Low-order divergence-free approximations for the Stokes problem on Worsey-Farin and Powell-Sabin splits

We derive low-order, inf-sup stable and divergence-free finite element approximations for the Stokes problem using Worsey-Farin splits in three dimensions and Powell-Sabin splits in two dimensions. The velocity space simply consists of continuous, piecewise linear polynomials, where as the pressure...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2021-05
Hauptverfasser: Fabien, Maurice, Guzman, Johnny, Neilan, Michael, Zytoon, Ahmed
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We derive low-order, inf-sup stable and divergence-free finite element approximations for the Stokes problem using Worsey-Farin splits in three dimensions and Powell-Sabin splits in two dimensions. The velocity space simply consists of continuous, piecewise linear polynomials, where as the pressure space is a subspace of piecewise constants with weak continuity properties at singular edges (3D) and singular vertices (2D). We discuss implementation aspects that arise when coding the pressure space, and in particular, show that the pressure constraints can be enforced at an algebraic level.
ISSN:2331-8422
DOI:10.48550/arxiv.2105.09214