Analysis of a stabilised finite element method for power-law fluids

07/27/2021
by   Gabriel R. Barrenechea, et al.
0

A low-order finite element method is constructed and analysed for an incompressible non-Newtonian flow problem with power-law rheology. The method is based on a continuous piecewise linear approximation of the velocity field and piecewise constant approximation of the pressure. Stabilisation, in the form of pressure jumps, is added to the formulation to compensate for the failure of the inf-sup condition, and using an appropriate lifting of the pressure jumps a divergence-free approximation to the velocity field is built and included in the discretisation of the convection term. This construction allows us to prove the convergence of the resulting finite element method for the entire range r>2 d/d+2 of the power-law index r for which weak solutions to the model are known to exist in d space dimensions, d ∈{2,3}.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/11/2022

Cut finite element method for divergence free approximation of incompressible flow: optimal error estimates and pressure independence

In this note we design a cut finite element method for a low order diver...
research
05/21/2021

A divergence-free finite element method for the Stokes problem with boundary correction

This paper constructs and analyzes a boundary correction finite element ...
research
05/19/2023

Least-Squares finite element method for the simulation of sea-ice motion

A nonlinear sea-ice problem is considered in a least-squares finite elem...
research
11/05/2020

Finite element appoximation and augmented Lagrangian preconditioning for anisothermal implicitly-constituted non-Newtonian flow

We devise 3-field and 4-field finite element approximations of a system ...
research
06/16/2021

Accurate and efficient hydrodynamic analysis of structures with sharp edges by the Extended Finite Element Method (XFEM): 2D studies

Achieving accurate numerical results of hydrodynamic loads based on the ...
research
01/24/2020

Convergence of a finite element method for degenerate two-phase flow in porous media

A finite element method with mass-lumping and flux upwinding, is formula...
research
05/19/2021

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 a...

Please sign up or login with your details

Forgot password? Click here to reset