Dear Javier,
reading through the documentation of the KellyErrorEstimator, I found a
section about boundary values. It says that only Dirichlet and Neumann
boundary conditions are considered. What is the problem you observe when
you use this estimator for you adaptiv mesh?
Best,
Bärbel
--
Bärbel Janssen
Mathematisches Institut
Universität Bern
Sidlerstrasse 5, CH-3012 Bern
Tel: +41 (0)31 631 88 47
[email protected]
On Tue, 8 May 2012, Javier Muñoz wrote:
Hello Barbel, thanks for your reply.
What I'm trying to solve is a heat conduction problem in a three
dimensional cube with a hole in the middle (representing a pipe
transporting fluid, a coupled 1d advective problem).
Here is a draft of the 3d domain with the boundary indicators:
^z / /
| / /
|/ 1 /
------------------------------
| |
| |
| |
| |
| 0 <circular | 0
| hole here |
| with b.i. 3> |
| | /
| | /
| |/
------------------------------ --> x
/ 2
/
/y
+Boundary indicator 0 is for heat flux zero. Neumann boundary condition
equal to 0. In the code I left this boundary unspecified because that's
the way to define a neumann boundary value equal to zero, is that right?
+Boundary indicator 1 is for robin boundary condition. The top surface
is under convective heat flux with an external constant temperature of
25 and a convective coefficient of 1. I define this boundary in the
assembly step as:
for (; cell!=endc; ++cell)
.....
for (unsigned int face = 0; face < GeometryInfo<3>::faces_per_cell;
++face)
{
if (cell->face(face)->at_boundary()
&&
cell->face(face)->boundary_indicator() == 1)
{
fe_face_values.reinit (cell,face);
for (unsigned int q_face_point = 0; q_face_point < n_face_q_points;
++q_face_point)
{
for (unsigned int i = 0; i < dofs_per_cell; ++i)
{
for (unsigned int j = 0; j < dofs_per_cell; ++j)
{
cell_matrix (i,j) += (1 *
fe_face_values.shape_value(i,q_face_point) *
fe_face_values.shape_value(j,q_face_point) *
fe_face_values.JxW(q_face_point));
}
cell_rhs (i) += (1 * /*constant temperature*/ 25 *
fe_face_values.shape_value(i,q_face_point) *
fe_face_values.JxW(q_face_point));
}
}
}
}
.....
+Boundary indicator 3 is for robin boundary condition (the hole's
interior boundary). I define this boundary in the assembly step as
(please note how I'm asking for the values from the 1d advective
problem):
//this loop comes immediately after the previous one
for (unsigned int face = 0; face < GeometryInfo<3>::faces_per_cell;
++face)
{
if (cell->face(face)->at_boundary()
&&
cell->face(face)->boundary_indicator() == 3)
{
fe_face_values.reinit (cell,face);
for (unsigned int q_face_point = 0; q_face_point <
n_face_q_points; ++q_face_point)
{
for (unsigned int i = 0; i < dofs_per_cell; ++i)
{
for (unsigned int j = 0; j < dofs_per_cell; ++j)
{
cell_matrix (i,j) += (1 *
fe_face_values.shape_value(i,q_face_point) *
fe_face_values.shape_value(j,q_face_point) *
fe_face_values.JxW(q_face_point));
}
cell_rhs (i) += (1 *
/*solution from 1d problem using y coordinate in 3d problem*/
VectorTools::point_value (dof_handler_1d,
solution_1d,Point<1> (cell->face(face)->center()(1))) *
fe_face_values.shape_value (i,q_face_point) *
fe_face_values.JxW(q_face_point));
}
}
}
}
....
+ and finally, boundary indicator 2. This is for the bottom face of my
cube. It is defined as a Dirichlet boundary condition (constant
temperature of 10C). I think it is necessary to define at least one
Dirichlet boundary condition for the Laplace equation to be solvable, is
this right? I define it as:
std::map<unsigned int,double> boundary_values;
VectorTools::interpolate_boundary_values (dof_handler_3d,
2,
ConstantFunction<3>(10),
boundary_values);
MatrixTools::apply_boundary_values (boundary_values,
system_matrix_3d,
solution_3d,
system_rhs_3d);
So, my question would be how do I tell the Kelly Error Estimator which
are the boundaries with Neumann boundary conditions and how I specify
its values? (for the current problem I'm not using any function for
Neumann's boundaries and I actually giving them a zero value). And, do I
need to give information about the robin boundary conditions to the
Kelly Error Estimator? If so, how do I do this? I'm not using any
function.
I hope my question is a bit more clear now. Perhaps I have misunderstood
completely how to use the Kelly Error Estimator for generating adaptive
meshes.
Kind Regards
Javier Munoz
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