Study guide: Introduction to finite element methods

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Approximate $f\sim x^9$ by various elements; code

Compute a mesh with $N_e$ elements, basis functions of degree $d$ , and approximate a given symbolic expression $f(x)$ by a finite element expansion $u(x) = \sum_jc_j\basphi_j(x)$ :

import sympy as sp
from fe_approx1D import approximate
x = sp.Symbol('x')

approximate(f=x*(1-x)**8, symbolic=False, d=1, N_e=4)
approximate(f=x*(1-x)**8, symbolic=False, d=2, N_e=2)
approximate(f=x*(1-x)**8, symbolic=False, d=1, N_e=8)
approximate(f=x*(1-x)**8, symbolic=False, d=2, N_e=4)

Approximate f∼x9 f\sim x^9 by various elements; code

Approximate $f\sim x^9$ by various elements; code