Thesis
Stabilised mixed finite element methods on anisotropic meshes
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2015
- Thesis identifier
- T14201
- Person Identifier (Local)
- 201268193
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- This thesis treats finite element methods for Stokes and Oseen equations on highly anisotropic meshes. The stability of the discrete saddle-point problem may be affected in a negative way by the anisotropies in the mesh P. The reason is a required compatibility condition (inf-sup condition) between the discrete velocity space Vₚ and the pressure space Mₚ. We identify subspaces G ⊂ Mₚ and derive uniform inf-sup conditions for the pair Vₚ × G. That is, the inf-sup constant βɢ is independent of properties of the mesh. These conditions are shown to be equivalent to the defiency [sup v∈Vₚ (div v, q)Ω/|v|1,Ω ≥ βɢ||Πɢq||0,Ω – ||q – Πɢq||0,Ω] for all [q ∈ Mₚ], where Πɢ : Mₚ → G is a surjective projection. The denition of the spaces G ⊂ Mₚ relies on a set of constraints. Using these results we propose uniformly stable mixed methods, either by using the pairs Vₚ × G (i.e., strongly imposing the constraints) or by adding a stabilisation term to the formulation using Vₚ × Mₚ (i.e., weakly imposing the constraints). The proposed stabilisation terms only act on the non-inf-sup stable part of the pressure, they vanish for members of G, and they are block diagonal. In addition, these properties ensure a local mass-conservation property also of the stabilised methods. The above claims are conrmed by several numerical experiments.
- Resource Type
- DOI
- Date Created
- 2015
- Former identifier
- 1246597
Relations
Items
| Thumbnail | Title | Date Uploaded | Visibility | Actions |
|---|---|---|---|---|
|
|
PDF of thesis T14201 | 2021-07-02 | Public | Download |