Conclusion

Finite elements, which first appeared in the 1950s, are undoubtedly the most widespread simulation technique, in both industrial and academic circles. For a short time in the 1990s, some thought that meshless methods would replace finite elements and become the dominant simulation technique. Today, some twenty years later, it seems unlikely that this will happen (unless a new meshless revolution takes place). Nevertheless, the research efforts of our community over these years have not been in vain. We are now able to perform increasingly complex and astonishing simulations. As a result, we understand finite elements much better, and have been able to really extend their field of applicability.

In short, meshless methods have natural areas of application, including large transformations, fragmentation, fracture, free and moving surfaces, etc., and have been shown...