Hi there,
can anybody tell me what COMSOL means by the word "node" in contrast to "vertex" or "degree of freedom" when it comes to the discretization? I have read
www.comsol.com/support/knowledgebase/875/
but am slightly confused about the fact that for linear elements both in 2D and 3D the number of nodes is smaller than the number of elements.
Let's assume we have only one dependend variable. Then the number of DOFs should equal the number of nodes, right?
Furthermore let's assume that we have linear Lagrange elements in 2D based on a triangle mesh. This means that the nodes coincide with the vertices of the triangle mesh. As each triangle has 3 vertices which are shared between surrounding triangles, I would have expected that we end up with about the same number of nodes as we have triangles.
Why does the knowledge base entry above then state the formula
(#nodes) = 0.5 * (#elements)
and even
(#nodes) = 0.3 * (#elements) for the 3D case?
How can there be less nodes/vertices than elements/triangles?
What is the relation between a "node" and a "vertex"?
Is it true that every DOF also is a node and that DOFs merely are collections of nodes with respect to the particular dependent variables?
I'm a bit confused here. I know my FEM theory from maths lectures at university, but it seems as if COMSOL uses the notions of "nodes", "vertices" and "DOFs" slightly differently.
Thanks a lot in advance,
Joerg
can anybody tell me what COMSOL means by the word "node" in contrast to "vertex" or "degree of freedom" when it comes to the discretization? I have read
www.comsol.com/support/knowledgebase/875/
but am slightly confused about the fact that for linear elements both in 2D and 3D the number of nodes is smaller than the number of elements.
Let's assume we have only one dependend variable. Then the number of DOFs should equal the number of nodes, right?
Furthermore let's assume that we have linear Lagrange elements in 2D based on a triangle mesh. This means that the nodes coincide with the vertices of the triangle mesh. As each triangle has 3 vertices which are shared between surrounding triangles, I would have expected that we end up with about the same number of nodes as we have triangles.
Why does the knowledge base entry above then state the formula
(#nodes) = 0.5 * (#elements)
and even
(#nodes) = 0.3 * (#elements) for the 3D case?
How can there be less nodes/vertices than elements/triangles?
What is the relation between a "node" and a "vertex"?
Is it true that every DOF also is a node and that DOFs merely are collections of nodes with respect to the particular dependent variables?
I'm a bit confused here. I know my FEM theory from maths lectures at university, but it seems as if COMSOL uses the notions of "nodes", "vertices" and "DOFs" slightly differently.
Thanks a lot in advance,
Joerg