Nik:
(1) trying to solve in 1D:
* I get errors of the following type:
*error: ‘class dealii::DoFAccessor<0, 1, 1, false>’ has no member
named ‘measure’
411 | re() / cell->face(face_no)->measure();* / I can make it run
by removing the calls to these functions and replace the penalty
factor which would involve them by a constant number, which according
to the output seems to work o.k. but might need further tuning of the
penalty constant (here just chosen as a constant of 100)./
Yes, that's because the measure of a face in 1d is hard to define -- what is
the measure of a point in a zero-dimensional space?
If you have a good idea for how the 'extent1/2' variables should be defined in
1d, let us know and we can patch the program so that it will also work in 1d.
(2) trying to solve for polynomial degree 0 (i.e. piecewise constant):
* /When I try to solve the default convergence_rate test case in step-74
with degree p = 0, I don't see a decrease in the L2 norm of the solution.
I tested different values for the penalty_factor for which the given
function would evaluate to 0 because of the p*(p+1) term. I tested just
removing the p*(p+1) term and also tested constants like 1000 or 0.001,
but in all cases, I got results similar to the table below, whre the L2
norm does not decrease. The table below is for the case with penalty term
/= 0.5 *(1./cell_extent_left+1./cell_extent_right);
degree = 0
| cycle | cells | dofs | L2 | L2...red.rate.log2 | H1 |
H1...red.rate.log2 | Energy |
| 0 | 16 | 16 | 3.016e-01 | - | 4.443e+00 | -
| 6.045e+00 |
| 1 | 64 | 64 | 2.273e-01 | 0.41 | 4.443e+00 | 0.00
| 5.680e+00 |
| 2 | 256 | 256 | 2.284e-01 | -0.01 | 4.443e+00 | 0.00
| 5.554e+00 |
| 3 | 1024 | 1024 | 2.368e-01 | -0.05 | 4.443e+00 | 0.00
| 5.497e+00 |
| 4 | 4096 | 4096 | 2.428e-01 | -0.04 | 4.443e+00 | 0.00
| 5.470e+00 |
| 5 | 16384 | 16384 | 2.462e-01 | -0.02 | 4.443e+00 | 0.00
| 5.456e+00 |
| 6 | 65536 | 65536 | 2.481e-01 | -0.01 | 4.443e+00 | 0.00
| 5.448e+00 |
Maybe this is well-known and it shouldn't work. However, it would be nice to
be able to solve with degree 0 because that would allow me to mimic a finite
volume type implemenation.
I don't know, and I don't know whether the people who wrote step-74 have
thought about the case. One would *hope* that the method also works for the
case p=0. A good first step would be to look at how the solution looks if you
visualize it -- that is often a good start towards debugging what is going wrong.
Best
W.
--
------------------------------------------------------------------------
Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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