Concepts of Solution and the Finite Element Method: a Philosophical Take on Variational Crimes

  • Nicolas FillionEmail author
  • Robert M. Corless
Research Article


Despite being one of the most dependable methods used by applied mathematicians and engineers in handling complex systems, the finite element method commits variational crimes. This paper contextualizes the concept of variational crime within a broader account of mathematical practice by explaining the tradeoff between complexity and accuracy involved in the construction of numerical methods. We articulate two standards of accuracy used to determine whether inexact solutions are good enough and show that, despite violating the justificatory principles of one, the finite element method nevertheless succeeds in obtaining its legitimacy from the other.


Mathematical solution Approximation Finite element method Variational crimes 



We would like to thank [removed for review]. We would also like to thank the two reviewers who made valuable suggestions.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of PhilosophySimon Fraser UniversityBurnabyCanada
  2. 2.Department of Applied MathematicsWestern UniversityLondonUK

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