Re: [firedrake] Poisson equation; homogeneous vs nonhomogeneous
[Re-adding firedrake@imperial.ac.uk to CC, please do keep the mailing list in the CC line so that others can see the response too. You'll likely get faster and/or more accurate help that way!] On 23/04/18 21:10, Eric M wrote:
revision: I put gx in VGrad as well. My outputs are as expected. Though it seems slightly strange to have what should be an exact function (gx) interpolated to a discontinuous space.
See below.
On Mon, Apr 23, 2018 at 2:51 PM, Eric M <eric.malitz@gmail.com <mailto:eric.malitz@gmail.com>> wrote:
Aha, there is a confusion here between what is a coefficient in some finite element space, and what is a symbolic expression. You start with u, which is a Function in some finite element space. Now grad(u)[0], or u.dx(0) (these actually produce the same thing) are symbolic expressions. If you want to look at the values, you first need to interpolate (or project) the expression into a suitable finite element space: e.g, if u is in FunctionSpace(mesh, "CG", 2) Then perhaps: VGrad = FunctionSpace(mesh, "DG", 1) gradu = project(grad(u), VGrad) gradu.dat.data[:] ...
For an exact solution g, I have gx, it's derivative. I wish to compare gx against the x derivative of a solution uk. I have:
V = FunctionSpace(mesh, "Lagrange", 2) Sigma = TensorFunctionSpace(mesh, "Lagrange", 2) gx=Function(V) gx.interpolate(x*exp((x**2+y**2)/2))
VGrad=FunctionSpace(mesh,"DG",1)
(solve a problem, split uk from the mixed solution so uk is in V)
gradu_x=project(grad(uk)[0],VGrad)
But now gradu_x and gx are different lengths. I see why we would use this VGrad. Does it make sense to do VGrad=FunctionSpace(mesh,"Lagrange",2) instead?
I suggested a DG space because in general the grad of some CG space is not continuous. But if you have some exact expression you can compare to, then you can compute norms directly: gx = x*exp((x**2 + y**2)/2) L2diff = norm(gx - grad(uk)[0]) Make sense? Cheers, Lawrence
It does make sense; though again I was trying to get a W^{1,\infty} norm specifically. Anyway it appears what I mentioned gives the expected results. Thanks again. On Tue, Apr 24, 2018 at 5:04 AM, Lawrence Mitchell < lawrence.mitchell@imperial.ac.uk> wrote:
[Re-adding firedrake@imperial.ac.uk to CC, please do keep the mailing list in the CC line so that others can see the response too. You'll likely get faster and/or more accurate help that way!]
On 23/04/18 21:10, Eric M wrote:
revision: I put gx in VGrad as well. My outputs are as expected. Though it seems slightly strange to have what should be an exact function (gx) interpolated to a discontinuous space.
See below.
On Mon, Apr 23, 2018 at 2:51 PM, Eric M <eric.malitz@gmail.com <mailto:eric.malitz@gmail.com>> wrote:
Aha, there is a confusion here between what is a coefficient in some finite element space, and what is a symbolic expression. You start with u, which is a Function in some finite element space. Now grad(u)[0], or u.dx(0) (these actually produce the same thing) are symbolic expressions. If you want to look at the values, you first need to interpolate (or project) the expression into a suitable finite element space: e.g, if u is in FunctionSpace(mesh, "CG", 2) Then perhaps: VGrad = FunctionSpace(mesh, "DG", 1) gradu = project(grad(u), VGrad) gradu.dat.data[:] ...
For an exact solution g, I have gx, it's derivative. I wish to compare gx against the x derivative of a solution uk. I have:
V = FunctionSpace(mesh, "Lagrange", 2) Sigma = TensorFunctionSpace(mesh, "Lagrange", 2) gx=Function(V) gx.interpolate(x*exp((x**2+y**2)/2))
VGrad=FunctionSpace(mesh,"DG",1)
(solve a problem, split uk from the mixed solution so uk is in V)
gradu_x=project(grad(uk)[0],VGrad)
But now gradu_x and gx are different lengths. I see why we would use this VGrad. Does it make sense to do VGrad=FunctionSpace(mesh,"Lagrange",2) instead?
I suggested a DG space because in general the grad of some CG space is not continuous. But if you have some exact expression you can compare to, then you can compute norms directly:
gx = x*exp((x**2 + y**2)/2)
L2diff = norm(gx - grad(uk)[0])
Make sense?
Cheers,
Lawrence
participants (2)
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Eric M
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Lawrence Mitchell