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The documentation on Raviart-Thomas element section 3.3.10 has some mistakes/incompleteness
-- The formula giving fh=f_h(x,y) has some typo: the last term \phi_{i_lj_l} should be replaced by \phi_{i_l}^k
-- The comments explain the orientation of the edges: from small to large indices of the vertices.
"for example we can" should be replaced by just "we"
Once the edge is oriented, we must give the orientation of the normal n_e, which is not said.
I propose to insert "Then the normal $n_e$ is oriented so as to point to the right with respect to the direction of the edge". This is coherent with the boundary convention of FreeFem : the domain is on the left, and here it means that the normal will be external on the boundary of the domain (if the boundary vertices are labeled increasingly in counterclock sense).
This choice of orientation corresponds to what I observe when I use RT0 in my FreeFem codes, with regards to the fact that according to the definition of the dof, one must have phi_i^k(m_i)\cdot n_i > 0.
If you take in the code the basis function and you take the scalar product with the normal, you see according to the sign of the result and the indices of the two vertices that the above orientation is the one that is set in FreeFem. Fig 3.35 illustrates the case i_c<i_a<i_b.
In consequence we see that the formulas for the basis functions phi_i^k in the documentation have a WRONG SIGN: there should be a minus in front of each of the three formulas.
The text was updated successfully, but these errors were encountered:
The documentation on Raviart-Thomas element section 3.3.10 has some mistakes/incompleteness
-- The formula giving
fh=f_h(x,y)
has some typo: the last term\phi_{i_lj_l}
should be replaced by\phi_{i_l}^k
-- The comments explain the orientation of the edges: from small to large indices of the vertices.$n_e$ is oriented so as to point to the right with respect to the direction of the edge". This is coherent with the boundary convention of FreeFem : the domain is on the left, and here it means that the normal will be external on the boundary of the domain (if the boundary vertices are labeled increasingly in counterclock sense).
"for example we can" should be replaced by just "we"
Once the edge is oriented, we must give the orientation of the normal
n_e
, which is not said.I propose to insert "Then the normal
This choice of orientation corresponds to what I observe when I use RT0 in my FreeFem codes, with regards to the fact that according to the definition of the dof, one must have
phi_i^k(m_i)\cdot n_i > 0
.If you take in the code the basis function and you take the scalar product with the normal, you see according to the sign of the result and the indices of the two vertices that the above orientation is the one that is set in FreeFem. Fig 3.35 illustrates the case
i_c<i_a<i_b
.In consequence we see that the formulas for the basis functions
phi_i^k
in the documentation have a WRONG SIGN: there should be a minus in front of each of the three formulas.The text was updated successfully, but these errors were encountered: