150 years anniversary of B.G. Galerkin: Bubnov-Galerkin method and its relation with other methods

This presentation is devoted to the method, which in Russian publications is often connected with names of two famous mechanicians I.G. Bubnov and B.G. Galerkin whose activity is closely related to the history of the Polytechnic Institute in Saint-Petersburg. In the international mathematical community, this method is much more recognized as the Galerkin method. Several years ago we have celebrated 100-year anniversary of the method originally presented in the paper "Rods and plates. Series in some questions of elastic equilibrium of rods and plates by B.G. Galerkin, Vestnik inzhenerov (19), 1915". Unfortunately, a note by I.G. Bubnov was published in Russian in 1913 and his very close idea did not receive such widespread publicity. In this presentation, we consider the main mathematical aspects of the method and its relation with the other approaches. We discuss the contributions of various scientists to the further development of the method, and analyze the influence that main ideas had on further development of the theory of differential equations.