dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Thu, Jun 28, 2007 at 10:17:09PM -0400, Jake Ostien wrote:
> Anders Logg wrote:
> >On Thu, Jun 28, 2007 at 12:17:50PM -0400, Jake Ostien wrote:
> >  
> >>Garth N. Wells wrote:
> >>    
> >>>Jake Ostien wrote:
> >>>      
> >>>>Hi,
> >>>>
> >>>>If even possible, does anyone know how to view the fully 
> >>>>discontinuous solution (without the interpolation to the vertices)?
> >>>>
> >>>>        
> >>>It's not possible at the moment. The best approach for now is to 
> >>>project the discontinuous solution onto a continuous basis, and plot 
> >>>the continuous field.
> >>>      
> >>OK.  Here's a related question, I need to check that my weakly enforced 
> >>Dirichlet BCs are being properly handled.  Right now I think I need to 
> >>sample the discontinuous function along a given subset of the boundary 
> >>(which I do by iterating through all the vertices and selected solution 
> >>components by position), and manually integrate those values along the 
> >>boundary for comparison with the prescribed value, say zero for 
> >>simplicity.  Is there a better way to do this?  I am observing some 
> >>noise (oscillations) in the projected solution near the boundaries and I 
> >>am trying to figure out why.
> >>
> >>-Jake
> >>    
> >
> >Sounds like you want to compute a functional of the computed solution?
> >  
> exactly
> >Say you want to check the L2 error of the computed solution along 
> >a subset of the boundary. In FFC, do this:
> >
> >element = FiniteElement(...)
> >
> >u = Function(element)
> >u0 = Function(element)
> >
> >e = u - u0
> >
> >M = e*e*ds
> >
> >Here, u is your computed solution, u0 is a boundary condition (you
> >want u = u0 on the boundary). Then the functional M will be the L2
> >error squared along a subset of the boundary.
> >
> >Assemble the functional in DOLFIN by
> >
> >double L2error = assemble(M, mesh, sub_domain);
> >
> >  
> OK, this was easy to do (many thanks, this was much, much simpler than 
> what I was going to try and do). 
> 
> Let me add a little context to the discussion.  As an exercise, I am 
> solving a 2D Linear Elasticity problem using DG1 vector elements.  I can 
> write down the answer on paper, so I am checking how well the method 
> performs.  I am finding that the weakly enforced Dirichlet conditions, 
> u[0] = 0.0 on x = 0.0, u[1] = 0.0 on y = 0.0 are showing oscillations 
> near the domain corners (the domain is the UnitSquare(#,#).  
> Qualitatively, the solutions look good if the mesh is fine enough, but 
> quantitatively, the functional I am calculating on the fixed Dirichlet 
> boundary is not identically zero.  I get numbers around 1e-05 to 1e-07 
> for the L2 norms.  I expect to get much closer to machine precision than 
> that, but maybe that assumption is misguided?  Anyone have any thoughts 
> or advice on this? 

I can't say how small the error should be, but I wouldn't expect
machine precision.

> >where M is the form (taking two arguments u and u0) and sub_domain is
> >the sub_domain you want to integrate over.
> >
> >  
> Just for the record, I was under the (possibly false) assumption that I 
> could not use SubDomains with discontinuous functions.  I don't remember 
> where I picked that up.  Is it true?  (I could test it fairly easily if 
> necessary)

I don't know of any such limitation.

/Anders


> Thanks again,
> Jake
> >/Anders
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> >  
>