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Smoothed finite element method
Smoothed Finite Element methods (S-FEM) 〔Liu, G.R., 2010 ''Smoothed Finite Element Methods'', CRC Press, ISBN 978-1-4398-2027-8.〕 are a particular class of numerical simulation algorithms for the simulation of physical phenomena. It was developed by combining meshfree methods with the finite element method. S-FEM are applicable to solid mechanics as well as fluid dynamics, but so far mainly applied for solid mechanics problems.
==Description==
The essential idea in the S-FEM is to use a finite element mesh (in particular triangular mesh) to construct numerical models of good performance. This is achieved by modifying the compatible strain field, or construct a strain field using only the displacements, hoping a Galerkin model using the modified/constructed strain field can deliver some good properties. Such a modification/construction can be performed within elements but more often beyond the elements (meshfree concepts): bring in the information from the neighboring elements. Naturally, the strain field has to satisfy certain conditions, and the standard Galerkin weakform needs to be modified accordingly to ensure the stability and convergence.
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