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In mathematics, in the area of numerical analysis, Galerkin methods are a class of methods for converting a continuous operator problem (such as a differential equation) to a discrete problem. In principle, it is the equivalent of applying the method of variation of parameters to a function space, by converting the equation to a weak formulation. Typically one then applies some constraints on the function space to characterize the space with a finite set of basis functions. The approach is usually credited to the Russian mathematician Boris Galerkin but the method was discovered by the Swiss mathematician Walther Ritz,〔"Le destin douloureux de Walther Ritz (1878-1909)", (Jean-Claude Pont, editor), Cahiers de Vallesia, 24, (2012), ISBN 978-2-9700636-5-0〕 to whom Galerkin refers. Often when referring to a Galerkin method, one also gives the name along with typical approximation methods used, such as Bubnov–Galerkin method (after Ivan Bubnov), Petrov–Galerkin method (after Georgii I. Petrov〔S. G. Mikhlin, "Variational methods in Mathematical Physics", Pergamon Press, 1964〕〔"Georgii Ivanovich Petrov (on his 100th birthday)", Fluid Dynamics, May 2012, Volume 47, Issue 3, pp 289-291, DOI 10.1134/S0015462812030015〕) or Ritz–Galerkin method〔A. Ern, J.L. Guermond, ''Theory and practice of finite elements'', Springer, 2004, ISBN 0-387-20574-8〕 (after Walther Ritz). Examples of Galerkin methods are: * the Galerkin method of weighted residuals, the most common method of calculating the global stiffness matrix in the finite element method,〔S. Brenner, R. L. Scott, ''The Mathematical Theory of Finite Element Methods'', 2nd edition, Springer, 2005, ISBN 0-387-95451-1〕〔P. G. Ciarlet, ''The Finite Element Method for Elliptic Problems'', North-Holland, 1978, ISBN 0-444-85028-7〕 * the boundary element method for solving integral equations, * Krylov subspace methods.〔Y. Saad, ''Iterative Methods for Sparse Linear Systems'', 2nd edition, SIAM, 2003, ISBN 0-89871-534-2〕 ==Introduction with an abstract problem== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Galerkin method」の詳細全文を読む スポンサード リンク
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