# How do you find the gradient of the edges (error estimation) in finite elements?

I am using the finite element method and need to find the errors associated with each of my elements. I am looking for help to find the error on the edges of the triangle, preferably by hand and not code.

For this I know $$R_K(u_h)=f+\Delta u_h=1$$ as f=1 and $$u_h$$ is linear.

Now for the edges we know the following, $$R_E(u_h)=-\underline{n}_E\cdot\nabla u_h \ \text{for} \ E\in\epsilon_\omega$$ where $$\omega$$ is our domain, noting that we have Dirichlet conditions on the boundaries s.t. $$u(0)=0$$. Which is where I become stuck.

Now I am considering the unit square with 4 equally spaced nodes, see the picture. After running the FEA code I get solutions of the form $$u_h =( 0.0194, 0.0186, 0.0203, 0.0217)$$, which is plotted below.

If someone can help me with finding $$R_E(u_h)$$ that would be great!