First-order system least-squares for interface problems

Fleurianne Bertrand*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

The two-phase flow problem with incompressible flow in the subdomains is studied in this paper. The Stokes flow problems are treated as first-order systems, involving stress and velocity and using the L2 norm to define a least-squares functional. A combination of H(div)-conforming Raviart–Thomas and standard H1-conforming elements is used for the discretization. The interface conditions are directly in the H(div)-conforming finite element space. The homogeneous least-squares functional is shown to be equivalent to an appropriate norm allowing the use of standard finite element approximation estimates. It also establishes the fact that the local evaluation of the least-squares functional itself constitutes an a posteriori error estimator to be used for adaptive refinement strategies.

Original languageEnglish
Pages (from-to)1711-1730
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume56
Issue number3
DOIs
Publication statusPublished - 2018
Externally publishedYes

Keywords

  • First-order system least-squares
  • Incompressible Newtonian flow
  • Interface conditions
  • Mixed finite element method
  • Parametric Raviart–Thomas element
  • Stokes

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