Stokes Problems with FEniCS::DOLFIN

We will consider the following 3D (Augmented Lagrangian) Stokes problems given by

where could be a function of the mesh size and is the deformation rate tensor given by .

The discretized domain is given by:

xml mesh boundary marks

In the following table,we present the results for some tests with different equation parameters and with different solving methods.

Direct Solver (H-T) (P2)3 × P1	Param\Method	Uzawa (H-T) (P2)3 × P1	Direct Stabilized (P1)3 × P1
system dims 5924902		system dims 5667692 + 257212	system dims 1028842
time=?	Test 1	time=55.4mnts iter=19	time=2.57mnts
Gmres Error=?		Loop Error=10-4 Gmres Error=10-5	Gmres Error=10-5
image: vel Bug?		image: vel image: vel1	image: vel
image: pressbound Bug?		image: pressbound	image: pressbound
image: presscut Bug?		image: presscut	image: presscut
code: dolfin		code: dolfin	code: dolfin
time= ?	Test 2	time=74.mnts iter=8 Note 1	time=4.4mnts
Gmres Error=? Note 2		Loop Error=10-4 Gmres Error=10-5	Gmres Error=10-5
image: vel Bug?		image: vel image: vel1	image: vel
image: pressbound Bug?		image: pressbound	image: pressbound
image: presscut Bug?		image: presscut	image: presscut
code: dolfin		code: dolfin	code: dolfin
TODO	Test 3	TODO	TODO

Note 1: In this example we can see the influence of the grad-div stabilization term on the number of Uzawa iterations.

Note 2: It seems difficult to fine tune the GMRES PETSc solver to get some acceptable results.

The test were made in a Ubuntu 8.04, Intel Duo Core 1.86GHz.

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