Adaptive Galerkin Particle Method

Adaptive procedures of a Galerkin particle method are presented. In the Galerkin particle method, the construction of shape functions and the domain integration of the weak form are entirely particle based. The stabilized conforming nodal integration is employed in the domain integration of the weak form. The Voronoi diagram used as the nodal representative domain in the stabilization of nodal integration is employed as the hierarchy for adaptive refinement. A recovery based error indicator is introduced in the adaptive analysis. Owing to the smooth shape functions in the Galerkin particle method, the stress recovery error indicator does not require any projection as was needed in the C° finite element methods.