Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems

Santiago Badia, Ramon Codina

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this paper we propose stabilized finite element methods for both Stokes' and Darcy's problems that accommodate any interpolation of velocities and pressures. Apart from the interest of this fact, the important issue is that we are able to deal with both problems at the same time, in a completely unified manner, in spite of the fact that the functional setting is different. Concerning the stabilization formulation, we discuss the effect of the choice of the length scale appearing in the expression of the stabilization parameters, both in what refers to stability and to accuracy. This choice is shown to be crucial in the case of Darcy's problem. As an additional feature of this work, we treat two types of stabilized formulations, showing that they have a very similar behavior.
Original languageEnglish
Pages (from-to)1971-2000
Number of pages30
JournalSIAM Journal on Numerical Analysis
Volume47
Issue number3
DOIs
Publication statusPublished - 2009
Externally publishedYes

Keywords

  • Stokes–Darcy's problem
  • stabilized finite element methods
  • characteristic length scale
  • orthogonal subgrid scales

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