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

Research on the Reform of the “Dual-Mode Dual-Track” Talent Cultivation Model for Architecture Majors in Higher Vocational Colleges under the Background of “Quality Improvement and Excellent Cultivation”

Under the background of “quality improvement and excellent cultivation”, the talent training mode of higher vocational colleges has aroused the attention of the society. As the key specialty of many higher vocational colleges, the construction specialty can explore a new professional and technical talent training mode through the implementation of “dual-mode dual-track” talent training mode, and promote the further development of the construction industry. By analyzing the reasons for the reform, this paper draws the reform strategy, hoping to promote the long-term development of higher vocational colleges