Abstract
In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the method of weighted residuals. This new formulation allows equal-order interpolation for the velocity and pressure fields. Finally, we show by counterexample that a direct equivalence between subgrid-based stabilized finite element methods and Galerkin methods enriched by bubble functions cannot be constructed for quadrilateral and hexahedral elements using standard bubble functions.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1291-1314 |
| Number of pages | 24 |
| Journal | International Journal for Numerical Methods in Fluids |
| Volume | 60 |
| Issue number | 12 |
| DOIs | |
| State | Published - Aug 30 2009 |
| Externally published | Yes |
Keywords
- Bubble functions
- Finite elements for fluids
- Mixed methods
- Multi-scale formulation
- Stabilized finite elements
- Stokes equations
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications
- Applied Mathematics