Accurate gradient computations at interfaces using finite element methods

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea from \cite{wheeler1974galerkin}. For 2D interface problems, the idea is to introduce a small tube near the interface and introduce the gradient as part of unknowns, which is similar to a mixed finite element method, except only at the interface. Thus the computational cost is just slightly higher than the standard finite element method. We present rigorous one dimensional analysis, which show second order convergence order for both of the solution and the gradient in 1D. For two dimensional problems, we present numerical results and observe second order convergence for the solution, and super-convergence for the gradient at the interface

Two Essays on the Microstructure of the Housing Market: Agents\u27 Diffused Effort and Sellers\u27 Behavior Bias

For the first essay, we generalize the classic Williams [1998 RFS] brokerage model by introducing the diffused effort. That is, the agent can cross-utilize effort spending on one listing to another one. Besides, the agent can manage heterogeneous housing assets. One counterintuitive finding in Williams’ paper is the absence of the agency problem. As a special case in our model, we recover the agency problem. We examine the positive externality due to the diffused effort and show that it depends on the agent’s inventory size. Hence there exists a trade-off between agents’ effort spending on existing listings and on finding a new listing. For the second essay, we model a home seller’s pricing decision under a generally defined prospect value function. We show a simple disposition effect is caused by reference dependence, but it only exists when the agent is risk neutral. Diminishing sensitivity will lead to a two-way disposition effect by generating a local reverse disposition effect, a range in which the seller’s asking price decreases with increasing potential loss. Loss aversion tends to magnify the disposition effect and hence mitigates the reverse disposition effect. One direct implication is that acclaimed tests on loss aversion such as Genesove and Mayer [2001] and Pope and Schweitzer [2011] are likely invalid. We present evidence consistent with the model by using multiple listing service data from Virginia. Our findings suggest that studies which predominantly focus on a one-way disposition effect can be overly simplistic and misleading as it depends on the strong assumption of risk neutrality

The Main Body and Legal Basis of American Graduate Degree Awarding Authority

The right to confer postgraduate degrees is involved a key measure to universities and its students. Nations in the world pay a very high attention to postgraduate education and play it core role. As we known, U.S. has rich resources and great influences in the field of higher education worldwide. And there are many students from all over the world to enroll American universities to study for master or doctor degree. Although the degree is divided into curriculum and paper degree, the quality of both are strictly regulated and guaranteed in the United States. The main body has become different types of universities and diversity pattern in the course of developing. The right to award degree was struggled by universities in the development of history, and it is a part of its charter. In the process, the legitimacy of awarding degree gradually was established. As so far, it is known as an important measure for the development of universities and students. There are different bodies of the right to grant graduate degrees in American universities, and the methods of obtaining graduate degrees are also different. How to ensure that the right to confer university degrees is not affected by the government and its actions? This paper will explicit from the point view of legal basis