# Re: [deal.II] discontinous contour over elements

```Bruno,

be discontinuous over C0 elements. I will give a try and do a L2 projection.
Surprisingly I did not experience it in my code before. I used standard
Lagrangian shape functions and continuous Galerkin method. I suppose dealii
used the same interpolation functions. I have to investigate why my simple code
does not have this discontinuous vorticity field.```
```
Thanks
D.

________________________________
Blais <blais.br...@gmail.com>
Sent: Thursday, January 16, 2020, 1:07 AM
To: deal.II User Group
Subject: Re: [deal.II] discontinous contour over elements

An easy way to carry the projection that Wolfgang suggested is to use an L2
projection.
The L2 projection matrix is only a mass matrix and your right hand side is
constructed by the integral of multiplication of the variable you want to
project with the test function. Generally, this matrix is very very easy to
invert. This will yield you the C0 representation of your discontinuous field
(vorticity) such that the error between your C0 projection and your original
field is minimized at the position of the gauss points.

This is a procedure we use to set the initial conditions in Lethe when the
initial condition is a complex function (for instance a Taylor-Green vortex).

On Wednesday, 15 January 2020 11:22:52 UTC-5, David Eaton wrote:
I understand the C0 element is piecewise linear across elements. However, I did
not experience the same issue in my own C++ code while I use C0 element with
the Petrov Galerkin stabilization terms. Actually, I am very confused at this
point. How could I get rid of it while using C0 element?

Thanks
D.

________________________________
Bangerth <bang...@colostate.edu>
Sent: Thursday, January 16, 2020, 12:05 AM
Subject: Re: [deal.II] discontinous contour over elements

On 1/14/20 10:04 PM, David Eaton wrote:
>
> Thank you for your suggestions. I am going to take a look at Lethe and compare
> with my implementation. In stabilized formulation, I used quadrilateral
> element, instead of P2 P1 Taylor-Hood element. The used element is only C0
> element. I also did not expect such a discontinuity between elements. Although
> I use P2 P1 Taylor-Hood element without stabilization terms, the discontinuity
> is still there. Probably I made mistakes somewhere  in setup. I also suspect
> that my solution is not converged. After taking a small relative tolerance
> 1e-8, the discontinuity still appears.

David, you did not understand what we were saying: If you use C0 elements
(think, piecewise linear) and you take derivatives to compute the vorticity,
then you automatically get a discontinuous function. That has nothing to do
with stabilization, solver tolerances, etc. It's just a consequence of the
fact that C0 elements and their shape functions have kinks and consequently
their derivatives are discontinuous.

Best
W.

--
------------------------------------------------------------------------
Wolfgang Bangerth          email:                 bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

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