An Adaptive hp-Version of the Multilevel Particle–Partition of Unity Method

This paper is concerned with the hp-adaptive multilevel solution of second order elliptic partial differential equations using the meshfree particle–partition of unity method. The proposed refinement scheme automatically constructs new discretization points (or particles), the meshfree analogue of an adaptive h-refinement, and local approximation spaces with better local resolution, a p-refinement. The refinement process is steered with the help of an a-posteriori subdomain-type error indicator. We present results of numerical experiments in two and three space dimensions which demonstrated the overall efficiency of the proposed scheme.