Some historic comments on finite elements

Oden, Tinsley

doi:10.1145/41579.41592

Cited by 8 publications

(5 citation statements)

References 33 publications

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“…There are other descriptions of these historical developments in the literature; see, for example, the nice article by Oden [33], which also contains the history of the development of the mathematical theory, the review of the Courant element by Babuška [2], the short description by Taylor [43], and the longer study by Leissa [30]. An extensive "glimpse" of the literature of variational calculus can be found at the end of Volume II of Giaquinta and Hildebrandt [18].…”

Section: Discussionmentioning

confidence: 99%

From Euler, Ritz, and Galerkin to Modern Computing

Gander¹,

Wanner

2012

SIAM Rev.

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Abstract. The so-called Ritz-Galerkin method is one of the most fundamental tools of modern computing. Its origins lie in Hilbert's "direct" approach to the variational calculus of EulerLagrange and in the thesis of Walther Ritz, who died 100 years ago at the age of 31 after a long battle with tuberculosis. The thesis was submitted in 1902 in Göttingen, during a period of dramatic developments in physics. Ritz tried to explain the phenomenon of Balmer series in spectroscopy using eigenvalue problems of partial differential equations on rectangular domains. While this physical model quickly turned out to be completely obsolete, his mathematics later enabled him to solve difficult problems in applied sciences. He thereby revolutionized the variational calculus and became one of the fathers of modern computational mathematics. We will see in this article that the path leading to modern computational methods and theory involved a long struggle over three centuries requiring the efforts of many great mathematicians.

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Section: Discussionmentioning

confidence: 99%

From Euler, Ritz, and Galerkin to Modern Computing

Gander¹,

Wanner

2012

SIAM Rev.

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“…We refer to the introduction in [56] that discusses the popularity of methods based on variational formulations and weighted residuals. Thus, as encouraged therein, the quest for the design of high-resolution methods based on variational/weighted-residual formulations is active to date.…”

Section: Introductionmentioning

confidence: 99%

A high-resolution Petrov–Galerkin method for the 1D convection–diffusion–reaction problem

Nadukandi

Oñate

García

2010

Computer Methods in Applied Mechanics and Engineering

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“…Although there exist certain efforts toward the writing of the history of the FEM [84,127] and the FDM [131,193], relatively little has been done for the BEM. The present article is aimed at taking a first step toward the construction of a history for the BEM.…”

Section: Introductionmentioning

confidence: 99%