# Projecting a vector field onto a H(div) space

I've got a uniform quadrangular mesh and for each node there's a vector quantity $u$ defined. I also have a non-aligned material interface across the mesh. Now I need that vector quantity to have a zero jump across the interface $[u\cdot n]=0$ where $n$ is the interface normal. I want to project $u$ into another space that satisfies this condition. Could I use Raviart-Thomas finite element for this case? I have never worked with RT elements and I was wondering if they could be built using an arbitrary direction instead of the element's normal (recall that the interface normal is not aligned with the elements and also that I am only interested in having $[u\cdot n]=0$, whereas the other components can have non-zero jumps) Thanks.

That said, I'm surprised that you need the condition $[u \cdot n]=0$. Typically, one would require that the flux across an interface separating two materials is continuous. The flux is usually a material constant times the vector-valued solution.
• Yes. $u$ would be my flux in this case. My problem is that my material interface is not explicitly defined. It's defined with a QUAD4 LAGRANGE element that takes 1 or 0 values. In the interface the element will have 0 and 1 as nodal values. This makes the material actually continuous, but with a strong gradient and discontinuous in the limit. May 3 '16 at 14:00
• So in that case, how exactly do you even define what it means for $[u \cdot n]$ to be zero? May 3 '16 at 15:05
• The normal can be calculated using several elements. It is true that given that the material field is actually continuous, there are no $[u \cdot n]$ and that I could just have $\nabla \cdot u$ (no body forces in my laplace equation) I wanted to enforce $[u \cdot n]$ because it would be the situation in the limit. Sorry I should have included more details in my question. May 3 '16 at 15:27