Examining the best-fit paradigm for FEM at element level

Himanshu Mishra*, Somenath Mukherjee

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Interestingly, an esoteric branch of pure mathematics called "functional analysis", more general and profound than variational calculus and originally developed by mathematicians, can be employed to explain clearly how the finite element machinery works. In a very abstract way, finite element results can be portrayed as "shadows" or orthogonal projections on predetermined function subspaces of the analytical results, known or unknown. Herein lies the philosophy of the finite element method. In the present work, an effort has been made to validate this important aspect of the finite element method at the element level through a particular differential equation representing a specific case of equilibrium.

Original languageEnglish (US)
Pages (from-to)573-588
Number of pages16
JournalSadhana - Academy Proceedings in Engineering Sciences
Volume29
Issue number6
DOIs
StatePublished - Jan 1 2004

Keywords

  • Function space
  • Function subspaces
  • Orthogonal projection
  • Projection theorem
  • Strain projections

ASJC Scopus subject areas

  • General

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