Dear Professor Wolfgang Bangerth,
Thanks the help from you and the others. The issue of discontinuous vorticity
field is resolved. Theoretically, I understand the gradient should be
discontinuous for C0 elements. However, I still want to convince myself with a
explanation. while I used Q2Q1 Taylor-Hood element, the discontinuous contour
still appear. What could be the reason for this? On the other hand, I have a
very simple FEM code using C0 elements without doing the projections. I just
simply assembly the matrix, use a Lagrangian shape function in C0 element and
solve it with a linear solver. It does give a continuous contour without doing
a projection. What could be the theoretical reason why it does not give a
discontinuous contour? Is L2 projection is necessary step while computing
gradients over elements for C0 elements?
Thank you
Best regards
David
________________________________
From: dealii@googlegroups.com <dealii@googlegroups.com> on behalf of Wolfgang
Bangerth <bange...@colostate.edu>
Sent: Thursday, January 16, 2020 12:05 AM
To: dealii@googlegroups.com <dealii@googlegroups.com>
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.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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