ap cloud we propose a new adaptive particle in cloud ap cloud method for obtaining optimal numerical solutions to the vlasov poisson equation unlike the traditional particle in cell pic method which is commonly used for solving this problem the ap cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non uniform unlike other adaptive techniques for pic our method balances the errors in pde discretization and monte carlo integration and discretizes the differential operators using a generalized finite difference gfd method based on a weighted least square formulation as a result ap cloud is independent of the geometric shapes of computational domains and is free of artificial parameters efficient and robust implementation is achieved through an octree data structure with 2 1 balance we analyze the accuracy and convergence order of ap cloud theoretically and verify the method using an electrostatic problem of a particle beam with halo simulation results show that the ap cloud method is substantially more accurate and faster than the traditional pic and it is free of artificial forces that are typical for some adaptive pic techniques

adaptive fuzzy output feedback control for output constrained nonlinear systems in the presence of input saturation abstract in this paper the problem of adaptive fuzzy output feedback control is investigated for a class of output constrained uncertain nonlinear systems with input saturation and unmeasured states to address output constraint and input constraint a barrier lyapunov function and an auxiliary design system are employed respectively fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy state observer is designed to estimate the unmeasured states by utilizing the fuzzy state observer and combining the adaptive backstepping technique with adaptive fuzzy control design an observer based adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that all the signals in the closed loop system are bounded and the input and output constraints are circumvented simultaneously a numerical example is provided to illustrate the effectiveness of the proposed approach

observer based adaptive fuzzy tracking control for a class of uncertain nonlinear mimo systems this paper addresses the adaptive fuzzy tracking control problem for a class of uncertain nonlinear mimo systems with the external disturbances the adaptive fuzzy controllers are designed under the constraint that only system output is available for measurement then it is needed to design a state observer to estimate the unmeasured states in the observer design procedure two prominent advantages are that it does not require the sign of the control gain coefficient to be known and only two parameters need to be adjusted on line for each subsystem by using lyapunov analysis method it is proven that all the signals in the closed loop system are guaranteed to be bounded and the system outputs track the reference signals to a bounded compact set the feasibility of the proposed approach is validated by using two simulation examples

adaptive finite element methods for elliptic equations with non smooth coefficients nous considerons une equation elliptique du second ordre a coefficients discontinus ou anisotropes dans un domaine borne en dimension 2 ou 3 et sa discretisation par elements finis le but de cet article est de demontrer des estimations d erreur a priori et a posteriori dans une norme appropriee qui soient independantes de la variation des coefficients

error analysis of nonconforming and mixed fems for second order linear non selfadjoint and indefinite elliptic problems the state of the art proof of a global inf sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite second order linear elliptic pdes this paper therefore first analyses a nonconforming finite element discretization which converges owing to some a priori l 2 l2 error estimates even for reduced regularity on non convex polygonal domains an equivalence result of that nonconforming finite element scheme to the mixed finite element method mfem leads to the well posedness of the discrete solution and to a priori error estimates for the mfem the explicit residual based a posteriori error analysis allows some reliable and efficient error control and motivates some adaptive discretization which improves the empirical convergence rates in three computational benchmarks

on the implementation of mixed methods as nonconforming methods for second order elliptic problems in this paper we show that mixed finite element methods for a fairly general second order elliptic problem with variable coefficients can be given a nonmixed formulation lower order terms are treated so our results apply also to parabolic equations we define an approximation method by incorporating some projection operators within a standard galerkin method which we call a projection finite element method it is shown that for a given mixed method if the projection method s finite element space m h satisfies three conditions then the two approximation methods are equivalent these three conditions can be simplified for a single element in the case of mixed spaces possessing the usual vector projection operator we then construct appropriate nonconforming spaces m h for the known triangular and rectangular elements the lowest order raviart thomas mixed solution on rectangular finite elements in r 2 and r 3 on simplices or on prisms is then implemented as a nonconforming method modified in a simple and computationally trivial manner this new nonconforming solution is actually equivalent to a postprocessed version of the mixed solution a rearrangement of the computation of the mixed method solution through this equivalence allows us to design simple and optimal order multigrid methods for the solution of the linear system

convergence of adaptive finite element methods for general second order linear elliptic pdes we prove convergence of adaptive finite element methods afems for general nonsymmetric second order linear elliptic pdes thereby extending the result of morin nochetto and siebert it siam j numer anal 38 2000 pp 466 488 it siam rev 44 2002 pp 631 658 the proof relies on quasi orthogonality which accounts for the bilinear form not being a scalar product together with novel error and oscillation reduction estimates which now do not decouple we show that afems are a contraction for the sum of energy error plus oscillation numerical experiments including oscillatory coefficients and both coercive and noncoercive convection diffusion pde illustrate the theory and yield optimal meshes

adaptive fuzzy backstepping output feedback tracking control of mimo stochastic pure feedback nonlinear systems with input saturation abstract in this paper the adaptive fuzzy backstepping output feedback tracking control problem is considered for a class of uncertain stochastic multi input and multi output mimo nonlinear systems in pure feedback form the stochastic mimo nonlinear systems under study have unknown nonlinear functions input saturation and immeasurable states by using fuzzy logic systems to identify the uncertain nonlinear system and a smooth function to approximate the input saturation a fuzzy state observer is designed and the estimations of the immeasurable states are obtained based on the backstepping recursive design technique an adaptive fuzzy output feedback tracking control approach is developed it is shown that the proposed control approach guarantees that all the signals of the resulting closed loop system are semi globally uniformly ultimately bounded sguub in mean square in the sense of probability and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing design parameters appropriately a simulation example is provided to show the effectiveness of the proposed approach

a posteriori error estimates for nonconforming finite element methods computable a posteriori error bounds for a large class of nonconforming finite element methods are provided for a model poisson problem in two and three space dimensions besides a refined residual based a posteriori error estimate an averaging estimator is established and an l 2 estimate is included the a posteriori error estimates are reliable and efficient the proof of reliability relies on a helmholtz decomposition

adaptive controller design for tracking and disturbance attenuation in parametric strict feedback nonlinear systems the authors develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for a class of nonlinear systems which are described in the parametric strict feedback form and are subject to additional exogenous disturbance inputs their approach to adaptive control is performance based where the objective for the controller design is not only to find an adaptive controller but also to construct an appropriate cost functional compatible with desired asymptotic tracking and disturbance attenuation specifications with respect to which the adaptive controller is worst case optimal three main issues of the paper are the backstepping methodology worst case identification schemes and singular perturbations analysis closed form expressions have been obtained for an adaptive controller and the corresponding value function a numerical example involving a third order system is given

the approximation power of moving least squares a general method for near best approximations to functionals on r d using scattered data information is discussed the method is actually the moving least squares method presented by the backus gilbert approach it is shown that the method works very well for interpolation smoothing and derivatives approximations for the interpolation problem this approach gives mclain s method the method is near best in the sense that the local error is bounded in terms of the error of a local best polynomial approximation the interpolation approximation in r d is shown to be a c function and an approximation order result is proven for quasi uniform sets of data points

adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small gain approach this paper considers the adaptive fuzzy robust control problem for a class of single input and single output siso stochastic nonlinear systems in strict feedback form the systems under study possess unstructured uncertainties unknown dead zone uncertain dynamics and unknown gain functions in the controller design fuzzy logic systems are adopted to approximate the unknown functions and the uncertain nonlinear system is therefore transformed into an uncertain parameterized system with unmodeled dynamics by combining the backstepping technique with the stochastic small gain approach a novel adaptive fuzzy robust control scheme is developed it is shown that the proposed control approach can guarantee that the closed loop system is input state practically stable isps in probability and the output of the system converges to a small neighborhood of the origin by appropriately tuning several design parameters simulation results are provided to illustrate the effectiveness of the proposed control approach

solving parabolic and hyperbolic equations by the generalized finite difference method classical finite difference schemes are in wide use today for approximately solving partial differential equations of mathematical physics an evolution of the method of finite differences has been the development of generalized finite difference gfd method that can be applied to irregular grids of points in this paper the extension of the gfd to the explicit solution of parabolic and hyperbolic equations has been developed for partial differential equations with constant coefficients in the cases of considering one two or three space dimensions the convergence of the method has been studied and the truncation errors over irregular grids are given different examples have been solved using the explicit finite difference formulae and the criterion of stability this has been expressed in function of the coefficients of the star equation for irregular clouds of nodes in one two or three space dimensions the numerical results show the accuracy obtained over irregular grids this paper also includes the study of the maximum local error and the global error for different examples of parabolic and hyperbolic time dependent equations

self organizing cmac control for a class of mimo uncertain nonlinear systems this paper presents a self organizing control system based on cerebellar model articulation controller cmac for a class of multiple input multiple output mimo uncertain nonlinear systems the proposed control system merges a cmac and sliding mode control smc so the input space dimension of cmac can be simplified the structure of cmac will be self organized that is the layers of cmac will grow or prune systematically and their receptive functions can be automatically adjusted the control system consists of a self organizing cmac socm and a robust controller socm containing a cmac uncertainty observer is used as the principal controller and the robust controller is designed to dispel the effect of approximation error the gradient descent method is used to online tune the parameters of cmac and the lyapunov function is applied to guarantee the stability of the system a simulation study of inverted double pendulums system and an experimental result of linear ultrasonic motor motion control show that favorable tracking performance can be achieved by using the proposed control system

design and analysis of fuzzy identifiers of nonlinear dynamic systems uses fuzzy systems as identifiers for nonlinear dynamic systems the author provides a theoretical justification for the fuzzy identifiers by proving that they are capable of following the output of a general nonlinear dynamic system to arbitrary accuracy in any finite time interval the fuzzy identifiers are constructed from a set of adaptable fuzzy if then rules and can combine both numerical information in the form of input output pairs obtained by exciting the system with an input signal and measuring the corresponding outputs and linguistic information in the form of if then rules about the behavior of the system in terms of vague and fuzzy words into their designs in a uniform fashion the author develops two fuzzy identifiers the first one is designed through the following four steps 1 define some fuzzy sets in the state space u spl sub r sup n of the system these fuzzy sets do not change 2 construct fuzzy rule bases of the fuzzy identifier which comprise rules whose if parts constitute all the possible combinations of the fuzzy sets defined in 1 3 design the fuzzy systems in the fuzzy identifier based on the fuzzy rule bases of 2 and 4 develop an adaptive law for the free parameters in the fuzzy identifier the second fuzzy identifier is designed in a similar way as the first one except that a the parameters characterizing the fuzzy sets in the state space change during the adaptation procedure and b the fuzzy systems and the adaptive law are different the author proves that 1 both fuzzy identifiers are globally stable in the sense that all variables in the fuzzy identifiers are uniformly bounded and 2 under some conditions the identification errors of both fuzzy identifiers converge to zero asymptotically finally the author simulates the fuzzy identifiers for identifying the chaotic glycolytic oscillator and the results show that 1 the fuzzy identifiers can approximate the chaotic system at a reasonable speed and accuracy without using any linguistic information and 2 by incorporating some fuzzy linguistic if then rules about the behavior of the system into the fuzzy identifiers the speed and accuracy of the fuzzy identifiers are greatly improved

adaptive finite element methods with convergence rates adaptive finite element methods for numerically solving elliptic equations are used often in practice only recently 12 17 have these methods been shown to converge however this convergence analysis says nothing about the rates of convergence of these methods and therefore does in principle not guarantee yet any numerical advantages of adaptive strategies versus non adaptive strategies the present paper modifies the adaptive method of morin nochetto and siebert 17 for solving the laplace equation with piecewise linear elements on domains in 2 by adding a coarsening step and proves that this new method has certain optimal convergence rates in the energy norm which is equivalent to the h1 norm namely it is shown that whenever s 0 and the solution u is such that for each n 1 it can be approximated to accuracy o n s in the energy norm by a continuous piecewise linear function on a triangulation with n cells using complete knowledge of u then the adaptive algorithm constructs an approximation of the same type with the same asymptotic accuracy while using only information gained during the computational process moreover the number of arithmetic computations in the proposed method is also of order o n for each n 1 the construction and analysis of this adaptive method relies on the theory of nonlinear approximation

a unifying theory of a posteriori error control for nonconforming finite element methods residual based a posteriori error estimates were derived within one unifying framework for lowest order conforming nonconforming and mixed finite element schemes in carstensen numer math 100 617 637 2005 therein the key assumption is that the conforming first order finite element space v h c annulates the linear and bounded residual l written v h c subseteq rm ker ell that excludes particular nonconforming finite element methods ncfems on parallelograms in that v h c not subset rm ker ell the present paper generalises the aforementioned theory to more general situations to deduce new a posteriori error estimates also for mortar and discontinuous galerkin methods the key assumption is the existence of some bounded linear operator pi v h c rightarrow v h nc with some elementary properties it is conjectured that the more general hypothesis h1 h3 can be established for all known ncfems applications on various nonstandard finite element schemes for the laplace stokes and navier lame equations illustrate the presented unifying theory of a posteriori error control for ncfem

a priori and computable a posteriori error estimates for an hdg method for the coercive maxwell equations abstract in this paper we present and analyze a hybridizable discontinuous galerkin hdg method for a mixed curl curl formulation of the steady state coercive maxwell equations with a discrete sobolev embedding type estimates for the discontinuous polynomials we provide a priori error estimates for the electric field and the lagrange multiplier in the energy norm with the smooth or minimal regularity assumption on the exact solution we have optimal convergence rate for the electric field and the lagrange multiplier in the energy norm the a priori error estimate for the electric field in the l 2 norm is also obtained by the duality argument and the approximation is also optimal for the electric field in the l 2 norm moreover by employing suitable helmholtz decompositions of the error together with the upper bound estimate for the lagrange multiplier we provide a computable residual based a posteriori error estimator which is derived based on the error measured in terms of a mesh dependent energy norm the efficiency of the a posteriori error estimator is also established three dimensional numerical results testing the performance of the a priori and a posteriori error estimates for the maxwell equations are given

solving second order non linear elliptic partial differential equations using generalized finite difference method the generalized finite difference method gfdm has been proved to be a good meshless method to solve several linear partial differential equations pde s wave propagation advection diffusion plates beams etc the gfdm allows us to use irregular clouds of nodes that can be of interest for modelling non linear elliptic pde s this paper illustrates that the gfd explicit formulae developed to obtain the different derivatives of the pde s are based on the existence of a positive definite matrix that it is obtained using moving least squares approximation and taylor series development also it is shown that in 2d a regular neighbourhood of eight nodes can be regarded as a generalization of a classical finite difference formula with a sixth order truncation error this paper shows the application of the gfdm to solving different non linear problems including applications to heat transfer acoustics and problems of mass transfer

some new residual based a posteriori error estimators for the mortar finite element methods in this paper we propose some new residual based a posteriori error estimators for the mortar finite element discretization of the second order elliptic equations with discontinuous coefficients reliability and efficiency of the estimators are given our analysis does not require any saturation assumptions and the mesh restrictions on the interface which are often needed in the literature numerical experiments are presented to confirm our theoretical analysis

direct adaptive fuzzy control for nonlinear systems with time varying delays this paper focuses on the problem of direct adaptive fuzzy control for nonlinear strict feedback systems with time varying delays based on the razumikhin function approach a novel adaptive fuzzy controller is designed the proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed loop system remain bounded different from the existing adaptive fuzzy control methodology the fuzzy logic systems are used to model the desired but unknown control signals rather than the unknown nonlinear functions in the systems as a result the proposed adaptive controller has a simpler form and requires fewer adaptation parameters

adaptive fuzzy fault tolerant control with guaranteed tracking performance for nonlinear strict feedback systems in this study we propose two backstepping based adaptive fuzzy fault tolerant control ftc methods for a class of nonlinear strict feedback systems with actuator failures first a traditional ftc tftc method is considered our analysis shows that tftc has poor tracking performance due to the existence of approximation errors and external disturbances inspired by the idea that the magnitudes of control inputs decrease as the error of the last step decreases in the backstepping procedure we propose a new prescribed performance ftc npp ftc method based on the improved error transformation technique compared with previous methods where only the output tracking error is guaranteed within the prescribed performance bound ppb we show that the state tracking error for each step between the intermediate control and virtual control remains within the ppb regardless of actuator faults the main advantage of the npp ftc method is that the tracking errors and magnitudes of the control inputs can be reduced by adjusting the ppb parameters of the errors in the first and last steps our simulation results demonstrate the effectiveness of the proposed npp ftc method

solving a chemotaxis haptotaxis system in 2d using generalized finite difference method abstract we study a mathematical model of cancer cell invasion of tissue extracellular matrix consisting of a system of reaction diffusion taxis partial differential equations which describes the interactions between cancer cells the matrix degrading enzyme and the host tissue we analyze the local stability of the constant equilibrium solutions to the chemotaxis haptotaxis system we derive a discretization of the system by means of the generalized finite difference method gfdm and we prove the convergence of the discrete solution to the analytical one also we provide several numerical examples on the applications of this meshless method over regular and irregular domains

adaptive control for nonlinear mimo time delay systems based on fuzzy approximation this paper focuses on the problem of adaptive control for a class of nonlinear multi input and multi output mimo systems with time delays a state feedback adaptive controller is constructed by backstepping technique fuzzy logic systems are used to approximate unknown nonlinear functions in the process of the controller design the main advantages of the proposed approach are twofold 1 the controller design is independent of the knowledge of the basis functions of fuzzy logic systems and 2 the suggested approach requires only m adaptive laws to control a nonlinear time delay system with m inputs simulation results illustrate the effectiveness of the proposed approach

global estimates for mixed methods for second order elliptic equations global error estimates in l2 92 l 9 and h s q 2 in r2 or a re derived for a mixed finite element method for the dirichlet problem for the elliptic operator lp div a grad p bp cp based on the raviart thomas nedelec space vh x wh c h div 92 x l2 g2 optimal order estimates are obtained for the approximation of p and the associated velocity field u a grad p bp in l2 g2 and h s 92 0 6 s k 1 and if q c r2 forp in lv2

solving second order non linear hyperbolic pdes using generalized finite difference method gfdm abstract the generalized finite difference method gfdm has been proved to be a good meshless method to solve several linear partial differential equations pdes wave propagation advection diffusion plates beams etc the gfdm allows us to use irregular clouds of nodes that can be of interest for modelling non linear parabolic pdes this paper illustrates that the gfd explicit formulae developed to obtain the different derivatives of the pde s are based in the existence of a positive definite matrix that it is obtained using moving least squares approximation and taylor series development criteria for convergence of fully explicit method using gfdm for different non linear parabolic pdes are given this paper shows the application of the gfdm to solving different non linear problems including applications to heat transfer acoustics and problems of mass transfer

convergence of adaptive finite element methods adaptive finite element methods fems have been widely used in applications for over 20 years now in practice they converge starting from coarse grids although no mathematical theory has been able to prove this assertion ensuring an error reduction rate based on a posteriori error estimators together with a reduction rate of data oscillation information missed by the underlying averaging process we construct a simple and efficient adaptive fem for elliptic partial differential equations we prove that this algorithm converges with linear rate without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance extensions to higher order elements and applications to saddle point problems are discussed as well

a hybrid method and unified analysis of generalized finite differences and lagrange finite elements abstract finite differences finite elements and their generalizations are widely used for solving partial differential equations and their high order variants have respective advantages and disadvantages traditionally these methods are treated as different strong vs weak formulations and are analyzed using different techniques fourier analysis or green s functions vs functional analysis except for some special cases on regular grids recently the authors introduced a hybrid method called adaptive extended stencil fem or aes fem conley et al 2016 which combines features of generalized finite differences and lagrange finite elements to achieve second order accuracy over unstructured meshes however its analysis was incomplete due to the lack of existing mathematical theory that unifies the formulations and analysis of these different methods in this work we introduce the framework of generalized weighted residuals to unify the formulation of finite differences finite elements and aes fem in addition we propose a unified analysis of the well posedness convergence and mesh quality dependency of these different methods we also report numerical results with aes fem to verify our analysis we show that aes fem improves the accuracy of generalized finite differences while reducing the mesh quality dependency and simplifying the implementation of high order finite elements

high order relaxation schemes for nonlinear degenerate diffusion problems several relaxation approximations to partial differential equations have been recently proposed examples include conservation laws hamilton jacobi equations convection diffusion problems and gas dynamics problems the present paper focuses on diffusive relaxation schemes for the numerical approximation of nonlinear parabolic equations these schemes are based on a suitable semilinear hyperbolic system with relaxation terms high order methods are obtained by coupling eno and weighted essentially nonoscillatory weno schemes for space discretization with implicit explicit imex schemes for time integration error estimates and a convergence analysis are developed for semidiscrete schemes with a numerical analysis for fully discrete relaxed schemes various numerical results in one and two dimensions illustrate the high accuracy and good properties of the proposed numerical schemes also in the degenerate case these schemes can be easily implemented on parallel computers and applied to more general systems of nonlinear parabolic equations in two and three dimensional cases

a novel adaptive fuzzy variable structure control for a class of nonlinear uncertain systems via backstepping abstract this paper presents a new design of adaptive fuzzy variable structure control to solve the traditional problem of model reference adaptive control mrac for a class of single input single output minimum phase uncertain nonlinear systems via backstepping instead of taking the tedious coordinate transformation and yielding a hard high gain controller we introduce smooth b spline type membership functions into the controller so as to compensate for the uncertainties much softer i e in a much smoother and locally weighted manner to be rigorous it is shown that the stability of the closed loop system can be assured and the tracking error can globally approach to an arbitrary preset dead zone range in order to demonstrate the effectiveness of the developed novel controller an example is extensively simulated to provide quite satisfactory performance

adaptive fuzzy robust output feedback control of nonlinear systems with unknown dead zones based on a small gain approach in this paper an adaptive fuzzy robust output feedback control problem is considered for a class of single input and single output nonlinear systems in a strict feedback form the considered systems possess the unstructured uncertainties unknown dead zone and the dynamics uncertainties and they do not assume the states being available for the controller design in the controller design fuzzy logic systems are first used to approximate the unstructured uncertainties and by utilizing the information of the bounds of the dead zone slopes and treating the time varying inputs coefficients as a system uncertainty a fuzzy state observer is designed to estimate the unmeasured states by combining a backstepping technique with a nonlinear small gain approach a new adaptive fuzzy robust output feedback control has been developed it is proved that the proposed fuzzy adaptive control approach can guarantee the semiglobal uniform ultimate boundedness for all the solutions of the closed loop systems simulation studies and comparisons with previous methods are included to illustrate the effectiveness of the proposed approach

non linear fokker planck equation solved with generalized finite differences in 2d and 3d abstract the generalized finite difference method gfdm has been proved to be a good meshless method to solve several both linear and nonlinear partial differential equations pdes wave propagation advection diffusion plates beams etc in this paper it is shown the application of the gfdm for solving the linear and nonlinear fokker planck equation in 2d and 3d criteria for convergence of fully explicit method using gfdm for fokker planck equation in 2d and 3d are given

quasi optimal convergence rate for an adaptive finite element method we analyze the simplest and most standard adaptive finite element method afem with any polynomial degree for general second order linear symmetric elliptic operators as is customary in practice the afem marks exclusively according to the error estimator and performs a minimal element refinement without the interior node property we prove that the afem is a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops this geometric decay is instrumental to derive the optimal cardinality of the afem we show that the afem yields a decay rate of the energy error plus oscillation in terms of the number of degrees of freedom as dictated by the best approximation for this combined nonlinear quantity

some new error estimates for ritz galerkin methods with minimal regularity assumptions new uniform error estimates are established for finite element approximations u h of solutions u of second order elliptic equations lu f using only the regularity assumption u 1 c f 1 using an aubin nitsche type duality argument we show for example that for arbitrary fixed e sufficiently small there exists an h 0 such that for 0 h h 0 u u h 0 e u u h 1 here s denotes the norm on the sobolev space h s other related results are established

convergence and quasi optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems recently an adaptive nonconforming finite element method anfem has been developed by carstensen and hoppe in numer math 103 251 266 2006 in this paper we extend the result to some nonsymmetric and indefinite problems the main tools in our analysis are a posteriori error estimators and a quasi orthogonality property in this case we need to overcome two main difficulties one stems from the nonconformity of the finite element space the other is how to handle the effect of a nonsymmetric and indefinite bilinear form an appropriate adaptive nonconforming finite element method featuring a marking strategy based on the comparison of the a posteriori error estimator and a volume term is proposed for the lowest order crouzeix raviart element it is shown that the anfem is a contraction for the sum of the energy error and a scaled volume term between two consecutive adaptive loops moreover quasi optimality in the sense of quasi optimal algorithmic complexity can be shown for the anfem the results of numerical experiments confirm the theoretical findings

poincare friedrichs inequalities for piecewise h 1 functions poincare friedrichs inequalities for piecewise h1 functions are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

multigrid algorithms for nonconforming and mixed methods for nonsymmetric and indefinite problems in this paper we consider multigrid algorithms for nonconforming and mixed finite element methods for nonsymmetric and or indefinite elliptic problems we show that a simple cal v cycle multigrid iteration using conforming coarse grid corrections converges at a uniform rate provided that the coarsest level in the multilevel iteration is sufficiently fine but independent of the number of multigrid levels various types of smoothers for the nonsymmetric and indefinite problems are discussed extensive numerical results are presented

robust a posteriori error estimation for nonconforming finite element approximation the equilibrated residual method for a posteriori error estimation is extended to nonconforming finite element schemes for the approximation of linear second order elliptic equations where the permeability coefficient is allowed to undergo large jumps in value across interfaces between differing media the estimator is shown to provide a computable upper bound on the error and up to a constant depending only on the geometry provides two sided bounds on the error the robustness of the estimator is also studied and the dependence of the constant on the jumps in permeability is given explicitly

adaptive control of a class of nonlinear pure feedback systems using fuzzy backstepping approach a controller is proposed for the robust backstepping control of a class of nonlinear pure feedback systems using fuzzy logic the proposed control scheme utilizes fuzzy logic systems to learn the behavior of the unknown plant dynamics filtered signals are employed to circumvent algebraic loop problems encountered in the implementation of the usual controllers and the approximation errors can be efficiently counteracted by employing smooth robust compensators most importantly the uniform ultimate boundedness of all signals in the closed loop system can be guaranteed and a priori knowledge of the plant dynamics is no longer required furthermore the proposed method can be used for adaptive control of a large class of single input single output nonlinear systems in both strict feedback and pure feedback forms and has great potential in many diverse applications the performance of the proposed approach is demonstrated through three simulation examples including one nonlinear pure feedback and two nonlinear strict feedback systems

adaptive neural control of uncertain mimo nonlinear systems with state and input constraints an adaptive neural control strategy for multiple input multiple output nonlinear systems with various constraints is presented in this paper to deal with the nonsymmetric input nonlinearity and the constrained states the proposed adaptive neural control is combined with the backstepping method radial basis function neural network barrier lyapunov function blf and disturbance observer by ensuring the boundedness of the blf of the closed loop system it is demonstrated that the output tracking is achieved with all states remaining in the constraint sets and the general assumption on nonsingularity of unknown control coefficient matrices has been eliminated the constructed adaptive neural control has been rigorously proved that it can guarantee the semiglobally uniformly ultimate boundedness of all signals in the closed loop system finally the simulation studies on a 2 dof robotic manipulator system indicate that the designed adaptive control is effective

convergence and optimality of adaptive mixed finite element methods the convergence and optimality of adaptive mixed finite element methods for the poisson equation are established in this paper the main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure of orthogonality a quasi orthogonality property is proved using the fact that the error is orthogonal to the divergence free subspace while the part of the error that is not divergence free can be bounded by the data oscillation using a discrete stability result this discrete stability result is also used to get a localized discrete upper bound which is crucial for the proof of the optimality of the adaptive approximation

direct adaptive fuzzy tracking control for a class of perturbed strict feedback nonlinear systems in this paper a novel direct adaptive fuzzy tracking control scheme is presented for a class of perturbed strict feedback nonlinear systems with unknown virtual control coefficients based on the mamdani type fuzzy logic system online approximation capability a direct adaptive fuzzy tracking controller is developed by using the backstepping approach the proposed design scheme guarantees that all the signals in the resulting closed loop system are uniform ultimate bounded and the tracking error converges to an arbitrarily small neighborhood of the origin in addition the number of the online adaptive parameters is not more than the order of the considered system and the possible controller singularity problem is removed by introducing the modified integral lyapunov functions finally two simulation examples are used to demonstrate the effectiveness of the proposed control scheme

framework for the a posteriori error analysis of nonconforming finite elements this paper establishes a unified framework for the a posteriori error analysis of a large class of nonconforming finite element methods the theory assures reliability and efficiency of explicit residual error estimates up to data oscillations under the conditions h1 h2 and applies to several nonconforming finite elements the crouzeix raviart triangle element the han parallelogram element the nonconforming rotated nr parallelogram element of rannacher and turek the constrained nr parallelogram element of hu and shi the p 1 element on parallelograms due to park and sheen and the dssy parallelogram element the theory is extended to include 1 irregular meshes with at most one hanging node per edge

systems of nonlinear hyperbolic equations associated with problems of classical electromagnetic theory abstract a broad survey of the influence of nonlinearity on diverse phenomena in classical electromagnetic theory is presented with the focus being on the plane wave nonlinear dielectric interaction problem and shock formation in distributed transmission lines connections with recent work in the are of quasilinear hyperbolic systems of balance laws are emphasized

on the efficiency of adaptive finite element methods for elliptic problems with discontinuous coefficients the successful implementation of adaptive finite element methods based on a posteriori error estimates depends on several ingredients an a posteriori error indicator a refinement coarsening strategy and the choice of various parameters the objective of the paper is to examine the influence of these factors on the performance of adaptive finite element methods for a model problem the linear elliptic equation with strongly discontinuous coefficients we derive a new a posteriori error estimator which depends locally on the oscillations of the coefficients around singular points extensive numerical experiments are reported to support our theoretical results and to show the competitive behaviors of the proposed adaptive algorithm

adaptive neural output feedback control of output constrained nonlinear systems with unknown output nonlinearity this paper addresses the problem of adaptive neural output feedback control for a class of special nonlinear systems with the hysteretic output mechanism and the unmeasured states a modified bouc wen model is first employed to capture the output hysteresis phenomenon in the design procedure for its fusion with the neural networks and the nussbaum type function two key lemmas are established using some extended properties of this model to avoid the bad system performance caused by the output nonlinearity a barrier lyapunov function technique is introduced to guarantee the prescribed constraint of the tracking error in addition a robust filtering method is designed to cancel the restriction that all the system states require to be measured based on the lyapunov synthesis a new neural adaptive controller is constructed to guarantee the prescribed convergence of the tracking error and the semiglobal uniform ultimate boundedness of all the signals in the closed loop system simulations are implemented to evaluate the performance of the proposed neural control algorithm in this paper

multilevel schwarz methods for elliptic problems with discontinuous coefficients in three dimensions multilevel schwarz methods are developed for a conforming finite element approximation of second order elliptic problems we focus on problems in three dimensions with possibly large jumps in the coefficients across the interface separating the subregions we establish a condition number estimate for the iterative operator which is independent of the coefficients and grows at most as the square of the number of levels we also characterize a class of distributions of the coefficients called quasi monotone for which the weighted l 2 projection is stable and for which we can use the standard piecewise linear functions as a coarse space in this case we obtain optimal methods i e bounds which are independent of the number of levels and subregions we also design and analyze multilevel methods with new coarse spaces given by simple explicit formulas we consider nonuniform meshes and conclude by an analysis of multilevel iterative substructuring methods

convergence of an adaptive mixed finite element method for kirchhoff plate bending problems some reliable and efficient a posteriori error estimators are produced for a mixed finite element method the hellan herrmann johnson h h j method for kirchhoff plate bending problems cf k hellan acta polytech scand civil engrg ser 46 1967 pp 1 28 l herrmann j eng mech div asce 93 1967 pp 13 26 c johnson numer math 21 1973 pp 43 62 based on these results with k 0 1 where k denotes the polynomial order of the discrete moment field space an adaptive mixed finite element method amfem is set up and its convergence and complexity are studied thoroughly the key points of the theoretical analysis include achieving a discrete helmholtz decomposition and a discrete inf sup condition which serve as the main tools in deducing the quasi orthogonality of the moment field and the discrete reliability of the estimator it is shown that the amfem is a contraction for the sum of the moment field error in an energy norm and the scaled error estimator between two consecutive adaptive loops moreover an estimate for the amfem s complexity via the number of elements is developed

paper instability analysis and improvement of robustness of adaptive control the effects of unmodeled high frequency dynamics and bounded disturbances on stability and performance of adaptive control schemes are analyzed five possible types of instability mechanisms parameter drift linear instability fast adaptation instability high frequency instability and throughput instability are analyzed using simple examples a procedure is used to construct lyapunov like functions for a modified adaptive controller applied to a dominant plant of relative degree one in the presence of parasitics and disturbances and obtain sufficient conditions under which none of the five types of instability can occur the modified scheme is robust in the sense that it guarantees the existence of a large region of attraction from which all the trajectories remain bounded and the state errors converge exponentially to a much smaller residual set the size of the region of attraction depends on the speed of parasitics in such a way that as the parasitics become infinitely fast the region of attraction becomes the whole space

deadzone compensation in motion control systems using neural networks a compensation scheme is presented for general nonlinear actuator deadzones of unknown width the compensator uses two neural networks nns one to estimate the unknown deadzone and another to provide adaptive compensation in the feedforward path the compensator nn has a special augmented form containing extra neurons whose activation functions provide a jump function basis set for approximating piecewise continuous functions rigorous proofs of closed loop stability for the deadzone compensator are provided and yield tuning algorithms for the weights of the two nns the technique provides a general procedure for using nns to determine the preinverse of an unknown right invertible function

adaptive output feedback fuzzy tracking control for a class of nonlinear systems this paper is concerned with the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems the dynamic feedback strategy begins with an input driven filter by utilizing fuzzy logic systems to approximate unknown and desired control input signals directly instead of the unknown nonlinear functions an output feedback fuzzy tracking controller is designed via a backstepping approach it is shown that the proposed fuzzy adaptive output controller can guarantee that all the signals remain bounded and that the tracking error converges to a small neighborhood of the origin simulations results are presented to demonstrate the effectiveness of the proposed methods

robust control for a class of uncertain nonlinear systems adaptive fuzzy approach based on backstepping a robust adaptive fuzzy control design approach is developed for a class of multivariable nonlinear systems with modeling uncertainties and external disturbances the controller design for the overall systems has been carried out through a number of simpler controller designs for a series of the relevant auxiliary systems based on the backstepping design technique for each auxiliary system an adaptive fuzzy logic system is introduced to learn the behavior of unknown dynamics and then a robust control algorithm is employed to efficiently compensate the approximation error and the external disturbances as well it is shown that the resulting closed loop systems guarantee a satisfactory transient and asymptotic performance a simulation example is also presented to illustrate the design procedure and controller performance

spectral methods in general relativistic astrophysics we present spectral methods developed in our group to solve three dimensional partial differential equations the emphasis is laid on equations arising from astrophysical problems in the framework of general relativity

fuzzy approximation based adaptive control of strict feedback nonlinear systems with time delays this paper focuses on the problem of adaptive control for a class of nonlinear time delay systems with unknown nonlinearities and strict feedback structure based on the lyapunov krasovskii functional approach a state feedback adaptive controller is constructed by backstepping the proposed adaptive controller guarantees that the system output converges into a small neighborhood of the reference signal and all the signals of the closed loop system remain bounded compared with the results that exist the main advantage of the proposed method is that the controller design is independent of the choice of the fuzzy membership functions therefore a priori knowledge of fuzzy approximators is not necessary for control design and the proposed approach requires only one adaptive law for an nth order system two numerical examples are used to illustrate the effectiveness of the proposed approach

error reduction and convergence for an adaptive mixed finite element method an adaptive mixed finite element method amfem is designed to guarantee an error reduction also known as saturation property after each refinement step the error for the fine mesh is strictly smaller than the error for the coarse mesh up to oscillation terms this error reduction property is established here for the raviart thomas finite element method with a reduction factor p 1 uniformly for the l 2 norm of the flux errors our result allows for linear convergence of a proper adaptive mixed finite element algorithm with respect to the number of refinement levels the adaptive algorithm surprisingly does not require any particular mesh design unlike the conforming finite element method the new arguments are a discrete local efficiency and a quasi orthogonality estimate the proof does not rely on duality or on regularity

adaptive fuzzy tracking control for a class of perturbed strict feedback nonlinear time delay systems this paper is concerned with the problem of adaptive fuzzy output tracking for a class of perturbed strict feedback nonlinear systems with time delays and unknown virtual control coefficients fuzzy logic systems in mamdani type are used to approximate the unknown nonlinear functions then the adaptive fuzzy tracking controller is designed by using the backstepping technique and lyapunov krasovskii functionals the proposed adaptive fuzzy controller guarantees that all the signals in the closed loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal an advantage of the proposed control scheme lies in that the number of the online adaptive parameters is not more than the order of the original system finally two examples are used to demonstrate the effectiveness of our results proposed in this paper

a convergent nonconforming adaptive finite element method with quasi optimal complexity in this paper we prove convergence and quasi optimal complexity of a simple adaptive nonconforming finite element method in each step of the algorithm the iterative solution of the discrete system is controlled by an adaptive stopping criterion and the local refinement is based on either a simple edge residual or a volume term depending on an adaptive marking strategy we prove that this marking strategy guarantees a strict reduction of the error augmented by the volume term and an additional oscillation term and quasi optimal complexity of the generated sequence of meshes

application of the generalized finite difference method to solve the advection diffusion equation the study of the advection diffusion equation continues to be an active field of research the subject has important applications to fluid dynamics as well as many other branches of science and engineering this paper shows the application of the generalized finite difference method to solve the advection diffusion equation by the explicit method the convergence of the method has been studied and the truncation error over irregular grids is given an example has been solved using the explicit finite difference formulae and the criterion of stability

convergence and domain decomposition algorithm for nonconforming and mixed methods for nonselfadjoint and indefinite problems in this paper the existence uniqueness and convergence of the solutions of nonconforming and mixed methods with non quasi uniform partition are proven for nonselfadjoint and indefinite second order elliptic problems under minimal regularity assumption moreover uniform convergence of the solution of nonconforming method is obtained meanwhile the domain decomposition algorithm which suits non quasi uniform partition is proposed for nonconforming and mixed methods

convergence analysis of an adaptive nonconforming finite element method an adaptive nonconforming finite element method is developed and analyzed that provides an error reduction due to the refinement process and thus guarantees convergence of the nonconforming finite element approximations the analysis is carried out for the lowest order crouzeix raviart elements and leads to the linear convergence of an appropriate adaptive nonconforming finite element algorithm with respect to the number of refinement levels important tools in the convergence proof are a discrete local efficiency and a quasi orthogonality property the proof does neither require regularity of the solution nor uses duality arguments as a consequence on the data control no particular mesh design has to be monitored