on monotonicity preserving stabilized finite element approximations of transport problems the aim of this work is to design monotonicity preserving stabilized finite element techniques for transport problems as a blend of linear and nonlinear shock capturing stabilization as linear stabilization we consider and analyze a novel symmetric projection stabilization technique based on a local scott zhang projector next we design a weighting of the aforementioned linear stabilization such that when combined with a finite element discretization enjoying a discrete maximum principle usually attained via nonlinear stabilization it does not spoil these monotonicity properties then we propose novel nonlinear stabilization schemes in the form of an artificial viscosity method where the amount of viscosity is proportional to gradient jumps at either finite element boundaries or nodes for the nodal scheme we prove a discrete maximum principle for time dependent multidimensional transport problems numerical experiments support the numerical analysis and we show that the resulting methods prov

realization of synchronization in time delayed systems with stochastic perturbation since noise is ubiquitous in both nature and artificial systems the stochastic perturbation influence on the dynamics of the unidirectionally coupled ikeda models is investigated in this paper on the one hand sufficient conditions on the complete synchronization between these noise perturbed and chaotic models are mathematically established and an estimation of the sample transverse lyapunov exponent is rigorously derived on the other hand specific examples and their numerical simulations are provided to illustrate the feasibility of our theoretical results moreover the results on the ikeda models are further generalized to a wide class of coupled nonlinear systems with multiple time delays and a common additive noise it is believed that the idea and approach developed in this paper could be further generalized to investigate some other problems on chaos synchronization and chaos control with stochastic perturbation

on the design of general purpose flux limiters for finite element schemes i scalar convection the algebraic flux correction afc paradigm is extended to finite element discretizations with a consistent mass matrix it is shown how to render an implicit galerkin scheme positivity preserving and remove excessive artificial diffusion in regions where the solution is sufficiently smooth to this end the original discrete operators are modified in a mass conserving fashion so as to enforce the algebraic constraints to be satisfied by the numerical solution a node oriented limiting strategy is employed to control the raw antidiffusive fluxes which consist of a convective part and a contribution of the consistent mass matrix the former offsets the artificial diffusion due to upwinding of the spatial differential operator and lends itself to an upwind biased flux limiting the latter eliminates the error induced by mass lumping and calls for the use of a symmetric flux limiter the concept of a target flux and a new definition of upper lower bounds make it possible to combine the advantages of algebraic fct and tvd schemes introduced previously by the author and his coworkers unlike other high resolution schemes for unstructured meshes the new algorithm reduces to a consistent high order galerkin scheme in smooth regions and is designed to provide an optimal treatment of both stationary and time dependent problems its performance is illustrated by application to the linear advection equation for a number of 1d and 2d configurations

stability and error estimates of a new high order compact adi method for the unsteady 3d convection diffusion equation abstract in this paper a new high order compact adi method for the unsteady convection diffusion equation in three dimension 3d is considered collecting the truncation error of the finite difference operator by the recursion method we derive a new high order compact finite difference scheme for the unsteady 1d convection diffusion equation firstly then based on the adi method applying a correction technique to reduce the error of the splitting term a high order compact adi method for the unsteady 3d convection diffusion equation is proposed in which we solve a series of 1d problems with strictly diagonal dominant tri diagonal structures instead of the high dimensional ones the scheme is proved to be unconditional stable moreover the regularity and error estimate of the numerical solution are derived finally some numerical examples are performed which confirm the theoretical prediction and show that much better computational accuracy results can be got by applying the new scheme

identification of delays and discontinuity points of unknown systems by using synchronization of chaos in this paper we present an approach in which synchronization of chaos is used to address identification problems in particular we are able to identify i the discontinuity points of systems described by piecewise dynamical equations and ii the delays of systems described by delay differential equations delays and discontinuities are widespread features of the dynamics of both natural and manmade systems the foremost goal of the paper is to present a general and flexible methodology that can be used in a broad variety of identification problems

adaptive approximation method for joint parameter estimation and identical synchronization of chaotic systems we introduce a numerical approximation method for estimating an unknown parameter of a primary chaotic system which is partially observed through a scalar time series specifically we show that the recursive minimization of a suitably designed cost function that involves the dynamic state of a fully observed secondary system and the observed time series can lead to the identical synchronization of the two systems and the accurate estimation of the unknown parameter the salient feature of the proposed technique is that the only external input to the secondary system is the unknown parameter which needs to be adjusted we present numerical examples for the lorenz system which show how our algorithm can be considerably faster than some previously proposed methods

on the stabilization of persistently excited linear systems we consider control systems of the type dot x ax alpha t bu where u in mathbf r a b is a controllable pair and alpha is an unknown measurable time varying signal with values in 0 1 satisfying a persistent excitation condition of the type int t t t alpha s ds geq mu for every t geq0 with 0 mu leq t independent of t we prove that such a system is stabilizable with a linear feedback depending only on the pair t mu if the eigenvalues of a have a nonpositive real part we also show that stabilizability does not hold for an arbitrary matrix a moreover the question of whether the system can be stabilized or not with an arbitrarily large rate of convergence gives rise to a bifurcation phenomenon depending on the parameter mu t

explicit runge kutta schemes and finite elements with symmetric stabilization for first order linear pde systems we analyze explicit runge kutta schemes in time combined with stabilized finite elements in space to approximate evolution problems with a first order linear differential operator in space of friedrichs type for the time discretization we consider explicit second and third order runge kutta schemes we identify a general set of properties on the space stabilization encompassing continuous and discontinuous finite elements under which we prove stability estimates using energy arguments then we establish l 2 norm error estimates with quasi optimal convergence rates for smooth solutions in space and time these results hold under the usual cfl condition for third order runge kutta schemes and any polynomial degree in space and for second order runge kutta schemes and first order polynomials in space for second order runge kutta schemes and higher polynomial degrees in space a tightened 4 3 cfl condition is required numerical results are presented for smooth and rough solutions the case of finite volumes is briefly discussed

a monotone finite element scheme for convection diffusion equations a simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection diffusion problems in any spatial dimension by properly averaging the pde coefficients on element edges the resulting finite element stiffness matrix is an m matrix under some mild assumption for the underlying generally unstructured finite element grids as a consequence the proposed edge averaged finite element scheme is particularly interesting for the discretization of convection dominated problems this scheme admits a simple variational formulation it is easy to analyze and it is also suitable for problems with a relatively smooth flux variable some simple numerical examples are given to demonstrate its effectiveness for convection dominated problems

nonlinear diffusion and discrete maximum principle for stabilized galerkin approximations of the convection diffusion reaction equation we investigate stabilized galerkin approximations of linear and nonlinear convectiondiffusion reaction equations we derive nonlinear streamline and cross wind diffusion methods that guarantee a discrete maximum principle for strictly acute meshes and first order polynomial interpolation for pure convectiondiffusion problems the discrete maximum principle is achieved using a nonlinear cross wind diffusion factor that depends on the angle between the discrete solution and the flow velocity for convectiondiffusion reaction problems two methods are considered residual based isotropic diffusion and the previous nonlinear cross wind diffusion factor supplemented by additional isotropic diffusion scaling as the square of the mesh size practical versions of the present methods suitable for numerical implementation are compared to previous discontinuity capturing schemes lacking theoretical justification numerical results are investigated in terms of both solution quality violation of maximum principle smearing of internal layers and computational costs

stabilized galerkin approximation of convection diffusion reaction equations discrete maximum principle and convergence we analyze a nonlinear shock capturing scheme for h1 conforming piecewise affine finite element approximations of linear elliptic problems the meshes are assumed to satisfy two standard conditions a local quasi uniformity property and the xu zikatanov condition ensuring that the stiffness matrix associated with the poisson equation is an m matrix a discrete maximum principle is rigorously established in any space dimension for convection diffusion reaction problems we prove that the shock capturing finite element solution converges to that without shock capturing if the cell peclet numbers are sufficiently small moreover in the diffusion dominated regime the difference between the two finite element solutions super converges with respect to the actual approximation error numerical experiments on test problems with stiff layers confirm the sharpness of the a priori error estimates

flux correction tools for finite elements flux correction in the finite element context is addressed criteria for positivity of the numerical solution are formulated and the low order transport operator is constructed from the discrete high order operator by adding modulated dissipation so as to eliminate negative off diagonal entries the corresponding antidiffusive terms can be decomposed into a sum of genuine fluxes rather than element contributions which represent bilateral mass exchange between individual nodes thereby essentially one dimensional flux correction tools can be readily applied to multidimensional problems involving unstructured meshes the proposed methodology guarantees mass conservation and makes it possible to design both explicit and implicit fct schemes based on a unified limiting strategy numerical results for a number of benchmark problems illustrate the performance of the algorithm

a maximum principle preserving finite element method for scalar conservation equations this paper introduces a first order viscosity method for the explicit approximation of scalar conservation equations with lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension provided the lumped mass matrix is positive definite the method is shown to satisfy the local maximum principle under a usual cfl condition the method is independent of the cell type for instance the mesh can be a combination of tetrahedra hexahedra and prisms in three space dimensions

a projection and an effect in a synaptic algebra abstract we study a pair p e consisting of a projection p an idempotent and an effect e an element between 0 and 1 in a synaptic algebra a generalization of the self adjoint part of a von neumann algebra we show that some of halmos s theory of two projections or two subspaces including a version of his cs decomposition theorem applies in this setting and we introduce and study two candidates for a commutator projection for p and e

failure of parameter identification based on adaptive synchronization techniques in this paper several examples as well as their numerical simulations are provided to show some possible failures of parameter identification based on the so called adaptive synchronization techniques these failures might arise not only when the synchronized orbit produced by the driving system is designed to be either some kind of equilibrium or to be some kind of periodic orbit but also when this orbit is deliberately designed to be chaotic the reason for emergence of these failures is theoretically analyzed in the paper and the boundedness of all trajectories generated by the coupled systems is rigorously proved moreover synchronization techniques are proposed to realize complete synchronization and unknown parameter identification in a class of systems where nonlinear terms are not globally lipschitz in addition unknown parameter identification is studied in coupled systems with time delays

stability and bifurcation in a neural network model with two delays abstract a simple neural network model with two delays is considered linear stability of the model is investigated by analyzing the associated characteristic transcendental equation for the case without self connection it is found that the hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold theorem an example is given and numerical simulations are performed to illustrate the obtained results

adaptive synchronization of neural networks with time varying delay and distributed delay abstract in this paper the adaptive synchronization of neural networks with time varying delay and distributed delay is discussed based on the lasalle invariant principle of functional differential equations and the adaptive feedback control technique some sufficient conditions for adaptive synchronization of such a system are obtained finally a numerical example is given to show the effectiveness of the proposed synchronization method

blending low order stabilised finite element methods a positivity preserving local projection method for the convection diffusion equation in this work we propose a nonlinear blending of two low order stabilisation mechanisms for the convection diffusion equation the motivation for this approach is to preserve monotonicity without sacrificing accuracy for smooth solutions the approach is to blend a first order artificial diffusion method which will be active only in the vicinity of layers and extrema with an optimal order local projection stabilisation method that will be active on the smooth regions of the solution we prove existence of discrete solutions as well as convergence under appropriate assumptions on the nonlinear terms and on the exact solution numerical examples show that the discrete solution produced by this method remains within the bounds given by the continuous maximum principle while the layers are not smeared significantly

on spurious oscillations at layers diminishing sold methods for convection diffusion equations part ii analysis for p1 and q1 finite elements abstract an unwelcome feature of the popular streamline upwind petrov galerkin supg stabilization of convection dominated convection diffusion equations is the presence of spurious oscillations at layers a review and a comparison of the most methods which have been proposed to remove or at least to diminish these oscillations without leading to excessive smearing of the layers are given in part i v john p knobloch on spurious oscillations at layers diminishing sold methods for convection diffusion equations part i a review comput methods appl mech engrg 196 2007 2197 2215 in the present paper the most promising of these sold methods are investigated in more detail for p 1 and q 1 finite elements in particular the dependence of the results on the mesh the data of the problems and parameters of the methods are studied analytically and numerically furthermore the numerical solution of the nonlinear discrete problems is discussed and the capability of adaptively refined grids for reducing spurious oscillations is examined our conclusion is that also for simple problems any of the sold methods generally provides solutions with non negligible spurious oscillations

edge stabilization for galerkin approximations of convection diffusion reaction problems n this paper we recall a stabilization technique for finite element methods for convection diffusion reaction equations originally proposed by j douglas jr and t dupont in computing methods in applied sciences second internat sympos versailles 1975 207 216 lecture notes in phys 58 springer berlin 1976 mr0440955 55 13823 the method uses least square stabilization of the gradient jumps across element boundaries we prove that the method is stable in the hyperbolic limit and prove optimal a priori error estimates we address the question of monotonicity of discrete solutions and present some numerical examples illustrating the theoretical results

use of synchronization and adaptive control in parameter estimation from a time series a technique is introduced for estimating unknown parameters when a time series of only one variable from a multivariate nonlinear dynamical system is given the technique employs a combination of two different control methods linear feedback for synchronizing system variables and adaptive control and is based on dynamic minimization of synchronization error the technique is shown to work even when the unknown parameters appear in the evolution equations of the variables other than the one for which the time series is given the technique not only establishes that explicit detailed information about all system variables and parameters is contained in a scalar time series but also gives a way to extract it out under suitable conditions illustrations are presented for lorenz and rossler systems and a nonlinear dynamical system in plasma physics also it is found that the technique is reasonably stable against noise in the given time series and the estimated value of a parameter fluctuates around the correct value with the error of estimation growing linearly with the noise strength for small noise

structure identification of uncertain general complex dynamical networks with time delay it is well known that many real world complex networks have various uncertain information such as unknown or uncertain topological structure and node dynamics the structure identification problem has theoretical and practical importance for uncertain complex dynamical networks at the same time time delay often appears in the state variables or coupling coefficients of various practical complex networks this paper initiates a novel approach for simultaneously identifying the topological structure and unknown parameters of uncertain general complex networks with time delay in particular this method is also effective for uncertain delayed complex dynamical networks with different node dynamics moreover the proposed method can be easily extended to monitor the on line evolution of network topological structure finally three representative examples are then given to verify the effectiveness of the proposed approach

a second order maximum principle preserving lagrange finite element technique for nonlinear scalar conservation equations this paper proposes an explicit at least second order maximum principle sat isfying lagrange finite element method for solving nonlinear scalar conservation equations the technique is based on a new viscous bilinear form introduced in guermond and nazarov com put methods appl mech engrg 272 2014 pp 198 213 a high order entropy viscosity method and the boris book zalesak flux correction technique the algorithm works for arbitrary meshes in any space dimension and for all lipschitz fluxes the formal second order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems

adaptive identification of time delays in nonlinear dynamical models this paper develops an adaptive synchronization strategy to identify both discrete and distributed time delays in nonlinear dynamical models in contrast with adaptive techniques for parameter estimation in the literature the adaptive strategy developed here for time delay identification invites more precise results that have physical and dynamical importance it is analytically and numerically found that distributed time delays in a model with an asymptotically stable steady state can be adaptively identified and which is different from the case of discrete time delays identification other aspects of the strategy developed here for time delay identification are illustrated by several representative dynamical models aside from illustrations for toy models and their generated data the strategy developed is used with experimental data to identify a time delay called transcriptional delay in a model describing the transcription of messenger rnas mrnas for notch signaling molecules

synchronization based estimation of all parameters of chaotic systems from time series by a simple combination of adaptive scheme and linear feedback with the updated feedback strength for a large class of chaotic systems it is proved rigorously by using the invariance principle of differential equations that all unknown model parameters can be estimated dynamically this approach supplies a systematic and analytical procedure for estimating parameters from time series and it is simple to implement in practice in addition this method is quite robust against the effect of noise and able to respond rapidly to changes in operating parameters of the experimental system lorenz and r ossler hyperchaos systems are used to illustrate the validity of this technique

stabilization role of inhibitory self connections in a delayed neural network abstract in a delayed hopfield neural network that is strongly connected with non inhibitory interconnections fast and inhibitory self connections lead to global convergence to a unique equilibrium of the network by applying monotone dynamical systems theory and an embedding technique we prove that this conclusion remains true without the requirement of strong connectivity or non inhibitory interconnections

linearity preserving monotone local projection stabilization schemes for continuous finite elements abstract this paper presents some new tools for enforcing discrete maximum principles and or positivity preservation in continuous piecewise linear finite element approximations to convection dominated transport problems using a linear first order advection equation as a model problem we construct element level bilinear forms associated with first order artificial diffusion operators and their two scale counterparts the underlying design philosophy is similar to that behind local projection stabilization lps techniques and variational multiscale vms methods the difference lies in the structure of the local stabilization operator and in the way in which the resolved scales are detected the proposed stabilization term penalizes the difference between the nodal values and cell averages of the finite element solution in a manner which guarantees monotonicity and linearity preservation the value of the stabilization parameter is determined using a multidimensional limiter function designed to prevent unresolvable fine scale effects from creating undershoots or overshoots the result is a nonlinear high resolution scheme capable of resolving moving fronts and internal boundary layers as sharp localized nonoscillatory features the use of variational gradient recovery makes it possible to add high order background dissipation leading to improved approximation properties in smooth regions the numerical behavior of the constrained schemes is illustrated by a grid convergence study for stationary and time dependent test problems in two space dimensions

a petrov galerkin finite element method for convection dominated flows an accurate upwinding technique for satisfying the maximum principle abstract in this paper we present a new petrov galerkin method for convection dominated flow problems which is conservative and satisfies the discrete maximum principle this method also possesses no spurious crosswind diffusion and gives very accurate solutions the method is representative of a class of methods which may be described as fixed mesh adaptive

edge based nonlinear diffusion for finite element approximations of convection diffusion equations and its relation to algebraic flux correction schemes for the case of approximation of convection diffusion equations using piecewise affine continuous finite elements a new edge based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle the diffusion operator is shown to be lipschitz continuous and linearity preserving using these properties we provide a full stability and error analysis which in the diffusion dominated regime shows existence uniqueness and optimal convergence then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters the performance of the method is illustrated on some numerical test cases in two space dimensions

on spurious oscillations at layers diminishing sold methods for convection diffusion equations part i a review abstract an unwelcome feature of the popular streamline upwind petrov galerkin supg stabilization of convection dominated convection diffusion equations is the presence of spurious oscillations at layers since the mid of the 1980s a number of methods have been proposed to remove or at least to diminish these oscillations without leading to excessive smearing of the layers the paper gives a review and state of the art of these methods discusses their derivation proposes some alternative choices of parameters in the methods and categorizes them some numerical studies which supplement this review provide a first insight into the advantages and drawbacks of the methods

a discontinuity capturing crosswind dissipation for the finite element solution of the convection diffusion equation abstract to avoid the local oscillations that still remain using the streamline upwind petrov galerkin formulation for the scalar convection diffusion equation the introduction of a nonlinear crosswind dissipation is proposed it is shown that the method is less overdiffusive than other discontinuity capturing techniques and has better numerical behavior the design of the crosswind diffusion is based on the study of the discrete maximum principle for some simple cases

analysis of algebraic flux correction schemes a family of algebraic flux correction afc schemes for linear boundary value problems in any space dimension is studied these methods main feature is that they limit the fluxes along each one of the edges of the triangulation and we suppose that the limiters used are symmetric for an abstract problem the existence of a solution existence and uniqueness of the solution of a linearized problem and an a priori error estimate are proved under rather general assumptions on the limiters for a particular but standard in practice choice of the limiters it is shown that a local discrete maximum principle holds the theory developed for the abstract problem is applied to convection diffusion reaction equations where in particular an error estimate is derived numerical studies show its sharpness

realization of parameters identification in only locally lipschitzian dynamical systems with multiple types of time delays most of the existing results for identifying parameters in dynamical systems through adaptive coupling techniques always require a uniform lipschitz condition on system vector fields however it is not this requirement but the only locally lipschitz condition that is more suitable for many nonlinear systems in real applications also time delays sometimes are essential for modeling real systems so that in addition to the discrete form time delays in the distributed form could be considered this paper thus considers the problem of parameters identification in only locally lipschitzian dynamical systems with multiple types of time delays through adaptive coupling techniques in particular the paper proposes some linear independence conditions for realization of parameters identification in both nonautonomous and autonomous systems and draws a comparison between these conditions and the persistent of excitation condition which is used frequently in the literature moreover the paper proposes an index t

weighting the edge stabilization a modification of the edge stabilization technique is proposed to improve the behavior of the method when solving conservation equations with nonsmooth data or nonsmooth solutions the key ingredient is tempering the edge stabilization in regions of large gradients through appropriate weights the new method is shown to preserve the convergence properties of the original method on smooth solutions and numerical tests indicate that it performs better on nonsmooth solutions

on oscillation of a logistic equation with several delays abstract for a scalar delay logistic equation y t y t k 1 m r k t 1 y h k t k h k t t a connection between oscillating properties of this equation the corresponding differential inequalities and the linear equation x t k 1 m r k t x h k t 0 is established explicit nonoscillation and oscillation conditions are presented

stability analysis of explicit entropy viscosity methods for non linear scalar conservation equations this material is based upon work supported by the department of homeland security under agreement 2008 dn 077 ari018 02 national science foundation grants dms 0811041 dms 0914977 dms 1015984 af office of scientific research grant fa99550 12 0358 and is partially supported by award kus c1 016 04 made by king abdullah university of science and technology kaust