[firedrake] function at a point

[Onno Bokhove]

Attached, see weak form in equation (20).

xp used in equation (20) is define in equation (19).

Hope that settles the question?

You should be familiar with some of this at it also emerged in your OMAE paper!

Regarding a time discretisation: any, but just do first order at the moment!


________________________________
From: firedrake-bounces at imperial.ac.uk <firedrake-bounces at imperial.ac.uk> on behalf of David Ham <David.Ham at imperial.ac.uk>
Sent: Thursday, February 23, 2017 2:17 PM
To: firedrake
Subject: Re: [firedrake] function at a point

Hi Onno,

I'm afraid I don't think we understand what you are asking for. Can you show us the maths please?

Regards,

David

On Thu, 23 Feb 2017 at 08:07 Onno Bokhove <O.Bokhove at leeds.ac.uk<mailto:O.Bokhove at leeds.ac.uk>> wrote:

Dear Firedrake(rs),


I am considering a "standard" FEM problem with the following variables h(chi,tau) and phi(chi,tau) as function of transformed coordinate chi and time tau in chi=[0,L].


In the weak formulation, the point value h(Lp,tau), so the function value at 0<chi=Lp<L

as well as, of course, the function h(chi,tau) appear in the space integral of the weak form.

In essence, due to a transformed moving boundary this point evaluation arises.


I can formulate the detailed (nonlinear) matrix-vector FEM and its time discretisation

because after the expansion of h(chi,tau) the coefficients h_j(tau) appear

and h(Lp,tau) = h_Np(tau) for j =Np, say, such that the distinction between function

and point values disappears.


I am struggling to see how I can do this on the weak form level in firedrake.

It would work in integral form by using a delta function after introducing h(Lp,tau)

as an auxiliary scalar variable but I assume that is not available?


What is the FD-tactic here which one can employ?


Thank you and best wishes,


Onno




--
Dr David Ham
Department of Mathematics
Imperial College London
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