Question #105900 on DOLFIN changed:
https://answers.launchpad.net/dolfin/+question/105900
Status: Open => Answered
Marie Rognes proposed the following answer:
Chris Richardson wrote:
> New question #105900 on DOLFIN:
> https://answers.launchpad.net/dolfin/+question/105900
>
> I want to use RT or BDM elements in a mixed-poisson type approach to solve
> Darcy flow.
>
> Because the "pressure" is discretised on P0 elements, I cannot define it on
> the boundary, so I have included a
> surface source term in the RHS. Is this the correct approach?
>
>
Yes, this looks correct.
> Unfortunately, although it works on the left hand end of my domain, the right
> hand end gives a slight discontinuity in slope.
>
>
I suspect that this is simply an artifact associated with plotting DG_0
functions.
A similar "dip" appears with this simple script:
from dolfin import *
mesh = UnitSquare(20, 20)
V = FunctionSpace(mesh,"DG",0)
f = Expression("- 2.0*x[0] + 1.0", degree=1)
g = project(f, V)
plot(g, interactive=True)
--
Marie
> Any help much appreciated,
> Chris
>
>
> mesh = UnitSquare(20,20)
> n= FacetNormal(mesh)
>
> R = FunctionSpace(mesh,"BDM",1)
> W = FunctionSpace(mesh,"DG",0)
> V = R+W
>
> (u,p) = TrialFunctions(V)
> (v,q) = TestFunctions(V)
>
> # boundary conditions
> def boundary0(x):
> return x[1]<DOLFIN_EPS
> def boundary1(x):
> return x[1]>1.0-DOLFIN_EPS
>
> u0 = Constant((0.0,0.0))
> bc0 = DirichletBC(V.sub(0), u0, boundary0)
> bc1 = DirichletBC(V.sub(0), u0, boundary1)
> bcs=[bc0,bc1]
>
> f=Expression("-1.0*(x[0]==0.0)+1.0*(x[0]==1.0)")
>
> # 'Permeability' k - gaussian in y
> k=Expression("1.0+exp(-40*pow(x[1]-0.5,2))")
>
> a = (k*dot(v,u) - div(v)*p + q*div(u))*dx
> L = dot(v,f*n)*ds
>
> # Compute solution
> problem = VariationalProblem(a, L,bcs)
> (u, p) = problem.solve().split()
>
> # Plot solution
> plot(p, interactive=True)
> plot(u, interactive=True)
>
>
>
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