Dear Wolfgang,
Thank you for your reply.
This problem is solved by adding
constraints.distribute (solution);
in
void MixedLaplaceProblem<dim>::solve ()
in my code.
Kind regards,
Jie
On Thursday, February 15, 2018 at 5:24:44 PM UTC+1, jie liu wrote:
>
>
> Dear all,
>
> I want to solve an 1D Poisson equation with the inhomogeneous boundary
> condition on the gradient (velocity) using the mixed FEM. The equation reads
>
>
>
> I used step-20 to implement the mixed FEM.
> Since this step cannot deal with the inhomogeneous boundary condtion on
> the gradient, I added some code of step-22.
> The changes are:
> (1) adding
> system_matrix.clear ();
> dof_handler.distribute_dofs (fe);
> DoFRenumbering::Cuthill_McKee (dof_handler);
> std::vector<unsigned int> block_component (dim+1,0);
> block_component[dim] = 1;
> DoFRenumbering::component_wise (dof_handler, block_component);
>
> {
> constraints.clear ();
> FEValuesExtractors::Vector velocities(0);
> DoFTools::make_hanging_node_constraints (dof_handler,
> constraints);
>
> VectorTools::interpolate_boundary_values (dof_handler,
> 1,
> GradientBoundary<dim>(),
> constraints,
> fe.component_mask(velocities
> )
> );
>
> }
> constraints.close ();
> of step-22 in
>
>> void MixedLaplaceProblem<dim>::make_grid_and_dofs ()
>>
> of step-20;
> (2) adding
> for (unsigned int i=0; i<dofs_per_cell; ++i)
> for (unsigned int j=i+1; j<dofs_per_cell; ++j)
> local_matrix(i,j) = local_matrix(j,i);
> cell->get_dof_indices (local_dof_indices);
>
> constraints.condense (system_matrix, system_rhs);
> of step-22 in
> void MixedLaplaceProblem<dim>::assemble_system ()
> of step-20.
>
> Pn elements are used for the solution and Pn+1 elements are used for the
> gradient.
> fe (FE_Q<dim>(degree+1), 1,
> FE_Q<dim>(degree), 1),
>
> Setting 'a' equal or not equal to zero, it works when 'b' is equal to zero
> (homogeneous Dirichlet boundary condition on the gradient).
> Specifically, the convergence order of the solution is one order higher
> than the element degree of the solution, and the convergence order of the
> gradient is equal to or one order lower than the element degree of the
> gradient.
> However, when 'b' is not equal to zero ( inhomogeneous Dirichlet boundary
> condition on the gradient), it does not work for the gradient, i.e. the
> convergence order of the solution is still one order higher than the
> element degree, but the convergence order of the gradient keeps 0.5 for
> different elements.
>
> Could anyone explain this? Thank you.
>
> Kind regards,
> Jie
>
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