On 08/11/17 09:13, Lawrence Mitchell wrote:

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On 03/11/17 20:15, Francis Poulin wrote:

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I don't suppose there is an easy way to find out the maximum of the boundary value in the numerical solution?

If you are imposing strong (Dirichlet) conditions, then the solution on the boundary nodes is, by definition, whatever you set it to. If you have some other means of enforcing boundary conditions and just want to know that the values are on the boundary, you could do: V = FunctionSpace(...) selector = DirichletBC(V, 0, "on_boundary") f = Function(V)

solve into f

boundary_values = f.dat.data_ro[selector.nodes, ...]

Note this assumes that inspecting the point values of your space makes sense: this is fine for CG and DG, not so for other spaces.

Hey, thanks very much! I didn't realize that the object returned by DirichletBC had a .nodes attribute. That's much more direct than the procedures in the other codes! (As usual for Firedrake.) This is very useful; in gratitude, I attach a simple example from Ostroumov, G. A. (1958). Free convection under the conditions of the internal problem. Technical Report [NACA-TM](https://wiki.memjet.local/display/lib/NASA+Technical+Memorandum)-1407, NACA, eq. 5.18, p. 34 lap w = -x in the first quadrant of the unit circle with w=0 on perimeter and y-axis and natural boundary conditions on x-axis, where the boundary maximum is to be sought. The exact solution is w=x(1-x**2-y**2)/8 with maximum w(1/sqrt(3), 0) = 1/12 sqrt(3). Using the same Gmsh-generated mesh as in the previous thread (again: -clscale 0.0625), but now also marking the x-axis as Physical Line 3, the nodal maximum is found as w=0.048122 at x=0.562500, the value being accurate to the fifth decimal place and the location as good as possible on the mesh.