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

## Abstract

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.

## Keywords

Mathematical solution Approximation Finite element method Variational crimes## Notes

### Acknowledgments

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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