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Hrennikoff's work discretizes the ___domain by using a [[Lattice (group)|lattice]] analogy, while Courant's approach divides the ___domain into finite triangular subregions to solve [[Partial differential equation#Linear equations of second order|second order]] [[elliptic partial differential equation]]s that arise from the problem of [[torsion (mechanics)|torsion]] of a [[cylinder (geometry)|cylinder]]. Courant's contribution was evolutionary, drawing on a large body of earlier results for PDEs developed by [[John William Strutt, 3rd Baron Rayleigh|Lord Rayleigh]], [[Walther Ritz]], and [[Boris Galerkin]].
The finite element method obtained its real impetus in the 1960s and 1970s by the developments of [[John Argyris|J. H. Argyris]] with co-workers at the [[University of Stuttgart]], [[Ray W. Clough|R. W. Clough]] with co-workers at [[University of California, Berkeley|UC Berkeley]], [[Olgierd Zienkiewicz|O. C. Zienkiewicz]] with co-workers [[Ernest Hinton]], [[Bruce Irons (engineer)|Bruce Irons]]<ref>{{Cite journal |last1=Hinton |first1=Ernest |last2=Irons |first2=Bruce |title=Least squares smoothing of experimental data using finite elements |journal=Strain |volume=4 |issue=3 |pages=24–27 |date=July 1968 |doi= 10.1111/j.1475-1305.1968.tb01368.x}}</ref> and others at [[Swansea University]], [[Philippe G. Ciarlet]] at the University of [[Pierre-and-Marie-Curie University|Paris 6]] and [[Richard H. Gallagher|Richard Gallagher]] with co-workers at [[Cornell University]]. Further impetus was provided in these years by available open-source finite element programs. NASA sponsored the original version of [[NASTRAN]]. UC Berkeley made the finite element programs SAP IV<ref>{{cite web |title=SAP-IV Software and Manuals |url=http://nisee.berkeley.edu/elibrary/getpkg?id=SAP4 |___location=NISEE e-Library, The Earthquake Engineering Online Archive |access-date=2013-01-24 |archive-date=2013-03-09 |archive-url=https://web.archive.org/web/20130309013628/http://nisee.berkeley.edu/elibrary/getpkg?id=SAP4 |url-status=live }}</ref> and later [[OpenSees]] widely available. In Norway, the ship classification society Det Norske Veritas (now [[DNV GL]]) developed [[SESAM (FEM)|Sesam]] in 1969 for use in the analysis of ships.<ref>{{cite book |title=Building Trust, The history of DNV 1864-2014 |author1=Gard Paulsen |author2=Håkon With Andersen |author3=John Petter Collett |author4=Iver Tangen Stensrud |date=2014 |publisher=Dinamo Forlag A/S |isbn=978-82-8071-256-1 |___location=Lysaker, Norway |pages=121, 436}}<!-- |access-date=30 June 2015 --></ref> A rigorous mathematical basis to the finite element method was provided in 1973 with the publication by [[Gilbert Strang]] and [[George Fix]].<ref>{{cite book |first1=Gilbert |last1=Strang |author-link1=Gilbert Strang |first2=George |last2=Fix |author-link2=George Fix |title=An Analysis of The Finite Element Method |url=https://archive.org/details/analysisoffinite0000stra |url-access=registration |publisher=Prentice Hall |year=1973 |isbn=978-0-13-032946-2}}</ref> The method has since been generalized for the [[numerical analysis|numerical modeling]] of physical systems in a wide variety of [[engineering]] disciplines, e.g., [[electromagnetism]], [[heat transfer]], and [[fluid dynamics]].<ref name="ZienkiewiczTaylor2013">{{cite book |author1=Olek C Zienkiewicz |author2=Robert L Taylor |author3=J.Z. Zhu |title=The Finite Element Method: Its Basis and Fundamentals |url=https://books.google.com/books?id=7UL5Ls9hOF8C |date=31 August 2013 |publisher=Butterworth-Heinemann |isbn=978-0-08-095135-5}}</ref><ref>{{cite book |first1=K.J. |last1=Bathe |author-link1= Klaus-Jürgen Bathe |title=Finite Element Procedures |publisher= Cambridge, MA: Klaus-Jürgen Bathe |year=2006 |isbn= 978-0979004902}}</ref>
==Technical discussion==
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