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Origins, milestones and directions of the finite element method. – A personal view. (English) Zbl 0878.65090

Ciarlet, P. G. (ed.) et al., Finite element methods (part 2), numerical methods for solids (part 2). Amsterdam: North-Holland (ISBN 0-444-81794-8). Handbook of Numerical Analysis 4, 3-67 (1995).
This article presents a history of the development of the finite element method (FEM). Particularly the following items are presented: (1) Variational approaches via extremum principles, (2) Some early applications of the FEM, (3) Weighted residual approaches, (4) Non-conforming approximation in plane problems together with necessary and sufficient condition of the convergence of the FEM, (5) Higher order elements and three-dimensional analysis, (6) Fluid mechanics and non-selfadjoint problems.
For the entire collection see [Zbl 0864.65001].

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65-03 History of numerical analysis
01A60 History of mathematics in the 20th century
01A65 Development of contemporary mathematics
76M10 Finite element methods applied to problems in fluid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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