Bubble elements formulations
4 months ago by
from fenics import * N = 20 mesh = UnitSquareMesh(N, N) V = FunctionSpace(mesh, "B", 3) # tried also CG bc = DirichletBC(V, 0., "on_boundary") u = TrialFunction(V) v = TestFunction(V) f = Expression("-x*x - x*x", degree =2) A = inner(grad(u), grad(v))*dx L = f*v*dx sol = Function(V) solve(A == L, sol) # Same with bc included
I have the following doubts:
1) The solution of the problem solver in Bubble space is very different to the one performed with CG elements, where I considered that Bubble elements are 0 on the boundary, and thus shouldn't require a boundary condition being imposed. On the other side, the CG solution was obtained with bc, to obtain a fair comparison.
2) I am not sure about what the degree does. I expect bubble elements to be of degree 3, and in fact when I use higher order elements, the solution is pretty much constant, which I really don't understand.
3) The last experiment I performed was solving this problem in an 'enhanced CG', writing the solution as u + bubble, but the bubble component was always zero. Any thoughts?
Thanks in advance!
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