A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

Implication of global warming on air-conditioned office buildings in Australia

With the accelerated trend of global warming, the thermal behavior of existing buildings, which were typically designed based on current weather data, may not be able to cope with the future climate. This paper quantifies, through computer simulations, the increased cooling loads imposed by potential global warming and probable indoor temperature increases due to possible undersized air-conditioning system. It is found from the sample office building examined that the existing buildings would generally be able to adapt to the increasing warmth of 2030 year Low and High scenarios projections and 2070 year Low scenario projection. However, for the 2070 year High scenario, the study indicates that the existing office buildings, in all capital cities except for Hobart, will suffer from overheating problems. When the annual average temperature increase exceeds 2°C, the risk of current office buildings subjected to overheating will be significantly increased. For existing buildings which are designed with current climate condition, it is shown that there is a nearly linear correlation between the increase of average external air temperature and the increase of building cooling load. For the new buildings, in which the possible global warming has been taken into account in the design, a 28-59% increase of cooling capacity under 2070 High scenario would be required to improve the building thermal comfort level to an acceptable standard.

Property cash flow studies : focusing on model consistency and data accuracy

The high degree of variability and inconsistency in cash flow study usage by property professionals demands improvement in knowledge and processes. Until recently limited research was being undertaken on the use of cash flow studies in property valuations but the growing acceptance of this approach for major investment valuations has resulted in renewed interest in this topic. Studies on valuation variations identify data accuracy, model consistency and bias as major concerns. In cash flow studies there are practical problems with the input data and the consistency of the models. This study will refer to the recent literature and identify the major factors in model inconsistency and data selection. A detailed case study will be used to examine the effects of changes in structure and inputs. The key variable inputs will be identified and proposals developed to improve the selection process for these key variables. The variables will be selected with the aid of sensitivity studies and alternative ways of quantifying the key variables explained. The paper recommends, with reservations, the use of probability profiles of the variables and the incorporation of this data in simulation exercises. The use of Monte Carlo simulation is demonstrated and the factors influencing the structure of the probability distributions of the key variables are outline. This study relates to ongoing research into functional performance of commercial property within an Australian Cooperative Research Centre.