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Metal mesh transparent electrodes present a promising alternative to Indium-Tin Oxide (ITO) due to their adjustable period and favourable trade-off between transmittance and conductivity. In this work, a template-free, non-high temperature hybrid additive manufacturing approach of the polyacrylonitrile (PAN)/Cu core–shell structure high-resolution metal mesh flexible transparent electrode (FTE) is proposed. The electric field-driven (EFD) 3D printing method was employed to print ultra-fine lines with widths as low as 1 μm. The composite-plating process combining electroless plating and electroplating has solved the structural defects of single deposition process. The prepared FTE has an excellent conductivity down to 1 Ω/sq and 89% light transmission (at 550 nm). Its exceptional mechanical properties and environmental stability make it suitable for diverse working environments. Even after undergoing 2000 bends at a radius of 3 mm, the resistance change rate remains as low as 1.4%. The resistance exhibits an approximately 8% change rate in the acid–base environment experiments conducted over 72 h. The flexible touch screen prepared with this FTE exhibits excellent writing performance in both flat and curved working scenarios. Furthermore, the significant potential of this FTE in the field of optoelectronics is effectively demonstrated through its exceptional luminescent performance in electroluminescent devices.

Flexible and stretchable transparent electrodes are widely used in smart display, energy, wearable devices and other fields. Due to the limitations of flexibility and stretchability of indium tin oxide electrodes, alternative electrodes have appeared, such as metal films, metal nanowires, and conductive meshes. However, few of the above electrodes can simultaneously have excellent flexibility, stretchability, and optoelectronic properties. Nanofiber (NF), a continuous ultra-long one-dimensional conductive material, is considered to be one of the ideal materials for high-performance transparent electrodes with excellent properties due to its unique structure. This paper summarizes the important research progress of NF flexible transparent electrodes (FTEs) in recent years from the aspects of NF electrode materials, preparation technology and application. First, the unique advantages and limitations of various NF materials are systematically discussed. Then, we summarize the preparation technology of various advanced NF FTEs, and point out the future development trend. We also discuss the application of NFs in solar cells, supercapacitors, electric heating equipments, sensors, etc, and analyze its development potential in flexible electronic equipment, as well as problems that need to be solved. Finally, the challenges and future development trends are proposed in the wide application of NF FTEs in the field of flexible optoelectronics.

Abstract The main aim of this paper is to apply a low order nonconforming EQ1rot $\mathit{EQ}_{1}^{\mathrm{rot}}$ finite element to solve the nonlinear Schrödinger equation. Firstly, the superclose property in the broken H1 $H^{1}$-norm for a backward Euler fully-discrete scheme is studied, and the global superconvergence results are deduced with the help of the special characters of this element and the interpolation postprocessing technique. Secondly, in order to reduce computing cost, a two-grid method is developed and the corresponding superconvergence error estimates are obtained. Finally, a numerical experiment is carried out to confirm the theoretical analysis.

Abstract In this paper, a low order nonconforming mixed finite element method (MFEM) is studied with EQ1rot $EQ_{1}^{\mathrm{rot}}$ element and zero order Raviart–Thomas (R–T) element for a class of nonlinear reaction–diffusion equations. On the one hand, a priori bound is proved using Lyapunov functional, which leads to the global existence and uniqueness of the approximation solutions. Further, the superclose estimates of order O(h2) $O(h^{2})$ for original variable u in broken H1 $H^{1}$ norm and the flux p=∇u $\boldsymbol{p}=\nabla u$ in (L2)2 $(L^{2})^{2}$ norm are obtained respectively for a semi-discrete scheme. On the other hand, a linearized Crank–Nicolson fully-discrete scheme is established and the superclose estimates of order O(h2+τ2) $O(h^{2}+\tau^{2})$ are also obtained unconditionally by making full use of the special characters of the above mixed finite elements (MFEs) and two different splitting techniques, which are used to deal with the consistency errors and nonlinear terms, respectively. These approaches circumvent the restrictive condition on a time step size arising as an inverse inequality used to prove a posteriori bounds in L∞ $L^{\infty}$ norm, which is necessary for nonlinear problems for the conventional finite element analysis. What is more, the corresponding global superconvergent results are derived through interpolated postprocessing techniques. Finally, numerical results are provided to confirm the theoretical analysis. Here h is the subdivision parameter and τ is the time step.

The purpose of this article is to apply EQrot 1 nonconforming finite element(FE) to solve a generalized nonlinear Schrödinger equation. First, a new important property of EQrot 1 nonconforming FE (see (2.3) of Lemma 2 below) is proved by use ofBHXlemma and the integral identities techniques. Second, a linearized Crank-Nicolson fully discrete scheme is constructed and the superclose error estimate of orderO(h2+τ2) for original variable u in broken H1-norm is also derived by using the properties of EQrot 1 element and the splitting argument for nonlinear terms, while previous works always only obtain convergent error estimates with this element. Furthermore, the global superconvergence is arrived at by the interpolated postprocessing technique. Finally, two numerical experiments are provided to confirm the theoretical analysis. Here, h is the subdivision parameter and τ is the time step. [ABSTRACT FROM AUTHOR]