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[Chris Richardson <question105900@xxxxxxxxxxxxxxxxxxxxx>]

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? 

Unfortunately, although it works on the left hand end of my domain, the right hand end gives a slight discontinuity in slope.

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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