Linear Algebra and Its Applications · Problem 6.5.4

Computations with Matrices — Gilbert Strang

Mathematics · finite-element-method

Problem

Solve

-u'' = 2

with a single hat function, but place its node at

x = \frac{1}{4}

instead of

x = \frac{1}{2}

. (Sketch this function

V_1

.) With boundary conditions

u(0) = u(1) = 0

, compare the finite element approximation with the true

u = x - x^2