Element-Free Galerkin (EFG) is a numerical method used for solving partial differential equations without the need for traditional mesh elements. Instead of dividing the domain into elements, EFG employs a set of nodes and uses shape functions based on moving least squares to approximate the solution. This approach allows for greater flexibility in handling complex geometries and evolving interfaces. The EFG method is particularly useful in problems involving fracture mechanics and material failure, where the formation of cracks can complicate mesh generation. By avoiding mesh dependency, EFG can provide more accurate results and simplify the modeling process in various engineering applications.