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Abstract. This paper presents an arbitrary order locking-free numerical scheme for linear elasticity on general polygonal/polyhedral partitions by using weak Galerkin (WG) finite element methods. Like other WG methods, the key idea for the linear elasticity is to introduce discrete weak strain and stress tensors which are defined and computed by solving inexpensive local problems on each element. Such local problems are derived from weak formulations of the corresponding differential operators through integration by parts. Locking-free error estimates of optimal order are derived in a discrete H 1 -norm and the usual L 2 -norm for the approximate displacement when the exact solution is smooth. Numerical results are presented to demonstrate the efficiency, accuracy, and the locking-free property of the weak Galerkin finite element method.

Abstract. A weak Galerkin (WG) finite element method for solving the stationary Stokes equations in two-or three-dimensional spaces by using discontinuous piecewise polynomials is developed and analyzed. The variational form we considered is based on two gradient operators which is different from the usual gradient-divergence operators. The WG method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape regularity. Optimal-order error estimates are established for the corresponding WG finite element solutions in various norms.Numerical results are presented to illustrate the theoretical analysis of the new WG finite element scheme for Stokes problems.

Flow-induced translocation of linear and ring polymers is studied by using a combination of multiparticle collision dynamics and molecular dynamics. The results show that both end capture and fold capture are present in the capture process of linear chains in weak flows, whereas fold capture becomes dominant in strong flows, resulting in similar behavior for the linear and ring chains in the strong flow regime. For narrow channels, the critical flux decreases with the increase of channel size, which is qualitatively consistent with the prediction by Wu et al.; for large channel sizes (which are still smaller than the polymer size), the critical flux is independent of channel size, in agreement with an earlier prediction by de Gennes et al. The presence of these two scaling regimes indicates that the confined blob exhibits a crossover from free draining to nondraining as the channel size increases. Moreover, we found that the conformation of the polymer exhibits a flow-induced coil–compact–stretch transition, and the transition does not appear to be first order. In addition, we observed that the monomers far from the channel and in the channel exhibit independent dynamics.

This article presents a conforming discontinuous Galerkin (conforming DG) scheme for second order elliptic equations on rectangular partitions. The new method is based on DG finite element space and uses a weak gradient arising from local Raviart Thomas space for gradient approximations. By using the weak gradient and enforcing inter-element continuity strongly, the scheme maintains the simple formulation of conforming finite element method while have the flexibility of using discontinuous approximations. Hence, the programming complexity of this new conforming DG scheme is significantly reduced compared to other existing DG methods. Error estimates of optimal order are established for the corresponding conforming DG approximations in various discrete Sobolev norms. Numerical results are presented to confirm the developed convergence theory.

In this article, a new weak Galerkin mixed finite element method is introduced and analyzed for the Helmholtz equation with large wave numbers. The stability and well‐posedness of the method are established for any wave number k without mesh size constraint. Allowing the use of discontinuous approximating functions makes weak Galerkin mixed method highly flexible in term of little restrictions on approximations and meshes. In the weak Galerkin mixed finite element formulation, approximation functions can be piecewise polynomials with different degrees on different elements and meshes can consist elements with different shapes. Suboptimal order error estimates in both discrete H1 and L2 norms are established for the weak Galerkin mixed finite element solutions. Numerical examples are tested to support the theory.

Artificial intelligence technology is an important transformative force for teaching innovation in the intelligent era. It is being widely used in American school teaching, including the design of intelligent tutoring systems to achieve precise problem solving, the machine learning technology to ensure personalized activity design, the creation of intelligent virtual reality to promote classroom teaching contextualization, and the development of intelligent evaluation systems to ensure the scientific evaluation of capabilities. In the process of advancing the teaching and application of artificial intelligence technology, the United States has built a linkage mechanism of federal leadership, university follow-up, and social collaboration and implemented the smart technology in school teaching and professors’ academic governance. This paper is aimed at studying the professors’ academic governance of American research universities by Internet data mining, historical analysis method, documentary method, survey method, and other methods. Professors’ academic governance is a vital part of the modern university system that causes the institutional reform of the internal governance structure of modern universities. The United States is a powerful country in higher education, and professors in American research universities have always participated in university academic governance for centuries. By studying the definition, history, and development and mode of operation of professors’ academic governance in American research universities, the results indicate a clear division of power and responsibility between the professors and administrators based on an artificial intelligence decision system in American research universities. Also, there is a good communication platform based on artificial intelligence environment for professors to discuss their opinions on academic affairs. Third, professors exercise academic power under the guarantee of diversified guaranteed systems based on the artificial intelligence evaluation system and the ideology of mutual respect based on the artificial intelligence management and service system. Studying the application of artificial intelligence techniques in operating mode and enlightenment of professors’ academic governance in an American research university is of great significance to promote the construction of other modern universities’ professors’ academic governance system.

In this article, we analyze convergence and supercloseness properties of a class of weak Galerkin (WG) finite element methods for solving second-order elliptic problems. It is shown that the WG solution is superclose to the Lagrange interpolant using Lobatto points. This supercloseness behavior is obtained through some newly designed stabilization terms. A postprocessing technique using polynomial preserving recovery (PPR) is introduced for the WG approximation. Superconvergence analysis is performed for the PPR recovered gradient. Numerical examples are provided to illustrate our theoretical results. K E Y W O R D Ssecond-order elliptic equation, polynomial preserving recovery, supercloseness, superconvergence, weak Galerkin method Numer Methods Partial Differential Eq. 2018;34:317-335.wileyonlinelibrary.com/journal/num