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I was not able to find the origin of the name Petrov in the Petrov-Galerkin method for the numerical approximation of PDEs.

Wikipedia refers to a certain Alexander G. Petrov, but it is still not clear who he was: on the Internet I found two persons called Alexander G. Petrov, both born during the 40's, but I think that the Petrov I am looking for should be born before, since Boris Galerkin lived in 1871-1945.

Can you suggest me any bibliographic resource to consult?

[EDIT: The Wikipedia page I was referring to now contains the correct name of Petrov]

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2 Answers 2

up vote 15 down vote accepted

The Petrov you are looking for is: Georgii Ivanovich Petrov (1912-1987), biographies are here and here and here.

I quote from the third biography:

G.I. Petrov was a prominent Russian scientist in the field of aerodynamics, gasdynamics, and space research. Even his first studies connected with the investigation of viscous laminar flows attracted the attention of the scientific community. In studying these problems Petrov not only was the first who applied the Galerkin method but also inventively advanced it. It was M.V. Keldysh who noted that they greatly advance the research in the field of fluid flow stability and for that reason the Galerkin method is now justly called the Galerkin-Petrov method.

The key reference is:

G. I. Petrov, Application of the method of Galerkin to a problem involving the stationary flow of a viscous fluid, Prikl. Matem. Mekh. 4, 3 (1940).

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Thank you very much for the detailed answer! – Paglia Oct 10 '13 at 15:52

I've recently found a very interesting SIAM review article [1] regarding the history of the Petrov-Galerkin method. The figure of G.I. Petrov seems to have contributed with a simple, but significant improvement to the Galerkin method:

In Russia, Petrov [2] proposed to use approximation spaces different from the test spaces, which led to the now-called Petrov–Galerkin family of methods.

I highly suggest the reading of [1], since the history of the Petrov-Galerkin method is particularly thrilling!

[1] Gander, M.J., and Wanner, G., "From Euler, Ritz, and Galerkin to Modern Computing", SIAM Review 54.4 (2012), pp. 627-666.

[2] G. I. Petrov, "Application of Galerkin’s method to the problem of stability of flow of a viscous fluid", J. Appl. Math. Mech., 4 (1940), pp. 3–12 (in Russian).

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