Galerkin Meshfree Methods: A Review and Mathematical Implementation Aspects

Abstract

Galerkin meshfree approaches are emerging in the field of numerical methods, which attracted the attention towards moving beyond finite element and finite difference methods. As compare to conventional mesh based finite element methods, the Galerkin meshfree methods i.e. element free Galerkin method, Local Petrov–Galerkin method, natural element method, radial point interpolation method exhibits some advantages in solution of multi-physics problem, large deformation problems, crack growth analysis due to its potential with handling variety of field behaviour. However, imposition of essential boundary conditions and nodal integration are major difficulties in Galerkin meshfree methods, this work also suggest methods for imposition of essential boundary conditions and some accurate numerical integration techniques for nodal integration. This paper gives systematic reviews and mathematical implementation aspects about Galerkin meshfree methods and its application in engineering problems i.e. structural, heat transfer, fluid dynamics and electromagnetics.