dolfin team mailing list archive

[Anders Logg <question95601@xxxxxxxxxxxxxxxxxxxxx>]

Question #95601 on DOLFIN changed:
https://answers.launchpad.net/dolfin/+question/95601

Anders Logg posted a new comment:
On Wed, Dec 30, 2009 at 02:00:23PM -0000, Andy R Terrel wrote:
> Question #95601 on DOLFIN changed:
> https://answers.launchpad.net/dolfin/+question/95601
>
>     Status: Open => Answered
>
> Andy R Terrel proposed the following answer:
> FFC will take care of interpolation of the computed function for you.
> So you combine your two forms into one:
>
> Error.ufl
> =======
> e3 = FiniteElement("Lagrange", "triangle", 3)
> e10 = FiniteElement("Quadrature", "triangle", 10)
> v = Coefficient(e3)
> w = Coefficient(e10)
> M= ((w - v) * (w - v)) * dx
>
>
> This can be done for any functional (so all your seminorms and what
> not).  I don't think this is in dolfin, I think a long time ago
> there were things like this but because the need to support so many
> different combinations of finite elements it got yanked.

Yes, this is something that is not handled automatically in C++
since it would require pregeneration of large amounts of code to cover
different function spaces.

Andy's solution is good, but you might run into stability problems
(round-off errors) for higher order function spaces.

Look at errornorm.py for a better way to compute the error:

  """Compute the error e = u - uh in the given norm. The parameter k
  denotes the degree of accuracy (degree of piecewise polynomials
  approximating u an uh).

  In simple cases, one may just define

    e = u - uh

  and evalute for example the square of the error in the L2 norm by

    e = u - uh
    assemble(e*e*dx, mesh)

  However, this is not stable w.r.t. round-off errors considering
  that the form compiler may expand the expression above to

    u*u*dx + uh*uh*dx - 2*u*uh*dx

  and this might get further expanded into thousands of terms for
  higher order elements. Thus, the error will be evaluated by adding
  a large number of terms which should sum up to something close to
  zero (if the error is small)."""

--
Anders

-- 
You received this question notification because you are a member of
DOLFIN Team, which is an answer contact for DOLFIN.