We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the ...corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal, the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method.
In this paper, a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed, based on a ...type of superconvergence result of the eigenfunction approximation. Its efficiency and reliability are proved by both theoretical analysis and numerical experiments.
•Propose a linearized Crank–Nicholson finite element method and derive an optimal L2 error estimate.•Employ the curl-conforming nature of the Nédelec element makes the numerical solution exactly ...divergence-free at a discrete level.•The linearized stability analysis for the numerical error function yields the full order L2 error estimate via an L∞ a-priori assumption at the previous time steps.•Present some numerical examples to show that the mesh condition is important.
In this paper, we study and analyze a second order numerical scheme for Maxwell’s equations with nonlinear conductivity, using the Nédelec Finite Element Method (FEM). A purely explicit treatment of the nonlinear term greatly simplifies the computational effort, since we only need to solve a constant-coefficient linear system at each time step. The curl-conforming nature of the Nédelec element assures its divergence-free property. In turn, we present the linearized stability analysis for the numerical error function to obtain an optimal L2 error estimate. In more details, an O(τ2+hs) error estimate in the L2 norm yields the maximum norm bound of the numerical solution, so that the convergence analysis could be carried out at the next time step. A few numerical examples in the transverse electric (TE) case in two dimensional spaces are also presented, which demonstrate the efficiency and accuracy of the proposed numerical scheme.
Using the unique micro-data of industrial enterprises' Nitrogen oxides (NOx) and Sulfur oxides (SOx) emissions covering 58,725 enterprise-year observations, this paper investigates how digitalization ...affect energy efficiency. The empirical results show that regional digitalization can significantly promote the improvement of energy efficiency of industrial enterprises. Specifically, the result of PSM-DID method indicates that the impact of digitalization on energy efficiency is significantly enhanced by the “National innovative pilot cities” policy, while the dynamic result validates the continuity of industrial enterprises' energy efficiency. Moreover, regional digitalization has superior impact on enterprises within eastern region enterprises, the manufacturing sector, and with elevated liquidity and profitability levels. Finally, moderating effect suggests that technological innovation expand the positive impact of digitalization on enterprises’ energy efficiency. This study confirms regional digitalization can promote the energy efficiency of Chinese industrial enterprises, providing the policy suggestions to the energy transition in China.
•Measure the regional digitalization level of Prefecture-level city and the energy efficiency at Industrial enterprise-level.•Findings demonstrated that digitalization increases energy efficiency.•The impact of digitalization on energy efficiency can be enhanced by the “National innovative pilot cities” policy.•Technological innovation expands the positive impact of digitalization on enterprises' energy efficiency.
This study investigates the relationship between climate policy uncertainty (CPU) risk and the volatility of sovereign bond return (SBV) in 43 economies from 2012 to 2021. It also innovatively ...examines how the volatility and asymmetry of CPU affect SBV. The study utilizes the GARCH-MIDAS model to handle mixed-frequency data and applies the DCC-GARCH and TVP-VAR-DY models to investigate dynamic correlations and spillover effects. The empirical results show that CPU negatively impacts SBV, while CPU's volatility or positive shocks tend to elevate SBV, especially in more climate-resilient developed economies. In addition, critical international events can influence dynamic correlations and spillover effects between CPU (or its volatility) and SBV, particularly when climate policy is highly valued. From a risk transmission standpoint within the sovereign bond system, CPU and its volatility exert positive net spillover effects on SBV in the majority of economies. This study offers valuable insights for investors and policymakers, aligning with the goals of sustainable development for effective management of CPU risks.
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•Climate policy uncertainty adversely affects sovereign bond volatility.•Positive shocks, climate policy uncertainty volatility boost bond volatility.•Climate policy uncertainty broadly impacts climate-resilient developed economies.•Global events influence the spillover effects of climate policy uncertainty.•Climate policy uncertainty is an informational transmitter to bond volatility.
This study examines how fiscal incentives affect policy choices of local governments in China. We construct a difference-in-differences model using the 2014 Chinese central government policy of ...controlling the increase in construction land in metropolitan cities as an exogenous shock. The results reveal a substitution relationship between land sales revenue and local government debt, wherein local governments tended to expand debt when land revenue was reduced. Moreover, this decline affected local government debt’s maturity structure, as local governments faced higher short-term debt pressure and more quickly adjusted the interest rate maturity structure, which could trigger new debt risks.
In this paper, we propose a method to improve the convergence rate of the lowest order Raviart–Thomas mixed finite element approximations for the second order elliptic eigenvalue problem. Here, we ...prove a supercloseness result for the eigenfunction approximations and use a type of finite element postprocessing operator to construct an auxiliary source problem. Then solving the auxiliary additional source problem on an augmented mixed finite element space constructed by refining the mesh or by using the same mesh but increasing the order of corresponding mixed finite element space, we can increase the convergence order of the eigenpair approximation. This postprocessing method costs less computation than solving the eigenvalue problem on the finer mesh directly. Some numerical results are used to confirm the theoretical analysis.
We propose a climate change attention (CCA) index based on Google search volume index (GSVI) from 2004 to 2021 and show that it is an economically and statistically significant negative predictor for ...next month’s energy stock returns. The index is extracted using principal component analysis (PCA), but the results are similar by using the equal-weighted average method. Compared with 14 traditional macroeconomic predictors, CCA performs the best and provides complementary information when added into bivariate and multivariate macro predictive models. When further considering the effect of CCA’s forecasting power over different periods, strong evidence is shown that this outperformance is especially prominent in economic depressions and down market conditions. From the asset allocation perspective, CCA can provide a mean-variance investor with significant economic gains under alternative risk aversions. Our empirical results prove that investors’ attention to climate change contains predictive information for excess returns of global traditional energy stock index.
This paper derives a general procedure to produce an asymptotic expansion for eigenvalues of the Stokes problem by mixed finite elements. By means of integral expansion technique, the asymptotic ...error expansions for the approximations of the Stokes eigenvalue problem by Bernadi–Raugel element and
Q
2
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P
1
element are given. Based on such expansions, the extrapolation technique is applied to improve the accuracy of the approximations.
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