Linear elements

For linear elements, we have a more complicated situation. First, u and $\nabla u\cdot\hat{n}$ aren't constant, so we can't take them out of the integrals. A given element has two or three nodes

Nodes are sitting at non-smooth points, so $H_{ij}-\hat{H}_{ij}$ is not $\frac{1}{2}\delta_{ij}$. Instead, equation 6.13 becomes

$$c_iu_i+\hat{H}_{ij}u_j=G_{ij}(\nabla u\cdot\hat{n})_j$$ (6.16)