finite elements for analysis of incompressible flow problems. It is well-known that the stability of mixed finite element discretizations is governed by the so-called inf-sup condition, which, in this case, depends on the choice of the discrete velocity and pressure spaces. We present a low-order choice of these spaces defined over convex polygonal partitions of the domain that satisfies the inf-sup condition and, as such, does not admit spurious pressure modes or exhibit locking. Within each element, the pressure field is constant while the velocity is represented by the usual isoparametric transformation of a linearly-complete basis. Thus, from a practical point of view, the implementation of the method is classical and does not require any special treatment. We present numerical results for both incompressible Stokes and stationary Navier-Stokes problems to verify the theoretical results regarding stability and convergence of the method.

Original languageEnglish (US)
Pages (from-to)134-151
Number of pages18
JournalInternational Journal for Numerical Methods in Fluids
Issue number2
StatePublished - Jan 20 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


  • Incompressible flow
  • Mixed variational problems
  • Polygonal finite elements
  • Stokes and Navier-Stokes equations
  • Voronoi meshes


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