SUPERCONVERGENCE OF MIXED COVOLUME METHOD ON QUADRILATERAL GRIDS FOR ELLIPTIC PROBLEMS

This paper considers the mixed covolume method for the second-order elliptic equations over quadrilaterals.Superconvergence results are established in this paper on quadrilateral grids satisfying the h^2-parallelogram condition when the lowest-order Raviart-Thomas space is employed in the mixed covolume method.The authors prove O(h^2) accuracy between the approximate velocity or pressure and a suitable projection of the real velocity or pressure in the L^2 norm.Numerical experiments illustrating the theoretical results are provided.

A STABILIZED EQUAL-ORDER FINITE VOLUME METHOD FOR THE STOKES EQUATIONS

我们为 Stokes 方程在矩形的格子上构造一个新稳定的有限体积方法。最低相等顺序的一致有限元素对(piecewise 双线性的速度和压力) 并且为速度和压力的 piecewise 常数测试空格在这个方法被采用。我们显示出这个方法的稳定性并且在 L2 标准在 H1 标准和压力为速度证明集中的第一最佳的率。另外，第二命令为在 L2 标准的速度的最佳的错误估计被导出。说明理论结果的数字实验被包括。

Subtle Side Chain Triggers Unexpected Two-Channel Charge Transport Property Enabling 80%Fill Factors and Efficient Thick-Film Organic Photovoltaics

To clearly show how important the impact of side chains on organic solar cells(OSCs)is,we designed three acceptors IDIC-CxPh(x=4,5,or 6)via subtle side-chain regulation.Despite this small change,significant distinctions were detected.IDIC-C4Ph devices achieve an optimal efficiency of 13.94%under thermal annealing,but thermal-assistant solvent-vapor annealing hugely suppresses the efficiencies to 10%.However,the C6Ph side chain endows extremely disordered stacking orientations,generating moderate efficiencies of~12.50%.Excitingly,the IDIC-C5Ph affords an unexpected two-channel p-p charge transport(TCCT)property,boosting the fill factor(FF)by up to 80.02%and efficiency to 14.56%,ranking the best among five-ring fused-ladder-type acceptors.Impressively,the special TCCT behavior of IDIC-C5Ph enables 470 nm thick-film OSC with a high FF of up to 70.12%and efficiency of 13.01%,demonstrating the great promise in fabricating largescale OSCs.

Construction and analysis of the quadratic finite volume methods on tetrahedral meshes

We construct and analyze a family of quadratic finite volume method(FVM)schemes over tetrahedral meshes.In order to prove the stability and the error estimate,we propose the minimum V-angle condition on tetrahedral meshes,and the surface and volume orthogonal conditions on dual meshes.Through the technique of element analysis,the local stability is equivalent to a positive definiteness of a 9 × 9 element matrix,which is difficult to analyze directly or even numerically.With the help of the surface orthogonal condition and the congruent transformation,this element matrix is reduced into a block diagonal matrix,and then we carry out the stability result under the minimum V-angle condition.It is worth mentioning that the minimum V-angle condition of the tetrahedral case is very different from a simple extension of the minimum angle condition for triangular meshes,while it is also convenient to use in practice.Based on the stability,we prove the optimal H^(1) and L^(2) error estimates,respectively,where the orthogonal conditions play an important role in ensuring the optimal L^(2) convergence rate.Numerical experiments are presented to illustrate our theoretical results.

Ambipolar tribotronic transistor of MoTe_(2)

Two-dimensional(2D)tribotronic devices have been successfully involved in electromechanical modulation for channel conductance and applied in intelligent sensing system,touch screen,and logic gates.Ambipolar transistors and corresponding complementary inverters based on one type of semiconductors are highly promising due to the facile fabrication process and readily tunable polarity.Here,we demonstrate an ambipolar tribotronic transistor of molybdenum ditelluride(MoTe_(2)),which shows typical ambipolar transport properties modulated by triboelectric potential.It is comprised of a MoTe_(2)transistor and a lateral sliding triboelectric nanogenerator(TENG).The induced triboelectric potential by Maxwell’s displacement current(a driving force for TENG)can readily modulate the transport properties of both electrons and holes in MoTe_(2)channel and effectively drive the transistor.High performance tribotronic properties have been achieved,including low cutoff current below 1 pA·μm^(−1)and high current on/off ratio of~103 for holes and electrons dominated transports.The working mechanism on how to achieve tribotronic ambipolarity is discussed in detail.A complementary tribotronic inverter based on single flake of MoTe_(2)is also demonstrated with low power consumption and high stability.This work presents an active approach to efficiently modulate semiconductor devices and logic circuits based on 2D materials through external mechanical signal,which has great potential in human–machine interaction,intelligent sensor,and other wearable devices.

FINITE VOLUME ELEMENT METHOD WITH LAGRANGIAN CUBIC FUNCTIONS

这份报纸在三角形的网孔上为泊松方程建立一个新有限体积元素计划。试用函数空间在三角形的分区上作为 Lagrangian 立方的有限元素空格被花，并且测试函数空格在双分区上被定义为 piecewise 常数空格。在关于三角形的网孔的一些弱状况下面，作者证明僵硬矩阵是一致地积极的明确并且是 O 的集中率(h 3 ) 在 H 1 标准。一些数字实验证实理论考虑。

CONVERGENCE OF FINITE VOLUME SCHEMES FOR HAMILTON-JACOBI EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS

我们与弱 Dirichlet 边界条件为时间依赖者 Hamilton-Jacobi 方程学习数字方法。我们首先建议抽象单调近似计划的一个新班并且得到 1/2 的集中率。然后，根据摘要，集中结果，由最新构造单调内部和边界点上的有限体积近似，我们与弱 Dirichlet 边界条件为时间依赖者 Hamilton-Jacobi 方程获得会聚的有限体积计划。最后给一些数字结果。[从作者抽象]

Monotonicity Correction for the Finite Element Method of Anisotropic Diffusion Problems

We apply the monotonicity correction to thefinite element method for the anisotropic diffusion problems,including linear and quadraticfinite elements on triangular meshes.When formulating thefinite element schemes,we need to calculate the integrals on every triangular element,whose results are the linear combination of the two-point pairs.Then we decompose the integral results into the main and remaining parts according to coefficient signs of two-point pairs.We apply the nonlinear correction to the positive remaining parts and move the negative remaining parts to the right side of thefinite element equations.Finally,the original stiffness matrix can be transformed into a nonlinear M-matrix,and the corrected schemes have the positivity-preserving property.We also give the monotonicity correction to the time derivative term for the time-dependent problems.Numerical experiments show that the correctedfinite element method has monotonicity and maintains the convergence order of the original schemes in H1-norm and L2-norm,respectively.

The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle

In this paper,we correct the finite volume element methods for diffusion equations on general triangular and quadrilateral meshes.First,we decompose the numerical fluxes of original schemes into two parts,i.e.,the principal part with a twopoint flux structure and the defective part.And then with the help of local extremums,we transform the original numerical fluxes into nonlinear numerical fluxes,which can be expressed as a nonlinear combination of two-point fluxes.It is proved that the corrected schemes satisfy the discrete strong extremum principle without restrictions on the diffusion coefficient and meshes.Numerical results indicate that the corrected schemes not only satisfy the discrete strong extremum principle but also preserve the convergence order of the original finite volume element methods.

A Finite Volume Method Based on the Constrained Nonconforming Rotated Q_(1)-Constant Element for the Stokes Problem

We construct a finite volume element method based on the constrained nonconforming rotated Q_(1)-constant element(CNRQ_(1)-P_(0))for the Stokes problem.Two meshes are needed,which are the primal mesh and the dual mesh.We approximate the velocity by CNRQ_(1)elements and the pressure by piecewise constants.The errors for the velocity in the H^(1)norm and for the pressure in the L^(2)norm are O(h)and the error for the velocity in the L^(2)norm is O(h^(2)).Numerical experiments are presented to support our theoretical results.