This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator ...This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis.展开更多
In this paper,we design a new error estimator and give a posteriori error analysis for a poroelasticity model.To better overcome“locking phenomenon”on pressure and displacement,we proposed a new error estimators bas...In this paper,we design a new error estimator and give a posteriori error analysis for a poroelasticity model.To better overcome“locking phenomenon”on pressure and displacement,we proposed a new error estimators based on multiphysics discontinuous Galerkin method for the poroelasticity model.And we prove the upper and lower bound of the proposed error estimators,which are numerically demonstrated to be computationally very efficient.Finally,we present numerical examples to verify and validate the efficiency of the proposed error estimators,which show that the adaptive scheme can overcome“locking phenomenon”and greatly reduce the computation cost.展开更多
This study presents a comprehensive evaluation of tropical cyclone(TC)forecast performance in the western North Pacific from 2013 to 2022,based on operational forecasts issued by the China Meteorological Administratio...This study presents a comprehensive evaluation of tropical cyclone(TC)forecast performance in the western North Pacific from 2013 to 2022,based on operational forecasts issued by the China Meteorological Administration.The analysis reveals systematic improvements in both track and intensity forecasts over the decade,with distinct error characteristics observed across various forecast parameters.Track forecast errors have steadily decreased,particularly for longer lead times,while error magnitudes have increased with longer forecast lead times.Intensity forecasts show similar progressive enhancements,with maximum sustained wind speed errors decreasing by 0.26 m/s per year for 120 h forecasts.The study also identifies several key patterns in forecast performance:typhoon-grade or stronger TCs exhibit smaller track errors than week or weaker systems;intensity forecasts systematically overestimate weaker TCs while underestimating stronger systems;and spatial error distributions show greater track inaccuracies near landmasses and regional intensity biases.These findings highlight both the significant advances in TC forecasting capability achieved through improved modeling and observational systems,and the remaining challenges in predicting TC changes and landfall behavior,providing valuable benchmarks for future forecast system development.展开更多
Conventional error cancellation approaches separate molecules into smaller fragments and sum the errors of all fragments to counteract the overall computational error of the parent molecules.However,these approaches m...Conventional error cancellation approaches separate molecules into smaller fragments and sum the errors of all fragments to counteract the overall computational error of the parent molecules.However,these approaches may be ineffective for systems with strong localized chemical effects,as fragmenting specific substructures into simpler chemical bonds can introduce additional errors instead of mitigating them.To address this issue,we propose the Substructure-Preserved Connection-Based Hierarchy(SCBH),a method that automatically identifies and freezes substructures with significant local chemical effects prior to molecular fragmentation.The SCBH is validated by the gas-phase enthalpy of formation calculation of CHNO molecules.Therein,based on the atomization scheme,the reference and test values are derived at the levels of Gaussian-4(G4)and M062X/6-31+G(2df,p),respectively.Compared to commonly used approaches,SCBH reduces the average computational error by half and requires only15%of the computational cost of G4 to achieve comparable accuracy.Since different types of local effect structures have differentiated influences on gas-phase enthalpy of formation,substituents with strong electronic effects should be retained preferentially.SCBH can be readily extended to diverse classes of organic compounds.Its workflow and source code allow flexible customization of molecular moieties,including azide,carboxyl,trinitromethyl,phenyl,and others.This strategy facilitates accurate,rapid,and automated computations and corrections,making it well-suited for high-throughput molecular screening and dataset construction for gas-phase enthalpy of formation.展开更多
Inborn errors of metabolism(IEM)are rare disorders,most are liver-based with liver transplantation(LT)emerging as an effective cure in the pediatric population.LT has been shown to offer a cure or deter disease progre...Inborn errors of metabolism(IEM)are rare disorders,most are liver-based with liver transplantation(LT)emerging as an effective cure in the pediatric population.LT has been shown to offer a cure or deter disease progression and provide symptomatic improvement in patients with IEM.Each metabolic disorder is unique,with the missing enzyme or transporter protein causing substrate deficiency or toxic byproduct production.Knowledge about the distribution of deficient enzymes,the percentage of enzymes replaced by LT,and the extent of extrahepatic involvement helps anticipate and manage complications in the perioperative period.Most patients have multisystem involvement and can be on complex dietary regimens.Metabolic decompensation can be triggered due to the stress response to surgery,fasting and other unanticipated complications perioperatively.Thus,a multidisciplinary team’s input including those from metabolic specialists is essential to develop disease and patient-specific strategies for the perioperative management of these patients during LT.In this review,we outline the classification of IEM,indications for LT along with potential benefits,basic metabolic defects and their implications,details of extrahepatic involvement and perioperative management strategies for LT in children with some of the commonly presenting IEM,to assist anesthesiologists handling this cohort of patients.展开更多
In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc...In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.展开更多
In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimati...In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimation between the spectral approximate solution and the exact solution is obtained.展开更多
In this paper,the Fourier collocation method for solving the generalized Benjamin-Ono equation with periodic boundary conditions is analyzed.Stability of the semi-discrete scheme is proved and error estimate in H^(1/2...In this paper,the Fourier collocation method for solving the generalized Benjamin-Ono equation with periodic boundary conditions is analyzed.Stability of the semi-discrete scheme is proved and error estimate in H^(1/2)-norm is obtained.展开更多
In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof ...In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.展开更多
An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same t...An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.展开更多
The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space ...The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space Vh × Wh H(div; × L2(). Optimal order estimates are obtained for the approximation of u, ut, the associated velocity p and divp respectively in L(0,T;L2()), L(0,T;L2()), L(0,T;L2()2), and L2(0, T; L2()). Quasi-optimal order estimates are obtained for the approximations of u, ut in L(0, T; L()) and p in L(0,T; L()2).展开更多
The subject of this work is to propose adaptive finite element methods based on an optimal maximum norm error control estimate.Using estimators of the local regularity of the unknown exact solution derived from comput...The subject of this work is to propose adaptive finite element methods based on an optimal maximum norm error control estimate.Using estimators of the local regularity of the unknown exact solution derived from computed approximate solutions,the proposed procedures are analyzed in detail for a non-trivial class of corner problems and shown to be efficient in the sense that they generate the correct type of refinement and lead to the desired control under consideration.展开更多
In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error est...In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson＇s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds.展开更多
Although the two-grid finite element decoupled scheme for mixed Navier-Stokes/ Darcy model in literatures has given the numerical results of optimal convergence order, the theoretical analysis only obtain the optimal ...Although the two-grid finite element decoupled scheme for mixed Navier-Stokes/ Darcy model in literatures has given the numerical results of optimal convergence order, the theoretical analysis only obtain the optimal error order for the porous media flow and a non-optimal error order for the fluid flow. In this article, we give a more rigorous of the error analysis for the fluid flow and obtain the optimal error estimates of the velocity and the pressure.展开更多
This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the p...This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context.展开更多
H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and unique...H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.展开更多
The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satis...The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes.展开更多
The wide-swath method based on multi-receiver is a novel and highly accurate wide-swath method, which requires a very precise view angle. The estimated angle has error because of the atmosphere refraction, angle error...The wide-swath method based on multi-receiver is a novel and highly accurate wide-swath method, which requires a very precise view angle. The estimated angle has error because of the atmosphere refraction, angle error of view and target height. A method is proposed in this paper to estimate the angle error from the return signal. The method makes use of the relationship between the view angle error and the signal correlation of the subswaths to estimate the angle error. The precision of this method is analyzed by the law of great number and it turns out to be in direct proportion to the root square number of averaging. The simulation result is given and the angle precision is 0.025°.展开更多
We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpol...We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpolation operator ink is introduced.With the help of ink(not elliptic projection),the optimal error estimate in L∞(J;L2(Ω)) norm of FEM is proved.展开更多
<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the...<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos.1236108412001130)。
文摘This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis.
基金supported by the National Natural Science Foundation of China(Grant Nos.12371393 and 11971150)Natural Science Foundation of Henan(Grant No.242300421047).
文摘In this paper,we design a new error estimator and give a posteriori error analysis for a poroelasticity model.To better overcome“locking phenomenon”on pressure and displacement,we proposed a new error estimators based on multiphysics discontinuous Galerkin method for the poroelasticity model.And we prove the upper and lower bound of the proposed error estimators,which are numerically demonstrated to be computationally very efficient.Finally,we present numerical examples to verify and validate the efficiency of the proposed error estimators,which show that the adaptive scheme can overcome“locking phenomenon”and greatly reduce the computation cost.
基金supported by the National Key R&D Program of China [grant number 2023YFC3008004]。
文摘This study presents a comprehensive evaluation of tropical cyclone(TC)forecast performance in the western North Pacific from 2013 to 2022,based on operational forecasts issued by the China Meteorological Administration.The analysis reveals systematic improvements in both track and intensity forecasts over the decade,with distinct error characteristics observed across various forecast parameters.Track forecast errors have steadily decreased,particularly for longer lead times,while error magnitudes have increased with longer forecast lead times.Intensity forecasts show similar progressive enhancements,with maximum sustained wind speed errors decreasing by 0.26 m/s per year for 120 h forecasts.The study also identifies several key patterns in forecast performance:typhoon-grade or stronger TCs exhibit smaller track errors than week or weaker systems;intensity forecasts systematically overestimate weaker TCs while underestimating stronger systems;and spatial error distributions show greater track inaccuracies near landmasses and regional intensity biases.These findings highlight both the significant advances in TC forecasting capability achieved through improved modeling and observational systems,and the remaining challenges in predicting TC changes and landfall behavior,providing valuable benchmarks for future forecast system development.
基金the support of the National Natural Science Foundation of China(22575230)。
文摘Conventional error cancellation approaches separate molecules into smaller fragments and sum the errors of all fragments to counteract the overall computational error of the parent molecules.However,these approaches may be ineffective for systems with strong localized chemical effects,as fragmenting specific substructures into simpler chemical bonds can introduce additional errors instead of mitigating them.To address this issue,we propose the Substructure-Preserved Connection-Based Hierarchy(SCBH),a method that automatically identifies and freezes substructures with significant local chemical effects prior to molecular fragmentation.The SCBH is validated by the gas-phase enthalpy of formation calculation of CHNO molecules.Therein,based on the atomization scheme,the reference and test values are derived at the levels of Gaussian-4(G4)and M062X/6-31+G(2df,p),respectively.Compared to commonly used approaches,SCBH reduces the average computational error by half and requires only15%of the computational cost of G4 to achieve comparable accuracy.Since different types of local effect structures have differentiated influences on gas-phase enthalpy of formation,substituents with strong electronic effects should be retained preferentially.SCBH can be readily extended to diverse classes of organic compounds.Its workflow and source code allow flexible customization of molecular moieties,including azide,carboxyl,trinitromethyl,phenyl,and others.This strategy facilitates accurate,rapid,and automated computations and corrections,making it well-suited for high-throughput molecular screening and dataset construction for gas-phase enthalpy of formation.
文摘Inborn errors of metabolism(IEM)are rare disorders,most are liver-based with liver transplantation(LT)emerging as an effective cure in the pediatric population.LT has been shown to offer a cure or deter disease progression and provide symptomatic improvement in patients with IEM.Each metabolic disorder is unique,with the missing enzyme or transporter protein causing substrate deficiency or toxic byproduct production.Knowledge about the distribution of deficient enzymes,the percentage of enzymes replaced by LT,and the extent of extrahepatic involvement helps anticipate and manage complications in the perioperative period.Most patients have multisystem involvement and can be on complex dietary regimens.Metabolic decompensation can be triggered due to the stress response to surgery,fasting and other unanticipated complications perioperatively.Thus,a multidisciplinary team’s input including those from metabolic specialists is essential to develop disease and patient-specific strategies for the perioperative management of these patients during LT.In this review,we outline the classification of IEM,indications for LT along with potential benefits,basic metabolic defects and their implications,details of extrahepatic involvement and perioperative management strategies for LT in children with some of the commonly presenting IEM,to assist anesthesiologists handling this cohort of patients.
基金supported by the National Basic Research Program under the Grant 2005CB321701the National Natural Science Foundation of China under the Grants 60474027 and 10771211.
文摘In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.
文摘In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimation between the spectral approximate solution and the exact solution is obtained.
基金supported by NSF of China(60874039)Leading Academic Discipline Project of Shanghai Municipal Education Commission(J50101)
文摘In this paper,the Fourier collocation method for solving the generalized Benjamin-Ono equation with periodic boundary conditions is analyzed.Stability of the semi-discrete scheme is proved and error estimate in H^(1/2)-norm is obtained.
文摘In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.
基金Supported by the National Natural Science Foundation of China (10601022)Natural Science Foundation of Inner Mongolia Autonomous Region (200607010106)Youth Science Foundation of Inner Mongolia University(ND0702)
文摘An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.
文摘The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space Vh × Wh H(div; × L2(). Optimal order estimates are obtained for the approximation of u, ut, the associated velocity p and divp respectively in L(0,T;L2()), L(0,T;L2()), L(0,T;L2()2), and L2(0, T; L2()). Quasi-optimal order estimates are obtained for the approximations of u, ut in L(0, T; L()) and p in L(0,T; L()2).
文摘The subject of this work is to propose adaptive finite element methods based on an optimal maximum norm error control estimate.Using estimators of the local regularity of the unknown exact solution derived from computed approximate solutions,the proposed procedures are analyzed in detail for a non-trivial class of corner problems and shown to be efficient in the sense that they generate the correct type of refinement and lead to the desired control under consideration.
基金supported by National Natural Science Foundation of China (11071226 11201122)
文摘In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson＇s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds.
基金Subsidized by NSFC(11571274 and 11171269)the Ph.D.Programs Foundation of Ministry of Education of China(20110201110027)
文摘Although the two-grid finite element decoupled scheme for mixed Navier-Stokes/ Darcy model in literatures has given the numerical results of optimal convergence order, the theoretical analysis only obtain the optimal error order for the porous media flow and a non-optimal error order for the fluid flow. In this article, we give a more rigorous of the error analysis for the fluid flow and obtain the optimal error estimates of the velocity and the pressure.
文摘This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context.
基金Supported by NNSF(10601022,11061021)Supported by NSF of Inner Mongolia Au-tonomous Region(200607010106)Supported by SRP of Higher Schools of Inner Mongolia(NJ10006)
文摘H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.
基金the Henan Natural Science Foundation(072300410320)the Henan Education Department Foundational Study Foundation(200510460311)
文摘The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes.
文摘The wide-swath method based on multi-receiver is a novel and highly accurate wide-swath method, which requires a very precise view angle. The estimated angle has error because of the atmosphere refraction, angle error of view and target height. A method is proposed in this paper to estimate the angle error from the return signal. The method makes use of the relationship between the view angle error and the signal correlation of the subswaths to estimate the angle error. The precision of this method is analyzed by the law of great number and it turns out to be in direct proportion to the root square number of averaging. The simulation result is given and the angle precision is 0.025°.
基金This research is supported by the Foundation for Talents for Next Century of Shandong University
文摘We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpolation operator ink is introduced.With the help of ink(not elliptic projection),the optimal error estimate in L∞(J;L2(Ω)) norm of FEM is proved.
文摘<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>
