I think I've found a way to implement this in FEniCS.
Since all the terms with \pi_h are in the following form: b(q,v) = <q, \pi_h(u
v)>, where q, u, v are all in V_h (the space of continuous piecewise linear
functions). Thus we can take the following detour:
(1) Let FEniCS assemble the matrix A and b without the the terms with \pi_h
(2) Notice that \pi_h(u v) is in V_h, and its degrees of freedom are just
\pi_h(u v) (p_i) = u(p_i) v(p_i), where p_i are the nodes. Thus we can take the
product of the degrees of freedom of u and v, and get the new function w =
\pi_h (u v), and let FEniCS assemble the bilinear form b(q,w) = <q, w>.
(3) Use the values of step (2) to fix the matrix A and b in step (1).
It's a little complicated, but it's doable.
Best,
Chong
----- Original Message ----
From: Chong Luo <luo.ch...@yahoo.com>
To: Anders Logg <l...@simula.no>
Cc: dolfin@lists.launchpad.net
Sent: Fri, February 5, 2010 4:42:30 PM
Subject: Re: [Dolfin] Interpolation operator in UFL form file?
I'm interested in this issue, because this extra \pi_h is important to ensure
the inf-sup condition for b(q,v). If there is this \pi_h in b(q,v), then it's
easy to prove that the inf-sup condition holds, while if \pi_h is not there,
the inf-sup condition might not be true.
The formulation with this \pi_h can be found for example in Ragnar Winther's
paper "A saddle point approach to the computation of harmonic maps".
Best,
Chong
----- Original Message ----
From: Chong Luo <luo.ch...@yahoo.com>
To: Anders Logg <l...@simula.no>
Cc: dolfin@lists.launchpad.net
Sent: Wed, February 3, 2010 11:33:50 AM
Subject: Re: [Dolfin] Interpolation operator in UFL form file?
Thank you for confirming that.
May I ask is it still not implemented in fenics but might be possible in the
future, or is it simply impossible in fenics?
Best,
Chong
----- Original Message ----
From: Anders Logg <l...@simula.no>
To: Chong Luo <luo.ch...@yahoo.com>
Cc: dolfin@lists.launchpad.net
Sent: Thu, January 21, 2010 2:06:26 PM
Subject: Re: [Dolfin] Interpolation operator in UFL form file?
On Thu, Jan 21, 2010 at 11:56:53AM -0800, Chong Luo wrote:
> Let V_h be the finite element space of continuous piecewise linear functions
> defined on a mesh. Let \pi_h be the interpolation operator into V_h. Is it
> possible to include \pi_h in a UFL form file?
>
> For example, if we have a bilinear form
> b(q, v) = \int_{\Omega} q \pi_h [v \cdot u] dx
> where q, u, v are all in V_h. Is it possible to specify b(q,v) in a UFL form
> file?
>
> Thank you!
>
> Best,
> Chong
No, that's not possible.
You can do
b(q, v) = \int_{\Omega} q v \cdot \pi_h u dx
but not
b(q, v) = \int_{\Omega} q \pi_h [v \cdot u] dx
--
Anders
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