Finite element approximation for the unsteady flow of implicitly constituted incompressible fluids

Thesis

This thesis provides qualitative convergence results of a sequence of numerical approximate solutions for the flow of incompressible fluids subject to an implicit constitutive relation.

The constitutive law between shear stress tensor and shear rate tensor is encoded by a (t,x)-dependent maximal monotone graph with q-growth, for q > 1.

For the finite element approximation, the assumptions result in a pair of (conforming) inf-sup stable finite element spaces for the velocity and the pressure and in the unsteady case a fully discrete approximation based on backward Euler time-stepping is investigated.

Authors: Tscherpel, T

• DOI: 10.5287/ora-gjnex1g7z
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: weak compactness; implicit constitutive models; graph approximation; time-stepping; finite element method; Lipschitz approximation; convergence