[firedrake] Question on mixed solves: RHS is not defined in product function space

[Lawrence Mitchell]

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On 22/01/15 15:17, Eike Mueller wrote:
> Dear firedrakers,
> 
> assume I want to do the following solve of a mixed system:
> 
> V1 = FunctionSpace(mesh, 'RT', 1) V2 = FunctionSpace(mesh, 'DG',
> 0)
> 
> W = V1 * V2 lmbda = 1 u, p = TrialFunctions(W) v, q =
> TestFunctions(W) f = Function(V1) g = Function(V2)
> 
> a = (p*q - q*div(u) + lmbda*inner(v, u) + div(v)*p)*dx
> 
> L = (dot(u,f)+p*g)*dx
> 
> u = Function(W) solve(a == L, u, solver_parameters=...)
> 
> But now I take out the line
> 
> L = (dot(u,f)+p*g)*dx
> 
> and assume that somewhere I calculate instead:
> 
> L1 = dot(TestFunction(V1),f)*dx L2 = TestFunction(V2)*g*dx

Can you define these two forms using the test functions v and q
respectively (rather than building new test functions on the
subspaces)?  Then everything should "just work".

Alternately, if you haven't already assembled L1 and L2, you could (to
get L), do:

v1 = TestFunction(V1)
v2 = TestFunction(V2)

L1 = dot(v1, f)*dx
L2 = v2*g*dx

import ufl
L1p = ufl.replace(L1, {v1, v})
L2p = ufl.replace(L2, {v2, v})

L = L1p + L2p

but that's effectively the same as just defining L1 and L2 using v and
q rather v1 and v2.  I guess you're separately using L1 and L2
somewhere in a non-mixed solve?

Cheers,

Lawrence

Cheers,

Lawrence
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