Global superconvergence of the lowest order mixed finite element on mildly structured meshes

In this paper, we develop global superconvergence estimates for the lowest order Raviart--Thomas mixed finite element method for second order elliptic equations with general boundary conditions on triangular meshes, where most pairs of adjacent triangles form approximate parallelograms. In particular, we prove the $L^{2}$-distance between the numerical solution and canonical interpolant for the vector variable is of order $1+\rho$, where $\rho\in(0,1]$ is dependent on the mesh structure. By a cheap local postprocessing operator $G_{h}$, we prove the $L^{2}$-distance between the exact solution and the postprocessed numerical solution for the vector variable is of order $1+\rho$. As a byproduct, we also obtain the superconvergence estimate for Crouzeix--Raviart nonconforming finite elements on triangular meshes of the same type.Comment: 24 pages, 5 figure

Educational process modelling with workflow and time Petri nets : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Computer Science at Massey University, Palmerston North, New Zealand

The research presented in this thesis describes how to use workflow management technology to model educational processes with a time axis. As workflow management technology has been widely used in modelling business processes, it has the potential to model educational processes. Based upon the components of workflow, educational processes and business processes have many common features such that educational processes can be modelled with workflow management technology. In addition, owing to the importance of the time component in processes, time Petri nets have been chosen as the design language for the modelling of the educational processes. The notation of time Petri nets has been illustrated in this thesis for the educational process. In this thesis, three different educational processes have been presented and modelled with workflow management technology as well as with time Petri nets individually. Furthermore, the architecture of the educational process management system has been constructed by adopting the reference model from the Workflow Management Coalition. To show the validity of using workflow management technology in the education domain, a sub-process of an educational process has been modelled and developed with certain developing techniques. It provides the potential research direction for further research on the modelling of educational process with workflow technology associated with a time component

Numerical Investigation of Evaporation Induced Self-Assembly of Sub-Micron Particles Suspended in Water

Self-assembly of sub-micron particles suspended in a water film is investigated numerically. The liquid medium is allowed to evaporate leaving only the sub-micron particles. A coupled CFD-DEM approach is used for the simulation of fluid-particle interaction. Momentum exchange and heat transfer between particles and fluid and among particles are considered. A history dependent contact model is used to compute the contact force among sub-micron particles. Simulation is done using the open source software package CFDEM which basically comprises of two other open source packages OpenFOAM and LIGGGHTS. OpenFOAM is a widely used solver for CFD related problems. LIGGGHTS, a modification of LAMMPS, is used for DEM simulation of granular materials. The final packing structure of the sub-micron particles is discussed in terms of distribution of coordination number and radial distribution function (RDF). The final packing structure shows that particles form clusters and exhibit a definite pattern as water evaporates away