Creeping flow

Verification of creepingFlow against closed-form solutions. All results are from FEAScript-core 0.4.0, solved with lusolve.

Couette flow

A 4 m × 2 m channel, $\mu = 1$: the bottom wall is fixed, the top wall moves with velocity 1, and both ends are stress-free.

The exact solution is

$$u = \frac{y}{2}, \qquad v = 0, \qquad p = 0.$$

The linear velocity profile lies in the Taylor-Hood element spaces, so the elements reproduce it exactly, and the remaining deviations are round-off. The table gives the largest deviation from the exact solution over all nodes.

Elements	Mesh	$\max \lvert u - y/2 \rvert$	$\max \lvert v \rvert$	$\max \lvert p \rvert$
Q2-Q1 quads	4 × 2 structured	3.3e-16	0	0
Q2-Q1 quads	Gmsh, 9-node quadrilaterals	1.1e-15	2.1e-15	1.9e-14
P2-P1 triangles	Gmsh, 6-node triangles	1.7e-15	1.0e-15	1.5e-14

The test requires every nodal value to match within 1e-10: creepingFlow2DCouette.