Journal title
Constructive Approximation
DOI
10.1007/s00365-022-09591-4
Volume
abs/2107.12954
Last updated
2024-04-12T14:18:10.73+01:00
Abstract
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 $r>\frac{2 d}{d+2}$ of the power-law index $r$ for which weak
solutions to the model are known to exist in $d$ space dimensions, $d \in
\{2,3\}$.
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 $r>\frac{2 d}{d+2}$ of the power-law index $r$ for which weak
solutions to the model are known to exist in $d$ space dimensions, $d \in
\{2,3\}$.
Symplectic ID
1189197
Submitted to ORA
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Journal Article