Stokes solvers

• Velocity boundary value problem

Velocity boundary value problem

The velocity problem for the Stokes equation is given by

\[\begin{split}\Delta u &= \nabla p \quad \mbox{ in } \Omega \, , \\ \nabla \cdot u &= 0 \quad \mbox{ in } \Omega \, , \\ u &= f \quad \mbox{ on } \Gamma \, .\end{split}\]

For solving the above problem, we represent \(u\) in \(\Omega\) using the combined field representation:

\[u = \alpha \mathcal{S}^{\textrm{stok}}[\sigma] + \beta \mathcal{D}^{\textrm{stok}}[\sigma] \,.\]

We have the following user callable routines:

• Velocity iterative solver

• Velocity post-processor

To see a demo of the use of these interfaces see examples/stokes/stok_vel_iter_example.f. This script can be run using make -f stok_vel_iter_example.make in the examples/stokes folder.