Custom function space

Question

Is it possible to add a custom function space, e.g. Fourier-like series of sinusoids? Can I use an existing space with limited coefficients e.g. polynomials of arbitrary order (high) with arbitrary coefficients. It would be a subspace of existing CG or DG spaces.

Answer 1

The R space is convenient for global functions like Fourier series etc. Consider
the following:

from fenics import *

n = 16
mesh = UnitIntervalMesh(n)

dim = 4
R = VectorFunctionSpace(mesh, "R", 0, dim=dim)
x = SpatialCoordinate(mesh)

omega = Constant(2.0*pi)

sinbasis = [sin((i+1)(omegax[0])) for i in range(dim)]

udofs = TrialFunction(R)
vdofs = TestFunction(R)
ubasis = [udofi * sini for udofi, sini in zip(udofs, sinbasis)]
vbasis = [vdofi * sini for vdofi, sini in zip(vdofs, sinbasis)]
u = sum(ubasis)
v = sum(vbasis)

a = inner(grad(u), grad(v))*dx(degree=4)
A = assemble(a)

print A.array()

Comments

Thank You for a quick response,

It's like a "chain rule", only coefficients in the series are subject to variation.
I'm not sure how to express the solution in terms of ubasis and vbasis. Does it belong to "R" space?

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I don't know what you mean by "chain rule".
Your solution will now be expressed in terms of the Fourier series.