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[[Image:Example_of_2D_mesh.png |thumb|2D [[FEM]] [[mesh]], the triangles are the elements, the [[vertex (graph theory)|vertices]] are the [[nodes]]{{dn|date=June 2012}} The [[finite element method]] ([[FEM]]) has been the tool of choice since its inception in the 1940's ([[Alexander Hrennikoff|Hrennikoff]], [[Richard Courant|Courant]]) for the simulation of structural mechanics. Today, the [[FEM]] is used to model a much wider range of physical phenomena. ]]
The '''extended finite element method (XFEM)''', also known as '''generalized finite element method (GFEM)''' or '''partition of unity method (PUM)''' is a numerical technique that extends the classical [[finite element method]] (FEM) approach by enriching the solution space for solutions to differential equations with discontinuous functions.
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