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From finite differences to finite elements. A short history of numerical analysis of partial differential equations. (English) Zbl 0977.65001

This paper gives a historical account of the development of the theory of numerical methods for partial differential equations. The emphasis is on stability theorems and error bounds for finite difference and finite element methods for linear problems, but there are also references to the literature for work on other methods, such as collocation and boundary element methods. The paper closes with a short review of work on the developments in linear algebra for solving the matrix equations arising from the discretization of elliptic partial differential equations.

MSC:

65-03 History of numerical analysis
01A60 History of mathematics in the 20th century
65N06 Finite difference methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N38 Boundary element methods for boundary value problems involving PDEs
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