## The keywards {e} and {e} 1, {e} 2, {e} 3

### The keywards {e} and {e} 1, {e} 2, {e} 3

Dear Peter,

According to the 4469-th line of DefUtils.F90, it seems the keywards {e} 1, {e} 2, {e} 3 are not the components of {e}. Would you please explain a bit about the relation of {e} i to {e}?

Many thanks

Zhenwen
nickwan

Posts: 4
Joined: 02 Jun 2015, 06:40

### Re: The keywards {e} and {e} 1, {e} 2, {e} 3

Hi Zhenwen

The {e} suffix in Dirichlet conditions, for example, applies the boundary condition to the edge elements, or more generally the Hcurl conforming elements. The {e} stands for "edge". The edge degree of freedom is already a vector oriented in the direction of the edge. Usually it is not possible to apply the BCs directly to that edge. The exception being zero.

Instead one gives components in the cartesian coordinate direction. The final definition of the edge dof will then be the dot product between the edge and the given vector i.e. the projection of the given vector to the edge direction.

For standard vector valued problem solved with nodal elements the components of the vector really do make the vector. But we also need 3 degrees of freedom (dofs) in 3D while in the edge formulation only one dof is needed.

-Peter
raback

Posts: 3208
Joined: 22 Aug 2009, 11:57
Location: Espoo, Finland

### Re: The keywards {e} and {e} 1, {e} 2, {e} 3

Dear Peter,

Many thanks for your detailed explanation.

My confusion mainly came from the 4469-th line of DefUtils.F90, where the quantities of {e} 1, 2, 3 add up to the quantity of {e}. Otherwise, no problem for me to distinguish an edge element from a node element.

Just three days ago, I found the executable file Elmer.exe does not really execute the 4469-th line of DefUtils.F90 in my job, thus there is no practical problem for me. To my understanding, {e} 1, {e} 2, {e} 3 allows one to impose the cartesian boundary forces on the boundary of edge elements. VectorHelmholtz Solver seems work fine with my imposed BCs.

Thank you very much once again

Zhenwen
nickwan

Posts: 4
Joined: 02 Jun 2015, 06:40