A unified study of continuous and discontinuous Galerkin methods

A unified study is presented in this paper for the design and analysis of different finite element methods(FEMs), including conforming and nonconforming FEMs, mixed FEMs, hybrid FEMs, discontinuous Galerkin(DG) methods, hybrid discontinuous Galerkin(HDG) methods and weak Galerkin(WG) methods.Both HDG and WG are shown to admit inf-sup conditions that hold uniformly with respect to both mesh and penalization parameters. In addition, by taking the limit of the stabilization parameters, a WG method is shown to converge to a mixed method whereas an HDG method is shown to converge to a primal method. Furthermore,a special class of DG methods, known as the mixed DG methods, is presented to fill a gap revealed in the unified framework.     

Robust a Simulation for Shallow Flows with Friction on Rough Topography

In this paper, we propose a robust finite volume scheme to numerically solve the shallow water equations on complex rough topography. The major difficulty of this problem is introduced by the stiff friction force term and the wet/dry interface tracking. An analytical integration method is presented for the friction force term to remove the stiffness. In the vicinity of wet/dry interface, the numerical stability can be attained by introducing an empirical parameter, the water depth tolerance, as extensively adopted in literatures. We propose a problem independent formulation for this parameter, which provides a stable scheme and preserves the overall truncation error of $\mathbb{O}$∆$x^3$. The method is applied to solve problems with complex rough topography, coupled with $h$-adaptive mesh techniques to demonstrate its robustness and efficiency.     

Deep-Red and Near-Infrared Iridium Complexes with Fine-Tuned Emission Colors by Adjusting Trifluoromethyl Substitution on Cyclometalated Ligands Combined with Matched Ancillary Ligands for Highly Efficient Phosphorescent Organic Light-Emitting Diodes

Six novel Ir(C^N)₂(L^X)-type heteroleptic iridium complexes with deep-red and near-infrared region (NIR)-emitting coverage were constructed through the cross matching of various cyclometalating (C^N) and ancillary (LX) ligands. Here, three novel C^N ligands were designed by introducing the electron-withdrawing group CF₃ on the ortho (o-), meta (m-), and para (p-) positions of the phenyl ring in the 1-phenylisoquinoline (piq) group, which were combined with two electron-rich LX ligands (dipba and dipg), respectively, leading to subsequent iridium complexes with gradually changing emission colors from deep red (≈660 nm) to NIR (≈700 nm). Moreover, a series of phosphorescent organic light-emitting diodes (PhOLEDs) were fabricated by employing these phosphors as dopant emitters with two doping concentrations, 5% and 10%, respectively. They exhibited efficient electroluminescence (EL) with significantly high EQE values: >15.0% for deep red light0 (λ_max = 664 nm) and >4.0% for NIR cases (λ_max = 704 nm) at a high luminance level of 100 cd m⁻². This work not only provides a promising approach for finely tuning the emission color of red phosphors via the easily accessible molecular design strategy, but also enables the establishment of an effective method for enriching phosphorescent-emitting molecules for practical applications, especially in the deep-red and near-infrared region (NIR).     

An extended Galerkin analysis for elliptic problems

A general analysis framework is presented in this paper for many different types of finite element methods(including various discontinuous Galerkin methods). For the second-order elliptic equation-div(α▽u) = f, this framework employs four different discretization variables, uh, p_h, uhand p_h, where uh and phare for approximation of u and p =-α▽u inside each element, and uhand phare for approximation of the residual of u and p·n on the boundary of each element. The resulting 4-field discretization is proved to satisfy two types of inf-sup conditions that are uniform with respect to all discretization and penalization parameters. As a result, many existing finite element and discontinuous Galerkin methods can be analyzed using this general framework by making appropriate choices of discretization spaces and penalization parameters.