Thank you very much for your reply. Of course, I meant Qn/Qn-1 not the FE
version on triaqngles.
I have now changed the constructor as follows (following step-43) (lines
290-299):
template <int dim>
MixedLaplaceProblem<dim>::MixedLaplaceProblem (const unsigned int degree)
:
degree (degree),
//fe (FE_RaviartThomas<dim>(degree), 1,
// FE_DGQ<dim>(degree-2), 1),
fe (FE_Q<dim>(degree), dim,
FE_Q<dim>(degree-1), 1),
dof_handler (triangulation)
{}
The code compiles but when I run it (dim=2, degree=2 and same with
degree=3), it produces the following error:
Number of active cells: 64
Total number of cells: 85
Number of degrees of freedom: 1539 (625+289)
--------------------------------------------------------
An error occurred in line <65> of file </mnt/dutita4/dv/jliu/Localdisk/
dealii-8.5.0/source/dofs/dof_tools_sparsity.cc> in function
void dealii::DoFTools::make_sparsity_pattern(const DoFHandlerType&,
SparsityPatternType&, const dealii::ConstraintMatrix&, bool, dealii::types::
subdomain_id) [with DoFHandlerType = dealii::DoFHandler<2>;
SparsityPatternType = dealii::BlockDynamicSparsityPattern;
dealii::types::subdomain_id
= unsigned int]
The violated condition was:
sparsity.n_rows() == n_dofs
Additional information:
Dimension 914 not equal to 1539.
Stacktrace:
-----------
#0 /mnt/dutita4/dv/jliu/Localdisk/dealii-8.5.0/lib/libdeal_II.g.so.8.5.0:
void dealii::DoFTools::make_sparsity_pattern<dealii::DoFHandler<2, 2>,
dealii::BlockDynamicSparsityPattern>(dealii::DoFHandler<2, 2> const&,
dealii::BlockDynamicSparsityPattern&, dealii::ConstraintMatrix const&,
bool, unsigned int)
#1 ./step-20: Step20::MixedLaplaceProblem<2>::make_grid_and_dofs()
#2 ./step-20: Step20::MixedLaplaceProblem<2>::run()
#3 ./step-20: main
--------------------------------------------------------
I guess that the problem is here:
BlockDynamicSparsityPattern dsp(2, 2);
dsp.block(0, 0).reinit (n_u, n_u);
dsp.block(1, 0).reinit (n_p, n_u);
dsp.block(0, 1).reinit (n_u, n_p);
dsp.block(1, 1).reinit (n_p, n_p);
dsp.collect_sizes ();
DoFTools::make_sparsity_pattern (dof_handler, dsp);
The system matrix needs to have 3x3 blocks since the block for (n_u, n_u)
no longer corresponds to a vector-valued FE space (RT) but to Qn x Qn.
Hence, I have to manually generate blocks of the form (n_u_x,n_u_x),
(n_u_x, n_u_y), etc. This would mean that I have to rewrite many parts of
the Schur complement solver, which hard codes the 2x2 block structure of
the matrix.
Now my question. Does deal.ii allow to consider Qn x Qn as an "inner"
vector-valued FE space and inject this as replacement for RTn, thereby
ending up in blocks (n_u, n_u), (n_u, n_p), and (n_p, n_u) and use Qn-1 as
replacement for DG ending up in blocks (n_u, n_p), (n_p, n_u), and (n_p,
n_p)? If this is possible, it would allow me to keep the Schur complent
implementation largely unchanged, isn't this right?
Many thanks for your help in advance.
Best,
Jie Liu
On Friday, September 15, 2017 at 6:15:44 PM UTC+2, Wolfgang Bangerth wrote:
>
> On 09/15/2017 09:51 AM, [email protected] <javascript:> wrote:
> > In the step-20, the mixed finite element method is used to solve a 2D
> > Laplace problem, where RT and DG elements are used for the velocity and
> > the pressure respectively. How does it work on spaces of Pn and Pn-1
> > elements?
> >
> > Since the velocity is a vector, the main problem becomes representing
> > the two components of the velocity both by Pn elements.
>
> Jie Liu -- I don't think I quite understand your question. Are you
> asking whether the program would work if one used Pn/Pn-1 elements
> instead of RT/DG elements?
>
> The short answer is that that's not going to work because Pn/Pn-1 are
> triangular elements. But you could use Qn/Qn-1 elements. I think that's
> what step-43 does, for example.
>
> Best
> W.
>
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> <javascript:>
> www: http://www.math.colostate.edu/~bangerth/
>
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