There have been substantial developments in meshfree methods,
particle methods, and generalized finite element methods since the
mid 1990s. The growing interest in these methods is in part due to
the fact that they offer extremely flexible numerical tools and can
be interpreted in a number of ways. For instance, meshfree methods
can be viewed as a natural extension of classical finite element
and finite difference methods to scattered node configurations with
no fixed connectivity. Furthermore, meshfree methods have a number
of advantageous features that are especially attractive when
dealing with multiscale phenomena: A-priori knowledge about the
solution's particular local behavior can easily be introduced into
the meshfree approximation space, and coarse scale approximations
can be seamlessly refined by adding fine scale information.
However, the implementation of meshfree methods and their
parallelization also requires special attention, for instance with
respect to numerical integration.
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