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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