Resumen
The hierarchical reconstruction (HR) (Liu et al 2007 SIAM J. Numer. Anal. 45 2442–67) can effectively reduce spurious oscillations without local characteristic decomposition for numerical capturing of discontinuous solutions. However, there are still small remaining overshoots/undershoots in the vicinity of discontinuities. HR with partial neighbouring cells (Xu et al 2009 J. Comput. Phys. 228 2194–212) essentially overcomes this drawback for the third order case, and in the mean time further improves the resolution of the numerical solution. Extending the technique to higher order cases we observe the returning of overshoots/undershoots. In this paper, we introduce a new technique to work with HR on partial neighbouring cells, which lowers the order of the remainder of the polynomial in the current cell while maintaining the theoretical order of accuracy, essentially eliminates overshoots/undershoots for the fourth and fifth order cases and reduces the numerical cost.

Resumen
The article focuses on the possibility of virtual humans for maintenance procedures. The design of complex physical systems must accommodate the human technicians who assemble and maintain them. Technicians need instructions guaranteeing successful and safe task performance. By integrating computer-graphic human models, 3D geometric environments and a system's functional models, designers and instruction authors gain a computational tool for automating task validation. Language-level instructions are interpreted as parameterized procedures that control embodied agent models to execute these tasks and report success and failure conditions. Interpreting these instructions requires integration of spatial, visual and functional reasoning. Instructions guides one to do things one has not done before or remind of forgotten tasks, supporting ones' efforts to assemble, operate and service a multitude of technological artifacts. But no computational procedure can guarantee a particular instruction will be executed correctly or successfully. INSET: Disassembly, Sequencing.