Classification and Overview of Meshfree Methods

This paper gives an overview over Meshfree Methods. Starting point is an extended and modified classification of Meshfree Methods due to three aspects: The construction of a partition of unity, the choice of an approximation either with or without using an extrinsic basis and the choice of test functions, resulting into a collocation, Bubnov-Galerkin or Petrov-Galerkin Meshfree Method. Most of the relevant Meshfree Methods are described taking into account their different origins and viewpoints as well as their advantages and disadvantages. Typical problems arising in meshfree methods like integration, treatment of essential boundary conditions, coupling with mesh-based methods etc.~are discussed. Some valuing comments about the most important aspects can be found at the end of each section. This text was revised in 2004