Study guide: Introduction to finite element methods

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Comparison with a finite difference discretization

The standard finite difference method for $-u''=2$ is $-\frac{1}{h^2}u_{i-1} + \frac{2}{h^2}u_{i} - \frac{1}{h^2}u_{i+1} = 2$

Multiply by $h$ !

The finite element method and the finite difference method are identical in this example.

(Remains to study the equations at the end points, which involve boundary values - but these are also the same for the two methods)