Convergence to Suitable Weak Solutions for a Finite Element Approximation of the Navier–Stokes Equations with Numerical Subgrid Scale Modeling

Santiago Badia, Juan Vicente Gutiérrez-Santacreu

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In this work we prove that weak solutions constructed by a variational multiscale method are suitable in the sense of Scheffer. In order to prove this result, we consider a subgrid model that enforces orthogonality between subgrid and finite element components. Further, the subgrid component must be tracked in time. Since this type of schemes introduce pressure stabilization, we have proved the result for equal-order velocity and pressure finite element spaces that do not satisfy a discrete inf-sup condition.

Original languageEnglish
Pages (from-to)386-413
Number of pages28
JournalJournal of Scientific Computing
Issue number1
Publication statusPublished - 1 Apr 2017
Externally publishedYes


  • Navier–Stokes equations
  • Stabilized finite element methods, Subgrid scales
  • Suitable weak solutions

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