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=== CutFEM ===
The Cut Finite Element Approach was developed in 2014.<ref>{{Cite web |last=celledoni |date=2023-02-27 |title=CutFEM: Discretizing Partial Differential Equations and Geometry |url=https://ecmiindmath.org/2023/02/27/cutfem-discretizing-partial-differential-equations-and-geometry/ |access-date=2023-10-13 |website=ECMI |language=en-US}}</ref> The approach is "to make the discretization as independent as possible of the geometric description and minimize the complexity of mesh generation, while retaining the accuracy and robustness of a standard finite element method."<ref>{{Cite journal |
===Generalized finite element method===
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The [[finite difference method]] (FDM) is an alternative way of approximating solutions of PDEs. The differences between FEM and FDM are:
* The most attractive feature of the FEM is its ability to handle complicated geometries (and boundaries) with relative ease. While FDM in its basic form is restricted to handle rectangular shapes and simple alterations thereof, the handling of geometries in FEM is theoretically straightforward.<ref name=":0" /><ref name=":1">{{Cite journal |last=Topper |first=Jürgen |date=January 2005 |title=Option pricing with finite elements |url=http://dx.doi.org/10.1002/wilm.42820050119 |journal=Wilmott |volume=2005 |issue=1 |pages=84–90 |doi=10.1002/wilm.42820050119 |doi-broken-date=2024-04-07 |issn=1540-6962}}</ref>
* FDM is not usually used for irregular CAD geometries but more often for rectangular or block-shaped models.<ref>{{Cite news|url=http://www.machinedesign.com/fea-and-simulation/what-s-difference-between-fem-fdm-and-fvm|title=What's The Difference Between FEM, FDM, and FVM?|date=2016-04-18|work=Machine Design|access-date=2017-07-28|archive-date=2017-07-28|archive-url=https://web.archive.org/web/20170728024918/http://www.machinedesign.com/fea-and-simulation/what-s-difference-between-fem-fdm-and-fvm|url-status=live}}</ref>
* FEM generally allows for more flexible mesh adaptivity than FDM.<ref name=":1" />
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