dolfin team mailing list archive

[Kristian Oelgaard <k.b.oelgaard@xxxxxxxxxx>]

Quoting Martin Sandve Alnæs <martinal@xxxxxxxxx>:

> On Wed, Jun 10, 2009 at 7:12 PM, Anders Logg<logg@xxxxxxxxx> wrote:
> > On Wed, Jun 10, 2009 at 06:46:53PM +0200, Martin Sandve Alnæs wrote:
> >> Not a linear form, but a functional. That's what norm does anyway.
> >>
> >> u = Function(element)
> >> x, y, z = tetrahedron.x
> >> L2 = (sin(2*pi*x) - u)**2*dx
> >>
> >> You still have to make sure you compile
> >> with sufficient quadrature order though.
> >
> > That may not be numerically stable depending on how the form compiler
> > expands the expression into terms. Use the function errornorm() which
>
> Which is only one of the reasons why quadrature
> based form compilers shouldn't expand expressions.
> SFC doesn't, and I don't think the latest FFC does
> either when using quadrature.

That is correct, it doesn't.

Kristian

> Martin
>
>
>
> > works around this and automatically computes the norm:
> >
> >  e = errornorm(u, u_h)
> >
> > Look at the documentation in errornorm.py for a longer explanation.
> >
> > --
> > Anders
> >
> >
> >
> >>
> >> On Wed, Jun 10, 2009 at 6:33 PM, Shawn Walker<walker@xxxxxxxxxxxxxxx>
> wrote:
> >> > Actually, I have a question about this.  I may have asked this before,
> so
> >> > forgive me if I repeat.
> >> >
> >> > Suppose my exact solution is sin(2*pi*x).  I would like to compute the
> exact
> >> > error against this function.  Is this doable?  I know you can resample
> it
> >> > with a higher order function, but that is lame!  Can't FFC treat it like
> a
> >> > linear form and use quadrature to evaluate it?  I know it isn't really a
> >> > linear form, but FFC wouldn't know the difference!  :) Maybe I am
> missing
> >> > something...
> >> >
> >> > - Shawn
> >> >
> >> > On Wed, 10 Jun 2009, Martin Sandve Alnæs wrote:
> >> >
> >> >> The norm definitions should use "inner" instead of "dot" to handle
> >> >> tensor fields as well.
> >> >>
> >> >> Martin
> >> >>
> >> >>
> >> >>
> >> >> On Wed, Jun 10, 2009 at 6:14 PM, Anders Logg<logg@xxxxxxxxx> wrote:
> >> >>>
> >> >>> On Wed, Jun 10, 2009 at 09:58:20AM -0500, Jehanzeb Hameed wrote:
> >> >>>>
> >> >>>> Thanks. So I guess that means no such facility is available in C/C++
> ?
> >> >>>
> >> >>> No, since the computation depends on the space the functions are in
> >> >>> and so the code needs to be generated. In C++, you need to define a
> >> >>> form file for the norm. Look at
> >> >>>
> >> >>>  site-packages/dolfin/norm.py
> >> >>>
> >> >>> for how to define the norms.
> >> >>>
> >> >>>
> >> >>>
> >> >>>> On Wed, Jun 10, 2009 at 2:03 AM, Anders Logg<logg@xxxxxxxxx> wrote:
> >> >>>>>
> >> >>>>> On Tue, Jun 09, 2009 at 05:11:48PM -0500, Jehanzeb Hameed wrote:
> >> >>>>>>
> >> >>>>>> Hello,
> >> >>>>>>
> >> >>>>>> Is there a builtin function in dolfin to compute L^2 or H_1 norms?
> If
> >> >>>>>> so, can you please point it out. If not, are there support
> functions
> >> >>>>>> (e.g. a Gauss Quadrature table, computation of Jacobians, etc)
> which
> >> >>>>>> can help in this?
> >> >>>>>
> >> >>>>> Yes, this is available in the DOLFIN Python interface:
> >> >>>>>
> >> >>>>>  norm(v)
> >> >>>>>
> >> >>>>> The default computes the L^2 norm. Several options are available:
> >> >>>>>
> >> >>>>>  L^2:     norm(v, 'L2')
> >> >>>>>  H^1:     norm(v, 'H1')      includes L^2 term
> >> >>>>>  H^1_0:   norm(v, 'H10')     does not include L^2 term
> >> >>>>>  H(div):  norm(v, 'Hdiv')    includes L^2 term
> >> >>>>>  H(div):  norm(v, 'Hdiv0')   does not include L^2 term
> >> >>>>>  H(curl): norm(v, 'Hcurl')   includes L^2 term
> >> >>>>>  H(curl): norm(v, 'Hcurl0')  does not include L^2 term
> >> >>>>>
> >> >>>>>
> >> >>>>> -----BEGIN PGP SIGNATURE-----
> >> >>>>> Version: GnuPG v1.4.9 (GNU/Linux)
> >> >>>>>
> >> >>>>> iEYEARECAAYFAkovWqUACgkQTuwUCDsYZdGb3gCfa2gWnzealWzkjPoRj8hf3cr/
> >> >>>>> 0EUAoJh4mpaIzRU9eCnnC+XWlupu6SV0
> >> >>>>> =so4c
> >> >>>>> -----END PGP SIGNATURE-----
> >> >>>>>
> >> >>>>> _______________________________________________
> >> >>>>> DOLFIN-dev mailing list
> >> >>>>> DOLFIN-dev@xxxxxxxxxx
> >> >>>>> http://www.fenics.org/mailman/listinfo/dolfin-dev
> >> >>>>>
> >> >>>>>
> >> >>>> _______________________________________________
> >> >>>> DOLFIN-dev mailing list
> >> >>>> DOLFIN-dev@xxxxxxxxxx
> >> >>>> http://www.fenics.org/mailman/listinfo/dolfin-dev
> >> >>>
> >> >>> -----BEGIN PGP SIGNATURE-----
> >> >>> Version: GnuPG v1.4.9 (GNU/Linux)
> >> >>>
> >> >>> iEYEARECAAYFAkov28sACgkQTuwUCDsYZdE8KQCdEI7wS27QaNw9knI2U9L+RVST
> >> >>> xeUAnRdLrrhAVzsBn6nO1b6CLEpF64ey
> >> >>> =a7iu
> >> >>> -----END PGP SIGNATURE-----
> >> >>>
> >> >>> _______________________________________________
> >> >>> DOLFIN-dev mailing list
> >> >>> DOLFIN-dev@xxxxxxxxxx
> >> >>> http://www.fenics.org/mailman/listinfo/dolfin-dev
> >> >>>
> >> >>>
> >> >> _______________________________________________
> >> >> DOLFIN-dev mailing list
> >> >> DOLFIN-dev@xxxxxxxxxx
> >> >> http://www.fenics.org/mailman/listinfo/dolfin-dev
> >> >>
> >> >
> >> _______________________________________________
> >> DOLFIN-dev mailing list
> >> DOLFIN-dev@xxxxxxxxxx
> >> http://www.fenics.org/mailman/listinfo/dolfin-dev
> >
> > -----BEGIN PGP SIGNATURE-----
> > Version: GnuPG v1.4.9 (GNU/Linux)
> >
> > iEYEARECAAYFAkov6WEACgkQTuwUCDsYZdGsogCgkGG4Q6P3KPmcgNMbNRmhGo3g
> > ewUAnitXpohiVKg7fdE4snDRe2pQ3QMU
> > =2TVq
> > -----END PGP SIGNATURE-----
> >
> > _______________________________________________
> > DOLFIN-dev mailing list
> > DOLFIN-dev@xxxxxxxxxx
> > http://www.fenics.org/mailman/listinfo/dolfin-dev
> >
> >
> _______________________________________________
> DOLFIN-dev mailing list
> DOLFIN-dev@xxxxxxxxxx
> http://www.fenics.org/mailman/listinfo/dolfin-dev
>