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The finite element method (fem for short) is a general method for approximating the solution of boundary value problems for partial differential equations. This method derives from the Ritz (or Gelerkin) method, characteristic for the finite element method being the choice of the finite dimensional space, namely, in the case of fem the finite dimensional space, corresponding to the original space of functions, is the span of a set of finite element basis functions, as we will see in the sequel.
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