sentences:  To calculate the deflection formula_12 minimizing the total potential energy formula_100 of the string, one writes this problem in the form 
  
  Next, one usually approximates formula_12 by some formula_105, a function in a finite-dimensional subspace of the true solution space.For example, one might let formula_105 be a continuous piecewise linear function in the energetic space, which gives the finite element method.The approximation formula_105 can be computed by solving a system of linear equations.