# How to calculate the interior value of triangular element in edge (vector) finite element?

I was using an edge (vector) finite element to solve electromagnetic diffusion (two-dimensional cases). The element that I used was a triangular element. I have got the result of the finite element in each edges element of the triangular element. But I don't know how to extract the value interior the triangular element.

How can I get the value interior the triangular element (in $$x$$ and $$y$$ directions)??

• Not only for this particular case, but in general, the solution to a finite element problem is a linear combination of the basis functions $\phi_i(x)$, e.g. the approximate solution $u(x)=\sum \alpha_i\phi_i(x)$ for $\alpha_i\in\mathrm{R}$. That is basically the way how you can get the value of the solution inside the element. Sep 2 '20 at 6:26
• Yes, I know about the linear combination. Let's say I already have the basis function and used it to build the sensitivity matrices (K) and I have done the calculation of linear equation K x = b where b is the bounndary condition. I got the result of x (the magnetic field that I want to calculate using finite element) in each edges of each elements. Then, I want to calculate the magnetic field (in x dan y directions) for each elements so I calculate the value inside the element and I don't know how to do it. Maybe could you give me some example or references??@AbdullahAliSivas Sep 3 '20 at 7:41
• Can you extend your question with the particular basis you use or provide a reference? I can give you a concrete answer in that case. Sep 3 '20 at 18:26
• I use vector trinagular basis function like in this paper researchgate.net/publication/… and the math that I want to solve using finite element is magnetic filed in this paper researchgate.net/publication/… Sep 9 '20 at 3:44
• Then I want to calculate value of the magnetic field interior of triangular element to extract the value of magnet field in z and y direction like in that paper. @AbdullahAliSivas could you give me the concrete answer of that case? Sep 9 '20 at 3:48