On 10/21/2011 03:43 AM, Lorenzo Alessio Botti wrote:
It seems that you are using HIERARCHIC basis functions with 
interior/side dofs decomposition. These basis are in general 
good for L^2 and C^0 spaces but might not be well suited for DPG.
I just guessing here, I'm not an expert of these kind of stabilized discretizations.
Why don't you simply switch to L^2 orthonormal HIERARCHIC basis 
without interior/side dofs decomposition. With this latter choice 
you can't impose C^0 continuity 
but you don't have modes with homogeneous traces.

On Oct 21, 2011, at 12:30 AM, Roy Stogner wrote:

At first glance I don't think there's a good way to avoid defining a
new element to give us side-only (not edge-only in 3D, right?) bases;
but I'm Cc'ing to libmesh-devel in case someone has an idea I've

---------- Forwarded message ----------
Date: Thu, 20 Oct 2011 17:19:42 -0500
From: Truman Ellis <truman@ices.utexas.edu>
To: Roy Stogner <roystgnr@ices.utexas.edu>
Subject: Trace Elements

I've got some degree of success with Convection-Diffusion with DPG, at least for first order. I am having an issue when it comes to second or
higher order representations of the variables, namely the trace variables. These are technically only defined on element edges, so any bubbles in
the basis never get constrained. It seems like I should define a new TRACE_HIERARCHIC element where I just remove any bubbles, but I'm not sure if
this is the most natural solution. Perhaps libMesh has some better way of implementing this like somehow prescribing edge based elements?

What do you think?

Truman Ellis

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Maybe it would help if I explained what kind of elements I need first. I basically have 2 kinds of of variables. Field variables are defined only on element interiors and thus need to be discontinuous between elements. Trace variables are defined only on element edges and thus need to be C0 continuous between two elements.

My initial approach was to define a new finite element type L2_HIERARCHIC for field variables where I just took the built in HIERARCHIC and broke the connectivity at nodes and edges. For trace variables I just used standard HIERARCHIC but only evaluated them along edges. Of course, as I explained earlier, this approach fails for second or higher order elements because of the homogeneous traces of the bubbles. The only idea I have for how to fix this is to define a new TRACE_HIERARCHIC element where I take the standard HIERARCHIC and somehow remove the basis functions which correspond to bubbles.

Lorenzo, were you recommending SZABAB elements? I'm not intimately familiar with the various element implementations we have in libMesh, but from a quick Google search it looks like they don't get any bubble modes until 4th order. Ideally I would like to push that to higher order since I would like to do hp adaptivity, but this is certainly a start.


Truman Ellis