M1 Mathematics, 2011-2012
MM26E Numerical Approximation of PDEs
Hervé Le Dret
$P_3$-Lagrange approximation
The $P_3$ shape functions.
A shape function corresponding to a vertex
A shape function corresponding to a point located at one third of an edge
The shape function corresponding to the center of gravity, also called a bubble due to the shape of its graph
Note that all these graphs are drawn using the FreeFem++ software to construct $P_1$ approximations of the polynomials on a fine mesh of the triangle, then the medit software (bottom of the page) to visualize the graphs in 3d, hence the faceted aspect which reflects the underlying fine mesh. In real life, these graphs are smooth. See also the images included in the class notes, made with Grapher (Mac OS X).
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