Anisotropic rectangular nonconforming finite element analysis for Sobolev equations

An anisotropic rectangular nonconforming finite element method for solving the Sobolev equations is discussed under semi-discrete and full discrete schemes. The corresponding optimal convergence error estimates and superclose property are derived, which are the same as the traditional conforming finite elements. Furthermore, the global superconvergence is obtained using a post-processing technique. The numerical results show the validity of the theoretical analysis.     

Existence Results for the Flow of Viscoelastic Fluids with an Integral Constitutive Law

We consider the flows of viscoelastic fluid which obey a constitutive law of integral type. Some theoretical results are proved: local existence, global existence with small data and uniqueness results for the initial boundary value problem.     

Assessment of adaptive and heuristic time stepping for variably saturated flow

The performance of improved initial estimates and ‘heuristic’ and ‘adaptive’ techniques for time step control in the iterative solution of Richards equation is evaluated. The so‐called heuristic technique uses the convergence behaviour of the iterative scheme to estimate the next time step whereas the adaptive technique regulates the time step on the basis of an approximation of the local time truncation error. The sample problems used to assess these various schemes are characterized by nonuniform (in time) boundary conditions, sharp gradients in the infiltration fronts, and discontinuous derivatives in the soil hydraulic properties. It is found that higher order initial solution estimates improve the convergence of the iterative scheme for both the heuristic and adaptive techniques, with greater overall performance gains for the heuristic scheme, as could be expected. It is also found that the heuristic technique outperforms the adaptive method under strongly nonlinear conditions. Previously reported observations suggesting that adaptive techniques perform best when accuracy requirements on the numerical solution are very stringent are confirmed. Overall both heuristic and adaptive techniques have their limitations, and a more general or mixed time stepping strategy combining truncation error and convergence criteria is recommended for complex problems. Copyright © 2006 John Wiley & Sons, Ltd.     

On 3D Lagrangian Navier–Stokes α Model with a Class of Vorticity-Slip Boundary Conditions

This paper concerns the 3-dimensional Lagrangian Navier–Stokes α model and the limiting Navier–Stokes system on smooth bounded domains with a class of vorticity-slip boundary conditions and the Navier-slip boundary conditions. It establishes the spectrum properties and regularity estimates of the associated Stokes operators, the local well-posedness of the strong solution and global existence of weak solutions for initial boundary value problems for such systems. Furthermore, the vanishing α limit to a weak solution of the corresponding initial-boundary value problem of the Navier–Stokes system is proved and a rate of convergence is shown for the strong solution.     

一种改进的GPS/DR组合位置自适应滤波算法

为解决自适应滤波算法中观测误差与状态误差估计的关键问题,在分析GPS/DR组合导航系统测量信息性质的基础上,提出了GPS光滑度计算方法,并在其基础上给出了GPS位置误差估计算法及状态误差协方差阵和观测误差协方差阵自适应调节算法。算法仿真实现了观测误差的直接测量,较好地解决了Sage-Husa自适应滤波算法中对误差特性估计不准确的问题。仿真结果表明：位置滤波输出的精度相比Sage-Husa算法有明显的提高。     

Constrained Substructure Model Updating Method Based on Local Mode

针对局部子结构为修正对象的情况提出了约束子结构修正法，实现只利用整体结构模态中对 应子结构部分的模态即可以修正子结构模型. 由脉冲响应结合特征系统实现法识别出子结构的低阶模态； 结合识别的模态和整体结构理论模型的高阶模态构造整体结构对应子结构位置的柔度矩 阵；利用柔度矩阵的物理意义，在子结构的边界上施加数值支座，把子结构从整体结构 中隔离出来成为约束子结构，同时构造出约束子结构的柔度矩阵；利用灵敏度的方法根 据构造出的约束子结构柔度矩阵，优化修正约束子结构，即间接等效地修正子结构模型. 通过一个平面桁架结构验证了约束子结构模型修正法的可行性与有效性，即使在5%或 10%的噪声影响下，仍能得到满意的修正结果. 关键词 模型修正，柔度矩阵，约束子结构，灵敏度，修正单元力     

Global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays

This paper is concerned with the global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays in the presence of disturbances. Firstly, the property with respect to the global stability in fixed time is developed for semi-Markovian switching nonlinear systems. Subsequently, a novel sliding manifold with double integration is presented based on the proposed principle of convergence in fixed time. Under the designed sliding mode controller, the state trajectory of synchronization error system is driven to the prescribed sliding manifold in fixed time. In addition, the global stability in fixed time of sliding mode dynamics is proved analytically. By means of the stochastic Lyapunov–Krasovskii functional approach, the synchronization condition is established in terms of linear matrix inequalities; moreover, the stochastic fixed settling-time can be determined to any desired values in advance, via the configuration of parameters in the proposed controller. Finally, two numerical examples are provided to demonstrate the validity of the theoretical results and the feasibility of the proposed approach.

     

GLOBAL ATTRACTOR FOR HASEGAWA-MIMA EQUATION

The long time behavior of solution of the Hasegawa-Mima equation with dissipation term was considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. Applying the uniform a priori estimates method, the existence of global attractor of this problem was proved, and also the dimensions of the global attractor was estimated.     

Data assimilation and pollution forecasting in Burgers' equation with model error function

This article presents a correction method for a better resolution of the problem of estimating and predicting pollution, governed by Burgers' equations. The originality of the method consists in the introduction of an error function into the system's equations of state to model uncertainty in the model. The initial conditions and diffusion coefficients, present in the equations for pollution and concentration, and also those in the model error equations, are estimated by solving a data assimilation problem. The efficiency of the correction method is compared with that produced by the traditional method without introduction of an error function.Three test cases are presented in this study in order to compare the performances of the proposed methods. In the first two tests, the reference is the analytical solution and the last test is formulated as part of the “twin experiment”.The numerical results obtained confirm the important role of the model error equation for improving the prediction capability of the system, in terms of both accuracy and speed of convergence.     

A LEVEL-VALUE ESTIMATION METHOD FOR SOLVING GLOBAL OPTIMIZATION

A level-value estimation method was illustrated for solving the constrained global optimization problem. The equivalence between the root of a modified variance equation and the optimal value of the original optimization problem is shown. An alternate algorithm based on the Newton's method is presented and the convergence of its implementable approach is proved. Preliminary numerical results indicate that the method is effective.     

Parameter estimation for chaotic systems using a geometric approach: theory and experiment

A method for estimating model parameters based on chaotic system response data is described. This estimation problem is made challenging by sensitive dependence to initial conditions. The standard maximum likelihood estimation method is practically infeasible due to the non-smooth nature of the likelihood function. We bypass the problem by introducing an alternative, smoother function that admits a better-defined maximum and show that the parameters that maximize this new function are asymptotically equivalent to maximum likelihood estimates. We use simulations to explore the influence of noise and available data on model Duffing and Lorenz oscillators. We then apply the approach to experimental data from a chaotic Duffing system. Our method does not require estimation of initial conditions and parameter estimates may be obtained even when system dynamics have been estimated from a delay embedding.     

Global existence of solutions to the periodic initial value problems for two-dimensional Newton-Boussinesq equations

A class of periodic initial value problems for two-dimensional Newton- Boussinesq equations are investigated in this paper. The Newton-Boussinesq equations are turned into the equivalent integral equations. With iteration methods, the local existence of the solutions is obtained. Using the method of a priori estimates, the global existence of the solution is proved.     

Adjoint Methods in Data Assimilation for Estimating Model Error

Data assimilation aims to incorporate measured observations into a dynamical system model in order to produce accurate estimates of all the current (and future) state variables of the system. The optimal estimates minimize a variational principle and can be found using adjoint methods. The model equations are treated as strong constraints on the problem. In reality, the model does not represent the system behaviour exactly and errors arise due to lack of resolution and inaccuracies in physical parameters, boundary conditions and forcing terms. A technique for estimating systematic and time-correlated errors as part of the variational assimilation procedure is described here. The modified method determines a correction term that compensates for model error and leads to improved predictions of the system states. The technique is illustrated in two test cases. Applications to the 1-D nonlinear shallow water equations demonstrate the effectiveness of the new procedure. This revised version was published online in July 2006 with corrections to the Cover Date.     

A low-complexity tracker design for uncertain nonholonomic wheeled mobile robots with time-varying input delay at nonlinear dynamic level

A low-complexity design problem of tracking scheme for uncertain nonholonomic mobile robots is investigated in the presence of unknown time-varying input delay. It is assumed that nonlinearities and parameters of robots and their bounds are unknown. Based on a nonlinear error transformation, a tracking control scheme ensuring preassigned bounds of overshoot, convergence rate, and steady-state values of a tracking error is firstly presented in the absence of input delay, without using any adaptive and function approximation mechanism to estimate unknown nonlinearities and model parameters and computing repeated time derivatives of certain signals. Then, we develop a low-complexity tracking scheme to deal with unknown time-varying input delay of mobile robots where some auxiliary signals and design conditions are derived for the design and stability analysis of the proposed tracking scheme. The boundedness of all signals in the closed-loop system and the guarantee of tracking performance with preassigned bounds are established through Lyapunov stability analysis. The validity of the proposed theoretical result is shown by a simulation example.     

On penalty function methods in the finite-element analysis of flow problems

In this paper the penalty function method is reviewed in the general context of solving constrained minimization problems. Mathematical properties, such as the existence of a solution to the penalty problem and convergence of the solution of a penalty problem to the solution of the original problem, are studied for the general case. Then the results are extended to a penalty function formulation of the Stokes and Navier-Stokes equations. Conditions for the equivalence of two penalty-finite element models of fluid flow are established, and the theoretical error estimates are verified in the case of Stokes's problem.     

Receding horizon control for multiple UAV formation flight based on modified brain storm optimization

Formation flight for unmanned aerial vehicles (UAVs) is a rather complicated global optimum problem. In the global optimum problem, the complex relationship between the controller parameters and the performance index, and the different kinds of constrains under complex combat field environment are taken into account. Brain storm optimization (BSO) is a brand-new swarm intelligence optimization algorithm inspired by a human being’s behavior of brainstorming. In this paper, in allusion to the drawbacks that the basic BSO algorithm traps into local optimum easily and has a slow convergent speed, some novel designs are proposed to enhance the performance of the optimization algorithm. The modified BSO is applied to solve the optimization problem based on the nonlinear Receding horizon control (RHC) mode of UAVs to seek the RHC control parameters for UAV formation flight. Series of comparative experimental results are presented to show the feasibility, validity, and superiority of our proposed method.     

A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere

In this paper we study solutions of an inverse problem for a global shallow water model controlling its initial conditions specified from the 40‐yr ECMWF Re‐analysis (ERA‐40) data sets, in the presence of full or incomplete observations being assimilated in a time interval (window of assimilation) with or without background error covariance terms. As an extension of the work by Chen et al. (Int. J. Numer. Meth. Fluids 2009), we attempt to obtain a reduced order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4D‐Var for a finite volume global shallow water equation model based on the Lin–Rood flux‐form semi‐Lagrangian semi‐implicit time integration scheme. Different approaches of POD implementation for the reduced inverse problem are compared, including a dual‐weighted method for snapshot selection coupled with a trust‐region POD adaptivity approach. Numerical results with various observational densities and background error covariance operator are also presented. The POD 4‐D Var model results combined with the trust‐region adaptivity exhibit similarity in terms of various error metrics to the full 4D Var results, but are obtained using a significantly lesser number of minimization iterations and require lesser CPU time. Based on our previous and current work, we conclude that POD 4‐D Var certainly warrants further studies, with promising potential of its extension to operational 3‐D numerical weather prediction models. Copyright © 2011 John Wiley & Sons, Ltd.     

INHOMOGENEOUS INITIAL-BOUNDARY VALUE PROBLEMFOR GINZBURG-LANDAU EQUATIONS

Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.     

ASYMPTOTIC THEORY OF INITIAL VALUE PROBLEMS FOR NONLINEAR PERTURBED KLEIN-GORDON EQUATIONS

Introduction InthispaperasymptotictheoryofthefollowinginitialvalueproblemforanonlinearKlein Gordonequationisconsidered.tt-Δ =εF(t,x,,ε),t>0,x∈R2,(0,x,ε)=0(x,ε),t(0,x,ε)=1(x,ε),x∈R2,(1)where(t,x)isarealvaluedunknownfunction,Δ=2i