M1 Mathematics, 2011-2012
MM26E Numerical Approximation of PDEs

Hervé Le Dret

$P_2$-Lagrange approximation

First of all, the $P_2$ shape functions.



A shape function corresponding to a vertex






A shape function corresponding to the middle of an edge


Next, a very coarse mesh of a disk.



Then the hat-functions of $P_2$-Lagrange approximation on this mesh.



A hat-function corresponding to an internal vertex






A hat-function corresponding to an internal middle of an edge