Numerical PDE HW 7

Finally more Finite Element (FE) stuff

Write out in detail and your own words a demonstration that the nodal values pictured in Table 3.7 determine a unique element in (Subscript[P, 5])(K) .

Write out in deatil and your own words a demonstration that the nodal values pictured in Table 3.7 determine functions that are continuous with continuous gradients across triangle boundaries.

Compute and plot the node functions for:

The function value at a vertex.

The normal derivative on an edge midpoint.

The two gradient values at a vertex

The three second derivative values at a vertex.