English

Algebraic representation of dual scalar products and stabilization of saddle point problems

Numerical Analysis 2022-02-28 v2 Numerical Analysis

Abstract

We provide a systematic way to design computable bilinear forms which, on the class of subspaces WVW^* \subseteq \mathcal{V}' that can be obtained by duality from a given finite dimensional subspace WW of an Hilbert space V\mathcal{V}, are spectrally equivalent to the scalar product of V\mathcal{V}'. Such a bilinear form can be used to build a stabilized discretization algorithm for the solution of an abstract saddle point problem allowing to decouple, in the choice of the discretization spaces, the requirements related to the approximation from the inf-sup compatibility condition, which, as we show, can not be completely avoided.

Keywords

Cite

@article{arxiv.1906.01296,
  title  = {Algebraic representation of dual scalar products and stabilization of saddle point problems},
  author = {Silvia Bertoluzza},
  journal= {arXiv preprint arXiv:1906.01296},
  year   = {2022}
}