I am solving the 2D Stokes equations with Dirichlet BCs, so I have 3
unknowns (u1, u2, p) with Dirichlet BCs on u1 and u2. Rather than
interpolate, I'd like to project the Dirichlet boundary values.
Looking at the documentation for VectorTools::project_boundary_values(),
the description of the "std::vector< unsigned int > component_map" input
describes exactly this scenario, seemingly indicating that using a
component_map will allow me to project values to 2 of the 3 components of
my finite element. However, reading the remainder of the description, and
attempting to use the component_map, this seems to be not the case. What
I'd need is a component_map of {0,1}....that is, the first
boundary_function should apply to u1, and the second boundary_function
should apply to u2. However, the map goes in the opposite
direction....that is, it is required to have 3 components {0,1,?}: u1 gets
the first boundary_function applied to it, u2 gets the second
boundary_function applied to it, and p gets the ? boundary function applied
to it.
Is this part of the documentation incorrect when it mentions the Stokes
problem as a use for the component_map? In any case, what is a recommended
method to projecting the boundary values for the Stokes problem?
Thanks,
Stephen
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