[re-adding firedrake to CC]

On 17 Apr 2018, at 20:56, Eric M <eric.malitz@gmail.com> wrote:

Thanks for the tips. For a scalar function I think I wrote diff=u-g; max(abs(diff.dat.data)) for instance. Can this be done for sigmak-sigma? I tried to do it with the components individually and it didn’t work.

You should be able to do: diff = assemble(sigmak - sigma) and then diff.dat.data should give you the point wise difference. What doesn't work?

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On Apr 17, 2018, at 8:14 AM, Lawrence Mitchell <lawrence.mitchell@imperial.ac.uk> wrote:

Hi Eric,

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On 17/04/18 04:14, Eric M wrote: Sorry, hit send too soon;

I am coding a mixed problem where the unknowns are the scalar function u and a Hessian D^2u.

Among the things I specify are the function spaces:

V = FunctionSpace(mesh, "Lagrange", 2) Sigma = TensorFunctionSpace(mesh, "Lagrange", 2) VS = V * Sigma

I specify some exact solutions:

u = Expression("exp((x[0]*x[0] + x[1]*x[1])/2)") u = Function(V).interpolate(u) sigma00expr= Expression(' (1+x[0]*x[0])*exp((x[0]*x[0]+x[1]*x[1])/2) ' ,degree=5) sigma01expr= Expression('x[0]*x[1]*exp((x[0]*x[0]+x[1]*x[1])/2) ' ,degree=5) sigma10expr= Expression(' x[0]*x[1]*exp((x[0]*x[0]+x[1]*x[1])/2) ' ,degree=5) sigma11expr= Expression(' (1+x[1]*x[1])*exp((x[0]*x[0]+x[1]*x[1])/2) ' ,degree=5)

So I would write these using UFL expressions, and then glue them together into a tensor:

x, y = SpatialCoordinate(mesh)

sigma00 = (1 + x**2)*exp((x**2 + y**2)/2) sigma01 = ...

etc...

Then you can write:

sigma = as_tensor([[sigma00, sigma01], [sigma10, sigma11]])

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And solve it:

solve(a == L, us, bcs=bcs, solver_parameters=sp_it) uk, sigmak = us.split()

Now I analyze uk in L2, H1, etc. error norms. But I can't figure out how to analyze sigmak, that is, extract the components to put in error norms. but this doesn't work here.

Now you can write:

diff = sigmak - sigma

and then L2norm = norm(diff, norm_type="L2")

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Even then, once I extract, say, sigmak00, how do I do for example: L2 norm of sigmak - sigma and L^infinity norm of sigmak - sigma ?

There's no builtin functionality for computing Linf norms, because they are tricky!

Hope this helps.

Lawrence