Finite element method: Difference between revisions

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===Generalized finite element method===
The generalized finite element method (GFEM) uses local spaces consisting of functions, not necessarily polynomials, that reflect the available information on the unknown solution and thus ensure good local approximation. Then a [[partition of unity]] is used to “bond”"bond" these spaces together to form the approximating subspace. The effectiveness of GFEM has been shown when applied to problems with domains having complicated boundaries, problems with micro-scales, and problems with boundary layers.<ref>{{cite journal | first1=Ivo | last1=Babuška | author1-link=Ivo Babuška | first2=Uday | last2=Banerjee | first3=John E. | last3=Osborn | author3-link=John E. Osborn (mathematician) | title=Generalized Finite Element Methods: Main Ideas, Results, and Perspective | journal=[[International Journal of Computational Methods]] | date=June 2004 | issue=1 | pages= 67–103 | doi=10.1142/S0219876204000083 | volume=1}}</ref>
 
===Mixed finite element method===