Finite Elements

• Common choice for the bases are the hat functions from Chapter 5.
• Hat functions only nonzero at two adjacent intervals
• Integration is local
• Second-order accuracy still maintained if coefficient functions replaced with interval endpoint average
• spatially localized contributions to the matrices = finite element method

Demo 10.6.4

c = x -> x^2;
q = x -> 4;
f = x -> sin(pi*x);
x,u = FNC.fem(c,q,f,0,1,50);
plot(x,u,label="",
    xaxis=(L"x"),yaxis=(L"u"),title="Solution by finite elements")