Convergence of a Mixed Finite Element–Finite Volume Scheme for the Isentropic Navier–Stokes System via Dissipative Measure-Valued Solutions

  • Eduard Feireisl
  • Mária Lukáčová-Medvid’ová

DOI: 10.1007/s10208-017-9351-2

Cite this article as:
Feireisl, E. & Lukáčová-Medvid’ová, M. Found Comput Math (2017). doi:10.1007/s10208-017-9351-2


We study convergence of a mixed finite element–finite volume numerical scheme for the isentropic Navier–Stokes system under the full range of the adiabatic exponent. We establish suitable stability and consistency estimates and show that the Young measure generated by numerical solutions represents a dissipative measure-valued solutions of the limit system. In particular, using the recently established weak–strong uniqueness principle in the class of dissipative measure-valued solutions we show that the numerical solutions converge strongly to a strong solutions of the limit system as long as the latter exists.


Compressible Navier–Stokes system Finite volume scheme Finite element scheme Stability Convergence Measure-valued solution 

Mathematics Subject Classification

65M12 65M60 76N10 35K61 

Copyright information

© SFoCM 2017

Authors and Affiliations

  • Eduard Feireisl
    • 1
  • Mária Lukáčová-Medvid’ová
    • 2
  1. 1.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPraha 1Czech Republic
  2. 2.Institute of MathematicsJohannes Gutenberg-University MainzMainzGermany

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