an encyclopedia of finite element definitions

De Rham families

You can find some information about how these familes are defined here

Exterior calculus nameCockburn–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