Stokes’ Flow Elements

Stokes’ flow elements neglect acceleration, and thus requires no additional stabilization.

4.1.1 Tr21Stokes element

Standard 6 node triangular element for stokes flow, with quadratic geometry, velocity and linear pressure. Both compressible and incompressible material behavior is supported (and also the seamless transition between the two). The element features are summarized in Table 62.


Keyword	Tr121Stokes
Description	Standard 6 node triangular element for stokes flow, with quadratic geometry, velocity and linear pressure
Specific parameters	-

Unknowns	Unknown pressure in nodes 1–3 with unknown velocity (V_u and V_v) in all 6 nodes.
Approximation	Quadratic approximation of geometry and velocity, linear pressure approximation.
Integration
Features	-
Status	Reliable
Tests/Examples	tests/fm/simpleNonlinearStokes.in, tests/fm/weakPeriodicTriangularObstacle.in

Table 62: Tr121Stokes element summary

4.1.2 Tet21Stokes element

Standard 10 node tetrahedral element for stokes flow, with quadratic geometry, velocity and linear pressure. The element features are summarized in Table 63.


Keyword	Tet21Stokes
Description	Standard 10 node tetrahedral element for stokes flow, with quadratic geometry, velocity and linear pressure
Specific parameters	-

Unknowns	Unknown pressure (P_f) in nodes 1–4, and unknown velocity (V_u, V_v, V_w) in all nodes.
Approximation	Quadratic approximation of geometry and velocity, linear pressure approximation.
Integration
Features	-
Status	Untested
Tests/Examples	-

Table 63: Tet21Stokes element summary

4.1.3 Hexa21Stokes element

Standard 27 node hexahedral element for stokes flow, with quadratic geometry, velocity and linear pressure. The element features are summarized in Table 64.


Keyword	Hexa21Stokes
Description	Standard 10 node tetrahedral element for stokes flow, with quadratic geometry, velocity and linear pressure
Specific parameters	-

Unknowns	Unknown pressure (P_f) in nodes 1–8, and unknown velocity (V_u, V_v, V_w) in all nodes.
Approximation	Quadratic approximation of geometry and velocity, linear pressure approximation.
Integration
Features	-
Status	Untested
Tests/Examples	-

Table 64: Hexa21Stokes element summary

4.1.4 Tr1BubbleStokes element

So called “Mini” element in 2D. A 3 node triangular element for stokes flow, with linear geometry and pressure. Velocity is enriched by a bubble function. Should not be used with materials that have memory (which is uncommon for flow problems). The element features are summarized in Table 65.


Keyword	Tr1BubbleStokes
Description	So called “Mini” 2D element
Specific parameters	-

Unknowns	Unknown pressure (P_f) in all nodes, and unknown velocity (V_u, V_v) in all nodes and one internal dof manager.
Approximation	Linear geometry and pressure. Velocity is enriched by a bubble function.
Integration
Features	-
Status	Untested
Tests/Examples	-

Table 65: Tr1BubbleStokes element summary

4.1.5 Tet1BubbleStokes element

So called “Mini” element in 3D. A 4 node tetrahedral element for stokes flow, with linear geometry and pressure. Velocity is enriched by a bubble function. Should not be used with materials that have memory (which is uncommon for flow problems). The element features are summarized in Table 66.


Keyword	Tet1BubbleStokes
Description	So called “Mini” 3D element
Specific parameters	-

Unknowns	Unknown pressure (P_f) in all nodes, and unknown velocity (V_u, V_v) in all nodes and one internal dof manager.
Approximation	Linear geometry and pressure. Velocity is enriched by a bubble function.
Integration
Features	-
Status	Untested
Tests/Examples	-

Table 66: Tet1BubbleStokes element summary

4.1 Stokes’ Flow Elements

4.1.1 Tr21Stokes element

4.1.2 Tet21Stokes element

4.1.3 Hexa21Stokes element

4.1.4 Tr1BubbleStokes element

4.1.5 Tet1BubbleStokes element