an encyclopedia of finite element definitions
You can find some information about how these familes are defined here
| Exterior calculus name | Cockburn–Fu name | \(H^k\) | \(\xrightarrow{\nabla}\) | \(H^{k-1}(\textbf{curl})\) | \(\xrightarrow{\nabla\times}\) | \(H^{k-1}(\text{div})\) | \(\xrightarrow{\nabla\cdot}\) | \(H^{k-1}\) |
| \(\mathcal{P}_{k}\Lambda^{r}(\Delta_d)\) | \(S_{1,k}^\unicode{0x25FA}\) | Lagrange | Nédélec (second kind) | Brezzi–Douglas–Marini | Lagrange | |||
| \(\mathcal{P}^-_{k}\Lambda^{r}(\Delta_d)\) | \(S_{2,k}^\unicode{0x25FA}\) | Lagrange | Nédélec (first kind) | Raviart–Thomas | Lagrange | |||
| \(\mathcal{Q}^-_{k}\Lambda^{r}(\square_d)\) | \(S_{4,k}^\square\) | Lagrange | Nédélec (first kind) | Q H(div) | Lagrange | |||
| \(\mathcal{S}_{k}\Lambda^{r}(\square_d)\) | \(S_{1,k}^\square\) | serendipity | serendipity H(curl) | serendipity H(div) | dPc | |||
| \(\mathcal{S}^-_{k}\Lambda^{r}(\square_d)\) | \(S_{2,k}^\square\) | serendipity | trimmed serendipity H(curl) | trimmed serendipity H(div) | dPc | |||
| \(S_{3,k}^\square\) | Tiniest tensor | Tiniest tensor H(curl) | Tiniest tensor H(div) | Lagrange |