Specifying initial values for mixed vector and scalar fields

Question

If I have a mixed problem with a vector (3D) and a scalar field like shown below:

# Define function space for system
mesh = BoxMesh(Point(0.0,0.0,0.0), Point(l,l,l), numElems,numElems,numElems)
P1 = VectorElement('Lagrange', tetrahedron, 1)
P2 = FiniteElement('Lagrange', tetrahedron, 1)
element = MixedElement([P1, P2])
V = FunctionSpace(mesh, element)

# Define test functions
v_1, v_2 = TestFunctions(V)

# Define initial conditions
w   = Function(V)
w_0 = Expression((('0.2','0.3','0.4'),'0.01'), degree=1)
w_n = project(w_0, V)

How do I declare w_0? I get an error on that line

Comments

Why don't you create the expressions separately? It would still work for the (bi)linear forms. Maybe some extra info would help.

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The equation I'm trying to solve is 2 nonlinear coupled Euler like equations with a velocity field and density like field. I would like to solve them as a mixed formulation. The question is, how do I initialize a scalar and a vector field like in the w_0 line above when using a mixed element?

Answer 1

Create the components of w0 separately and use assign (or FunctionAssigner) to join the components into the mixed function:

# Define initial conditions
e_u0 = Expression(('0.2', '0.3', '0.4'), degree=1)
e_p0 = Expression('0.1', degree=1)

u0 = interpolate(e_u0, V.sub(0).collapse())
p0 = interpolate(e_p0, V.sub(1).collapse())

w = Function(V)
assign(w, [u0, p0])