English

Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization

Analysis of PDEs 2019-05-13 v2 Numerical Analysis

Abstract

We prove that weak solutions obtained as limits of certain numerical space-time discretizations are suitable in the sense of Scheffer and Caffarelli-Kohn-Nirenberg. More precisely, in the space-periodic setting, we consider a full discretization in which the theta-method is used to discretize the time variable, while in the space variables we consider appropriate families of finite elements. The main result is the validity of the so-called local energy inequality.

Keywords

Cite

@article{arxiv.1710.01579,
  title  = {Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization},
  author = {Luigi C. Berselli and Simone Fagioli and Stefano Spirito},
  journal= {arXiv preprint arXiv:1710.01579},
  year   = {2019}
}

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16 pages