Galerkin Method
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. Often when referring to a Galerkin method,S one also gives the name along with typical approximation methods used, such as Bubnov-Galerkin method (after Ivan Bubnov), Petrov–Galerkin method (after Alexander G. Petrov) or Ritz–Galerkin method (after Walther Ritz).
The approach is credited to the Russian mathematician Boris Galerkin.
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,
- Boundary element method for solving integral equations
- Krylov subspace methods
Read more about Galerkin Method: Analysis of Galerkin Methods
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