Imposing essential boundary conditions in mesh-free methods

Imposing essential boundary conditions s a key issue in mesh-free methods. The mesh-free interpolation does not verify the Kronecker delta property and, therefore, the imposition of prescribed values is not as straightforward as for the finite element method. The aim of this paper is to present a general overview on the existing technique to enforce essential boundary conditions in galerkin based mesh-free methods. Special attention is paid to the mesh-free coupling with the finite elements for the imposition to prescribed values and to methods based on a modification of the Galerkin weak form. Particular examples are used to analyze and compare their performance in different situations.