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[Graham Rowlands <question159192@xxxxxxxxxxxxxxxxxxxxx>]

Question #159192 on DOLFIN changed:
https://answers.launchpad.net/dolfin/+question/159192

Description changed to:
Greetings,

I'm solving the Fokker-Planck equation in 2D just fine in the time-
dependent case (Crank-Nicolson using dolfin in the usual manner I've
seen around here.) I'm now trying to find the steady state solution
without waiting for the dynamic simulation to converge. This is
apparently much more difficult for me to wrap my head around.

The equation (with implied summation over repeated indices):
du/dt = d/dx_i (A_i * u) + d/dx_i (d/dx_j (B^2_ij * u ) ))

maps to the following ufl code in weak form in the steady state:
drift          = -dot(A,grad(v))*u
diffusion  = -dot(dot(B,div(B)),grad(v))*u + 0.5*dot(dot(B*B.T,grad(u)),grad(v))

a = (drift + diffusion)*dx  # bilinear
L = f*v*dx                            # Linear, where f is set to 0.0 in the cpp code

I seem to just get the trivial solution when trying the
VariationalProblem(a,L,bcs) approach, and I guess I'm rather unsure how
to work on relaxing this system in a similar way to that seen in the
non-linear approach.

Many thanks to all involved,
Graham

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