discontinuous galerkin approximations of the stokes and navier stokes equations numerical schemes to compute approximate solutions of the evolutionary stokes and navier stokes equations are studied the schemes are discontinuous in time and conforming in space and of arbitrarily high order fully discrete error estimates are derived and dependence of the viscosity constant is carefully tracked it is shown that the errors are bounded by projection errors of the exact solution which exhibit optimal rates when the solutions are smooth

unbiased estimation with square root convergence for sde models in many settings in which monte carlo methods are applied there may be no known algorithm for exactly generating the random object for which an expectation is to be computed frequently however one can generate arbitrarily close approximations to the random object we introduce a simple randomization idea for creating unbiased estimators in such a setting based on a sequence of approximations applying this idea to computing expectations of path functionals associated with stochastic differential equations sdes we construct finite variance unbiased estimators with a square root convergence rate for a general class of multidimensional sdes we then identify the optimal randomization distribution numerical experiments with various path functionals of continuous time processes that often arise in finance illustrate the effectiveness of our new approach

convergence analysis and error estimates for a parallel algorithm for solving the navier stokes equations this paper is concerned with the analysis of the convergence and the derivation of error estimates for a parallel algorithm which is used to solve the incompressible navier stokes equations as usual the main idea is to split the main differential operator this allows to consider independently the two main difficulties namely nonlinearity and incompressibility the results justify the observed accuracy of related numerical results

long term dissipativity of time stepping algorithms for an abstract evolution equation with applications to the incompressible mhd and navier stokes equations abstract this paper examines the long term dissipativity and unconditional non linear stability of time integration algorithms for the incompressible mhd equations the results apply as a particular case to the uncoupled incompressible navier stokes equations the analysis is performed in the setting defined by an abstract evolution equation possessing the same long term dissipative structure as the above physical systems a general class of time stepping schemes is analyzed in this context showing the non linear unconditional stability and long term dissipativity of particular members of this family of algorithms in particular algorithms showing these strong properties which additionally involve the solution of a linear problem at each time step are identified a particular linear algorithm is shown to exhibit optimal long term dissipative properties and to possess an algorithmic global attractor these abstract results apply rigorously to galerkin mixed finite element discretizations of the problem to this end it is shown that such galerkin type projection inherits the dissipative properties of the continuum problem computational aspects involved in the numerical implementation of these methods are addressed and illustrated in representative numerical simulations

the asymptotic efficiency of simulation estimators a decision theoretic framework is proposed for evaluating the efficiency of simulation estimators the framework includes the cost of obtaining the estimate as well as the cost of acting based on the estimate the cost of obtaining the estimate and the estimate itself are represented as realizations of jointly distributed stochastic processes in this context the efficiency of a simulation estimator based on a given computational budget is defined as the reciprocal of the risk the overall expected cost this framework is appealing philosophically but it is often difficult to apply in practice e g to compare the efficiency of two different estimators because only rarely can the efficiency associated with a given computational budget be calculated however a useful practical framework emerges in a large sample context when we consider the limiting behavior as the computational budget increases a limit theorem established for this model supports and extends a fairly well known efficiency principle

multilevel splitting for estimating rare event probabilities we analyze the performance of a splitting technique for the estimation of rare event probabilities by simulation a straightforward estimator of the probability of an event evaluates the proportion of simulated paths on which the event occurs if the event is rare even a large number of paths may produce little information about its probability using this approach the method we study reinforces promising paths at intermediate thresholds by splitting them into subpaths which then evolve independently if implemented appropriately this has the effect of dedicating a greater fraction of the computational effort to informative runs we analyze the method for a class of models in which roughly speaking the number of states through which each threshold can be crossed is bounded under additional assumptions we identify the optimal degree of splitting at each threshold as the rarity of the event increases it should be set so that the expected number of subpaths reaching each threshold remains roughly constant thus implemented the method is provably effective in a sense appropriate to rare event simulations these results follow from a branching process analysis of the method we illustrate our theoretical results with some numerical examples for queueing models

the postprocessed mixed finite element method for the navier stokes equations refined error bounds a postprocessing technique for mixed finite element methods for the incompressible navier stokes equations is analyzed the postprocess which amounts to solving a linear stokes problem is shown to increase the order of convergence of the method to which it is applied by one unit times the logarithm of the mesh diameter in proving the error bounds some superconvergence results are also obtained contrary to previous analysis of the postprocessing technique in the present paper we take into account the loss of regularity suffered by the solutions of the navier stokes equations at the initial time in the absence of nonlocal compatibility conditions of the data as in h g heywood and r rannacher siam j numer anal 25 1988 pp 489 512 where the same hypothesis is assumed no better than fifth order convergence is achieved

flow rate boundary problems for an incompressible fluid in deformable domains formulations and solution methods in this paper we consider the numerical solution of the interaction of an incompressible fluid and an elastic structure in a truncated computational domain as well known in this case there is the problem of prescribing realistic boundary data on the artificial sections when only partial data are available this problem has been investigated extensively for the rigid case in this work we start considering the compliant case by focusing on the flow rate conditions for the fluid we propose three formulations of this problem different algorithms for its numerical solution and carry out several 2d numerical simulations with the aim of comparing the performances of the different algorithms

stability and convergence of the higher projection method for the time dependent viscoelastic flow problem abstract in this paper the time discrete higher order projection method is proposed and analyzed for the time dependent viscoelastic flow problem our numerical method is based on the time iterative discrete schemes by the projection method the considered problem is decoupled into two linear subproblems one is for the velocity and the other is for the pressure unconditional stability of the numerical schemes is established convergence results for the velocity and pressure are also derived our main results of this paper are that the convergence analysis for the velocity is weakly second order and for the pressure is weakly first order finally some numerical examples are provided to confirm the performances of the developed numerical algorithms

a posteriori error estimations for mixed finite element approximations to the navier stokes equations a posteriori estimates for mixed finite element discretizations of the navier stokes equations are derived we show that the task of estimating the error in the evolutionary navier stokes equations can be reduced to the estimation of the error in a steady stokes problem as a consequence any available procedure to estimate the error in a stokes problem can be used to estimate the error in the nonlinear evolutionary problem a practical procedure to estimate the error based on the so called postprocessed approximation is also considered both the semidiscrete in space and the fully discrete cases are analyzed some numerical experiments are provided

finite element approximation of the nonstationary navier stokes problem i regularity of solutions and second order error estimates for spatial discretization this is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary navier stokes equations second order error estimates are proven for spatial discretization using conforming or nonconforming elements the results indicate a fluid like behavior of the approximations even in the case of large data so long as the solution remains regular the analysis is based on sharp a priori estimates for the solution particularly reflecting its behavior as t to 0 and as t to infty it is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the navier stokes equations as it depends on nonlocal compatibility conditions for the data the results which are presented here are independent of such compatibility conditions which cannot be verified in practice

adaptive mimo antenna selection via discrete stochastic optimization recently it has been shown that it is possible to improve the performance of multiple input multiple output mimo systems by employing a larger number of antennas than actually used and selecting the optimal subset based on the channel state information existing antenna selection algorithms assume perfect channel knowledge and optimize criteria such as shannon capacity or various bounds on error rate this paper examines mimo antenna selection algorithms where the set of possible solutions is large and only a noisy estimate of the channel is available in the same spirit as traditional adaptive filtering algorithms we propose simulation based discrete stochastic optimization algorithms to adaptively select a better antenna subset using criteria such as maximum mutual information bounds on error rate etc these discrete stochastic approximation algorithms are ideally suited to minimize the error rate since computing a closed form expression for the error rate is intractable we also consider scenarios of time varying channels for which the antenna selection algorithms can track the time varying optimal antenna configuration we present several numerical examples to show the fast convergence of these algorithms under various performance criteria and also demonstrate their tracking capabilities

the stabilized extrapolated trapezoidal finite element method for the navier stokes equations abstract we consider a fully discrete stabilized finite element method for the navier stokes equations which is unconditionally stable and has second order temporal accuracy of o k 2 hk spatial error the method involves a simple artificial viscosity stabilization of the linear system for the approximation of the new time level connected to anti diffusion of its effects at the old time level lowering the cell reynolds number of the oseen problem to o 1 the method requires only the solution of one linear system arising from an oseen problem per time step the effectiveness of the method is illustrated in several numerical experiments

calculation of incompressible viscous flows by an unconditionally stable projection fem this paper investigates the numerical performance of a finite element implementation of a new incremental fractional step method to compute steady and unsteady incompressible viscous flows under general boundary conditions and using unstructured meshes a variational framework is adopted which accommodates two different spaces for representing and approximating the velocity fields calculated respectively in the viscous and inviscid phases of the method but which leads to a very simple numerical scheme in terms of only one discrete velocity field an unconditionally stable semi implicit approximation of the nonlinear term is used to eliminate any time step restriction as far as the numerical stability is concerned numerical results for five test problems in two dimensions are reported to illustrate the flexibility of the proposed method

first order decoupled finite element method of the three dimensional primitive equations of the ocean this paper is concerned with a first order fully discrete decoupled method for solving the three dimensional 3d primitive equations of the ocean with the dirichlet boundary conditions on the side where a decoupled semi implicit scheme is used for the time discretization and the p 1 p 1 p 1 p 1 p 1 finite element for velocity pressure and density is used for the spatial discretization of these equations the h 1 l 2 h 1 optimal error estimates for the numerical solution u h n p h n theta h n and the l 2 optimal error estimate for u n h theta h n are established under the restriction of 0 h le beta 1 and 0 tau le beta 2 for some positive constants beta 1 and beta 2 moreover numerical investigations are provided to show that the first order decoupled method is of almost unconditional convergence with accuracy mathcal o h tau in the h 1 norm and mathcal o h 2 tau in the l 2 norm for solving the 3d primitive equations of the ocean numerical results are gi

a sequential regularization method for time dependent incompressible navier stokes equations the objective of the paper is to present a method called the sequential regularization method srm for the nonstationary incompressible navier stokes equations from the viewpoint of regularization of differential algebraic equations daes and to provide a way to apply a dae method to partial differential algebraic equations pdaes the srm is a functional iterative procedure it is proved that its convergence rate is o epsilon m where m is the number of the srm iterations and epsilon is the regularization parameter the discretization and implementation issues of the method are considered in particular a simple explicit difference scheme is analyzed and its stability is proved under the usual step size condition of explicit schemes it appears that the srm formulation is new in the navier stokes context unlike other regularizations or pseudocompressibility methods in the navier stokes context the regularization parameter epsilon in the srm need not be very small and the regularized problem in the sequence may be essentially nonstiff in time direction for any epsilon hence the stability condition is independent of epsilon even for explicit time discretization numerical experiments are given to verify our theoretical results

almost sure approximations to the robbins monro and kiefer wolfowitz processes with dependent noise we study a recursive algorithm which includes the multidimensional robbins monro and kiefer wolfowitz processes the assumptions on the disturbances are weaker than the usual assumption that they be a martingale difference sequence it is shown that the algorithm can be represented as a weighted average of the disturbances this representation can be used to prove asymptotic results for stochastic approximation procedures as an example we approximate the one dimensional kiefer wolfowitz process almost surely by brownian motion and as a byproduct obtain a law of the iterated logarithm

unbiased estimators and multilevel monte carlo multilevel monte carlo mlmc and recently proposed unbiased estimators are closely related this connection is elaborated by presenting a new general class of unbiased estimators which admits previous debiasing schemes as special cases new lower variance estimators are proposed which are stratified versions of earlier unbiased schemes under general conditions essentially when mlmc admits the canonical square root monte carlo error rate the proposed new schemes are shown to be asymptotically as efficient as mlmc both in terms of variance and cost the experiments demonstrate that the variance reduction provided by the new schemes can be substantial

optimal unbiased estimation for expected cumulative discounted cost abstract we consider estimating an expected infinite horizon cumulative discounted cost reward contingent on an underlying stochastic process by monte carlo simulation an unbiased estimator based on truncating the cumulative cost at a random horizon is proposed explicit forms for the optimal distributions of the random horizon are given and explicit expressions for the optimal random truncation level are obtained leading to a full analysis of the bias variance tradeoff when comparing this new class of randomized estimators with traditional fixed truncation estimators moreover we characterize when the optimal randomized estimator is preferred over a fixed truncation estimator by considering the tradeoff between bias and variance this comparison provides guidance on when to choose randomized estimators over fixed truncation estimators in practice numerical experiments substantiate the theoretical results

application of finite element method in aeroelasticity the subject of this paper is the numerical simulation of the interaction of two dimensional incompressible viscous flow and a vibrating airfoil which can rotate around the elastic axis and oscillate in the vertical direction the numerical simulation consists of the finite element approximation of the navier stokes equations coupled with the system of ordinary differential equations describing the airfoil motion the arbitrary lagrangian eulerian ale formulation of the navier stokes equations stabilization the finite element discretization and coupling of both models is discussed moreover the reynolds averaged navier stokes rans system of equations together with the spallart almaras turbulence model is also discussed the computational results of aeroelastic calculations are presented and compared with the nastran code solutions

on error estimates of the projection methods for the navier stokes equations second order schemes we present in this paper a rigorous error analysis of several projection schemes for the approximation of the unsteady incompressible navier stokes equations the error analysis is accomplished by interpreting the respective projection schemes as second order time discretizations of a perturbed system which approximates the navier stokes equations numerical results in agreement with the error analysis are also presented

a staggered space time discontinuous galerkin method for the three dimensional incompressible navier stokes equations on unstructured tetrahedral meshes in this paper we propose a novel arbitrary high order accurate semi implicit space time discontinuous galerkin method for the solution of the three dimensional incompressible navier stokes equations on staggered unstructured curved tetrahedral meshes as is typical for space time dg schemes the discrete solution is represented in terms of space time basis functions this allows to achieve very high order of accuracy also in time which is not easy to obtain for the incompressible navier stokes equations similarly to staggered finite difference schemes in our approach the discrete pressure is defined on the primary tetrahedral grid while the discrete velocity is defined on a face based staggered dual grid while staggered meshes are state of the art in classical finite difference schemes for the incompressible navier stokes equations their use in high order dg schemes is still quite rare a very simple and efficient picard iteration is used in order to derive a space time pressure correction algorithm that achieves also high order of accuracy in time and that avoids the direct solution of global nonlinear systems formal substitution of the discrete momentum equation on the dual grid into the discrete continuity equation on the primary grid yields a very sparse five point block system for the scalar pressure which is conveniently solved with a matrix free gmres algorithm from numerical experiments we find that the linear system seems to be reasonably well conditioned since all simulations shown in this paper could be run without the use of any preconditioner even up to very high polynomial degrees for a piecewise constant polynomial approximation in time and if pressure boundary conditions are specified at least in one point the resulting system is in addition symmetric and positive definite this allows us to use even faster iterative solvers like the conjugate gradient method the flexibility and accuracy of high order space time dg methods on curved unstructured meshes allows to discretize even complex physical domains with very coarse grids in both space and time the proposed method is verified for approximation polynomials of degree up to four in space and time by solving a series of typical 3d test problems and by comparing the obtained numerical results with available exact analytical solutions or with other numerical or experimental reference data to the knowledge of the authors this is the first time that a space time discontinuous galerkin finite element method is presented for the three dimensional incompressible navier stokes equations on staggered unstructured tetrahedral grids high order staggered space time dg scheme for the 3d incompressible navier stokes equations primal grid based on curved tetrahedra dual grid based on non standard five point hexahedra new discretization of the viscous terms on the main grid using lifting operators on the dual grid very simple space time pressure correction algorithm providing also high order in time all linear systems have maximum sparsity and use the smallest possible optimal five point stencil

a large deviations perspective on the efficiency of multilevel splitting we analyze the performance of a multilevel splitting method for rare event simulation related to one recently proposed in the telecommunications literature this method splits promising paths into subpaths at intermediate levels to increase the number of observations of a rare event in our previous paper 1997 we gave sufficient conditions in specific classes of models for this method to be asymptotically optimal here we focus on necessary conditions in a general setting we show through a variety of results the importance of choosing the intermediate thresholds in a way consistent with the most likely path to a rare set both when the number of levels is fixed and when it increases with the rarity of the event in the latter case we give very general necessary conditions based on large deviations rate functions these indicate that even when the intermediate levels are chosen appropriately the method will frequently fail to be asymptotically optimal we illustrate the conditions with examples

assessing asymptotic stability of linear continuous time varying systems by computing the envelope of all trajectories in this note necessary and sufficient numerical conditions for asymptotic stability and for uniform asymptotic stability of linear continuous time varying systems are derived for a given set of initial conditions a tube containing all the trajectories of the system is constructed in the state space at each instant of time there exists an initial condition inside the set such that the resulting trajectory attains the border of the tube based on the above formulation necessary and sufficient conditions for asymptotic stability and for uniform asymptotic stability are expressed through the solution of a linear differential lyapunov equation the conditions can deal with the stability of periodic systems as well one of the main characteristics of the proposed necessary and sufficient conditions is that the only assumption on the dynamical matrix of the time varying system is continuity examples from the literature illustrate the superiority of the proposed conditions when compared to other methods

asymptotic behavior and time discretization analysis for the non stationary navier stokes problem the asymptotic behavior and the euler time discretization analysis are presented for the two dimensional non stationary navier stokes problem if the data and f t satisfy a uniqueness condition corresponding to the stationary navier stokes problem we then obtain the convergence of the non stationary navier stokes problem to the stationary navier stokes problem and the uniform boundedness stability and error estimates of the euler time discretization for the non stationary navier stokes problem

stability and convergence of semi implicit time stepping algorithm for stationary incompressible magnetohydrodynamics abstract for the stationary incompressible magnetohydrodynamics mhd equations we provide a new uniqueness assumption a0 and show the exponential stability of the solution then the semi implicit time stepping algorithm is used to solve the stationary mhd equations the algorithm is proved to be unconditionally stable the discrete velocity and magnetic field are bounded in l 0 l for any space and time step sizes the error estimates for the algorithm are deduced under the uniqueness conditions finally numerical experiments are performed to testify our theoretical analysis

a priori error estimates of fully discrete finite element galerkin method for kelvin voigt viscoelastic fluid flow model abstract in this article a finite element galerkin method is applied to the kelvin voigt viscoelastic fluid model when its forcing function is in l l 2 some new a priori bounds for the velocity as well as for the pressure are derived which are independent of inverse powers of the retardation time the second order error estimate in l l 2 norm the first order error estimate in l h 0 1 norm for the velocity and the first order error estimate in l l 2 norm for the pressure for the semidiscrete method are derived which hold uniformly with respect to as 0 with the initial condition only in h 2 h 0 1 further under the smallness assumption on the data these error estimates are shown to be uniform in time as t for the complete discretization of the semidiscrete system a first order accurate backward euler method is applied and fully discrete error estimates are established finally numerical experiments are conducted to verify the theoretical results the results derived in this article are sharper than those derived earlier for finite element analysis of the kelvin voigt fluid model in the sense that the error estimates in this article hold true uniformly even as 0

finite time stability of linear time varying systems analysis and controller design the note deals with the finite time analysis and design problems for continuous time time varying linear systems necessary and sufficient conditions and a sufficient condition for finite time stability are devised moreover sufficient conditions for the solvability of both the state and the output feedback problems are stated such results require the feasibility of optimization problems involving differential linear matrix inequalities some numerical examples illustrate the effectiveness of the proposed approach

high order direct stokes solvers with or without temporal splitting numerical investigations of their comparative properties a recently proposed direct stokes solver which decouples the velocity and pressure operators without calling for a temporal scheme is numerically analyzed in comparison first with the splitting scheme proposed by g karniadakis m israeli and s orszag in j comput phys 97 1991 pp 414 443 and with the unique grid bbb p n bbb p n 2 uzawa approach for the space accuracy and computational costs the chebyshev collocation approximation is used to analyze the spectra of the continuous temporal evolution operators and their discrete time versions from the first to the fourth order an explicit boundary condition is also involved in the proposed stokes solver and it is numerically shown that the trace of bf delta bf u on the boundary must be evaluated through its bf nabla times bf nabla times contribution only otherwise the ellipticity is lost before proceeding to the time discretization the explicit evaluation of the rotational boundary term does not prevent the first and second order in time schemes from being unconditionally stable while the schemes built at the next two higher orders are limited by the usual explicit cal o n 4 stability criterion on the time step the proposed bf u p decoupling gives this limitation a less restrictive coefficient and supplies the expected temporal orders on the whole explored range of time step sizes the effective accuracy obtained for the navier stokes 2d solutions has been measured for the re 1000 lid driven cavity problem and has been found equivalent to what is supplied by the much more expensive uzawa decoupling method

on the convergence of a time discretization scheme for the navier stokes equations version linearisee du schema d euler implicite utilisee pour l approximation des solutions des equations de navier stokes dans un domaine bidimensionnel

synthesis of controllers for finite time stabilisation of ltv continuous time systems using a discrete time approach a methodology for the synthesis of state feedback controllers guaranteeing the finite time stability of linear time varying continuous time systems is proposed in this paper the main approach co

gradient estimation for multicomponent maintenance systems with age replacement policy we consider multicomponent maintenance systems with an f failure group age replacement policy it keeps failed components idling until f components are failed and then replaces all failed components together with the nonfailed components whose age has passed the critical threshold age n for components of type n with each maintenance action costs are associated we derive various unbiased gradient estimators based on the measure valued differentiation approach for the gradient of the average cost each estimator has its own domain of applicability we also compare the performance of our gradient estimators when applied to stochastic optimization with other general gradient free methods

efficient estimation and filtering for multivariate jump diffusions abstract this paper develops estimators of the transition density filters and parameters of multivariate jump diffusion models the drift volatility jump intensity and jump magnitude are allowed to be state dependent and non affine it is not necessary to diagonalize the volatility matrix our density and filter estimators converge at the canonical rate typically associated with exact monte carlo estimation our parameter estimators have the same asymptotic distribution as maximum likelihood estimators which are often intractable for the class of models we consider the results of this paper enable the empirical analysis of previously intractable models of asset prices and economic time series

on a linearized backward euler method for the equations of motion of oldroyd fluids of order one in this paper a linearized backward euler method is discussed for the equations of motion arising in the oldroyd model of viscoelastic fluids some new a priori bounds are obtained for the solution under realistically assumed conditions on the data further the exponential decay properties for the exact as well as the discrete solutions are established finally a priori error estimates in bh 1 and bl 2 norms are derived for the the discrete problem which are valid uniformly for all time t 0

error estimates for the spectral approximation of the nonstationary stokes problem this paper analyzes a discretization of the nonstationary stokes problem with periodic nonperiodic boundary conditions fourier legendre spectral approximations are considered with respect to the space variables while the time discretization is based on the second order crank nicolson scheme optimal convergence estimates are proved for the velocity field

finite element approximations of the nonstationary navier stokes problem part iv error estimates for second order time discretization this paper provides an error analysis for the crank nicolson method of time discretization applied to spatially discrete galerkin approximations of the nonstationary navier stokes equations second order error estimates are proven locally in time under realistic assumptions about the regularity of the solution for approximations of an exponentially stable solution these local error estimates are extended uniformly in time as text t to infty

error analysis of fully discrete velocity correction methods for incompressible flows a fully discrete version of the velocity correction method proposed by guermond and shen 2003 for the time dependent navier stokes equations is introduced and analyzed it is shown that when accounting for space discretization additional consistency terms which vanish when space is not discretized have to be added to establish stability and optimal convergence error estimates are derived for both the standard version and the rotational version of the method these error estimates are consistent with those by guermond and shen 2003 as far as time discretiztion is concerned and are optimal in space for finite elements satisfying the inf sup condition

a gauge uzawa finite element method for the time dependent viscoelastic oldroyd flows abstract in this paper we present the gauge uzawa finite element method for the time dependent viscoelastic oldroyd flow this method is a fully discrete projection method whereas most projection methods have been studied without space discretization and the ensuing analysis may not extend to this case we also give the stability analysis and the optimal error analysis the analysis is based on an iterated time discrete system with which the error function is split into a temporal error and a spatial error in order to show the effect of the method we present some numerical results the numerical results confirm our analysis and show clearly the stability and optimal convergence of the gauge uzawa finite element method for the viscoelastic oldroyd flow

analysis of numerical errors in large eddy simulation we consider the question of numerical errors in large eddy simulation it is often claimed that straightforward discretization and solution using centered methods of models for large eddy motion can simulate the motion of turbulent flows with complexity independent of the reynolds number and dependence only on the resolution delta of the eddies sought this report considers this question analytically is it possible to prove error estimates for discretizations of actually used large eddy models whose error constants depend only on delta but not re we consider the most common simplest and most mathematically tractable model and the most mathematically clear discretization in two cases we prove such an error estimate and try to explain why our technique of proof fails in the most general case our analysis aims to assume as little time regularity on the true solution as possible

semi discrete stabilized finite element methods for navier stokes equations with nonlinear slip boundary conditions based on regularization procedure based on the pressure projection stabilized methods the semi discrete finite element approximation to the time dependent navier stokes equations with nonlinear slip boundary conditions is considered in this paper because this class of boundary condition includes the subdifferential property then the variational formulation is the navier stokes type variational inequality problem using the regularization procedure we obtain a regularized problem and give the error estimate between the solutions of the variational inequality problem and the regularized problem with respect to the regularized parameter varepsilon which means that the solution of the regularized problem converges to the solution of the navier stokes type variational inequality problem as the parameter varepsilon longrightarrow 0 moreover some regularized estimates about the solution of the regularized problem are also derived under some assumptions about the physical data the pressure projection stabilized finite element methods are used to the regularized problem and some optimal error estimates of the finite element approximation solutions are derived

technical communique necessary and sufficient conditions for finite time stability of impulsive dynamical linear systems sufficient conditions for the finite time stability fts of impulsive dynamical linear systems idlss have been provided in amato ambrosino cosentino and de tommasi 2011 in this brief note we show that when time dependent idlss are dealt with the sufficient condition for fts derived in amato ambrosino cosentino et al 2011 is also necessary moreover an alternative necessary and sufficient condition for fts is proposed which is based on the solution of a coupled differential difference lyapunov equation this condition turns out to be more efficient from the computational point of view the proposed approach is illustrated through some examples

on convergent schemes for diffuse interface models for two phase flow of incompressible fluids with general mass densities we are concerned with convergence results for fully discrete finite element schemes suggested in grun and klingbeil j comput phys in press doi 10 1016 j jcp 2013 10 028 they were developed for the diffuse interface model in h abels h garcke and g grun math models methods appl sci 22 2012 1150013 which describes two phase flow of immiscible incompressible viscous fluids we formulate general conditions on discretization spaces and projection operators which allow us to prove compactness of discrete solutions with respect to both time and space and which hence permit us to establish convergence of the scheme to a generalized solution we identify a simple quantitative and physical criterion to decide whether this generalized solution is in fact a weak solution in this case our analysis provides another pathway to establish existence of weak solutions to the aforementioned model in two and in three space dimensions our argument is particularly based on higher regularity results

simulating discounted costs we numerically estimate via simulation the expected infinite horizon discounted cost d of running a stochastic system a naive strategy estimates a finite horizon approximation to d we propose alternatives all are ranked with respect to asymptotic variance as a function of computer time budget and discount rate when semi markov and or regenerative structure or neither is assumed in this setting the naive truncation estimator loses it may triumph however when the computer time budget is modest the discount rate is large and the process simulated is not regenerative or has long cycle lengths

stability and convergence of second order time discrete projection method for the linearized oldroyd model abstract in this paper we consider the second order time discrete projection method for the linearized oldroyd model based on the time iterative discrete scheme by the projection method the original problem is decoupled into two linear subproblems and each subproblem can be solved easily unconditional stability and the corresponding convergence results of the numerical solutions are derived our main results are that the convergence orders in time for the velocity in l 2 norm is second order and for the pressure in h 1 norm is first order finally some numerical examples are provided to verify the performances of the developed numerical method

a finite element penalty method for the linearized viscoelastic oldroyd fluid motion equations abstract in this paper a fully discrete finite element penalty method is considered for the two dimensional linearized viscoelastic fluid motion equations arising from the oldroyd model for the non newton fluid flows with the finite element method for the spatial discretization and the backward euler scheme for the temporal discretization the velocity and pressure are decoupled in this method which leads to a large reduction of the computational scale under some realistic assumptions the unconditional stability of the fully discrete scheme is proved moreover the optimal error estimates are obtained which are better than the existing results finally some numerical results are given to verify the theoretical analysis the difference between the motion of the newton and non newton fluid is also observed

finite time stabilization of linear time varying continuous systems in this technical note the problem of finite time stabilization of linear time varying continuous systems is considered necessary and sufficient conditions based upon the solution to some lyapunov differential matrix equations are proposed for particular cases of interest from these conditions the design of time varying state feedback controller guaranteeing the finite time closed loop stability is presented numerical experiments illustrate the potentialities of the approach

sample path properties of self similar processes with stationary increments a real valued process x x t u is self similar with exponent h h ss if x a d ahx for all a 0 sample path properties of h ss processes with stationary increments are investigated the main result is that the sample paths have nowhere bounded variation if 0 1 in which case they are singular however nowhere bounded variation may occur also for h 1 examples exhibiting this combination of properties are constructed as well as many others most are obtained by subordination of random measures to point processes in ir2 that are poincar6 i e invariant in distribution for the transformations t x at b ax of r in a final section it is shown that the self similarity and stationary increment properties are preserved under composition of independent processes x1 a x2 x1 x2 t l some interesting examples are obtained this way

sensitivity estimation for gaussian systems in this paper we address the construction of efficient algorithms for the estimation of gradients of general performance measures of gaussian systems exploiting a clever coupling between the normal and the maxwell distribution we present a new gradient estimator and we show that it outperforms both the single run based infinitesimal perturbation analysis ipa estimator and the score function sf estimator in the one dimensional case for a dense class of test functions next we present an example of the multi dimensional case with a system from the area of stochastic activity networks our numerical experiments show that this new estimator also has significantly smaller sample variance than ipa and sf to increase efficiency in addition to variance reduction we present an optimized method for generating the maxwell distribution which minimizes the cpu time

an incremental pressure correction finite element method for the time dependent oldroyd flows abstract in this paper we present an incremental pressure correction finite element method for the time dependent oldroyd flows this method is a fully discrete projection method as we all know most projection methods have been studied without space discretization then the ensuing analysis may not extend to this case we also give the stability analysis and the optimal error analysis the analysis is based on a time discrete error and a spatial discrete error in order to show the effectiveness of the method we also present some numerical results the numerical results confirm our analysis and show clearly the stability and optimal convergence of the incremental pressure correction finite element method for the time dependent oldroyd flows

unstable asymptotics for nonstationary queues we relate laws of large numbers and central limit theorems for nonstationary counting processes to corresponding limits for their inverse processes we apply these results to develop approximations for queues that are unstable in a nonstationary manner we obtain unstable nonstationary analogs of the queueing relation l w and associated central limit theorem versions for modeling and to obtain the first limits we can construct nonstationary point processes as random time transformations of familiar point processes such as renewal processes and stationary point processes we deduce the asymptotic behavior of the nonstationary point process from the asymptotic behavior of the familiar point process and the time transformation

finite time stabilization of linear time varying systems by piecewise constant feedback most existing methods for finite time stabilizing controller design of linear time varying systems involve solving differential linear matrix equations due to the non convexity of the problem it requires a high computational burden this paper proposes a numerical method to solve finite time stabilization problems successive approximations are performed to estimate the evolution of system states accordingly a gain switched state feedback controller can be obtained by solving a sequence of linear matrix inequalities lmis based optimization problems the proposed algorithm is used to design the mass spring system and the autopilot system of the btt missile comparison with existing methods is given and the simulation results show the effectiveness of the proposed method

closed form control laws for linear time varying systems closed form control laws are developed for continuous linear time varying ltv systems based on approximate solutions to a receding horizon control problem these control laws can be derived in the first or higher order closed forms once obtained the control laws need no explicit gain scheduling or online integrations to implement the notion of practical stability is used and practical or uniform asymptotic stability of the closed loop system depending on conditions imposed on the system is established

on an efficient second order backward difference newton scheme for mhd system abstract for the 2d 3d time dependent magnetohydrodynamics mhd system we propose a new second order backward difference formula newton scheme sbdfn which is a combination of second order backward difference approximation of the time derivative terms and newton treatment of the nonlinear terms meanwhile the finite element method is applied as spatial discretization firstly the optimal convergence of spatially semi discrete form is deduced secondly the stability and well posedness of sbdfn scheme are provided under c where c is independent of h based on these results optimal error estimates of the scheme in time are proved by negative norm technique finally numerical experiments are carried out to validate the theoretical analysis

the efficiency of one long run versus independent replication in steady state simulation we evaluate the efficiency of one long run versus independent replications in steady state discrete event simulation assuming that an initial portion of each replication will be deleted to allow the process to approach steady state we provide supporting evidence in favor of one long run but we also show that multiple replications can be more efficient the advantage of one long run increases if the amount deleted increases or if the covariance function decreases more quickly assuming it is nonnegative and decreasing thus assuming that the amount deleted depends on the way the process approaches steady state one long run tends to be efficient when the covariance function decays rapidly compared to the rate the process approaches steady state we also discuss ways to determine the initial portion to delete we consider the case of an exponential covariance function in detail and use it as a basis for approximations we also consider the m g queueing model and reflected brownian motion the latter

decoupled schemes for unsteady mhd equations ii finite element spatial discretization and numerical implementation in this article a decoupled fully discrete scheme for solving 2d magnetohydrodynamics mhd equations is proposed the decoupled scheme is used for time discretization and the finite element method is used for spatial discretization firstly the almost unconditional stability t c of this scheme is established then optimal l2 and h1 error estimates of numerical solution are provided finally a numerical example is presented to confirm our theoretical results and show the high efficiency of the decoupled scheme

simulated likelihood estimators for discretely observed jump diffusions abstract this paper develops an unbiased monte carlo approximation to the transition density of a jump diffusion process with state dependent drift volatility jump intensity and jump magnitude the approximation is used to construct a likelihood estimator of the parameters of a jump diffusion observed at fixed time intervals that need not be short the estimator is asymptotically unbiased for any sample size it has the same large sample asymptotic properties as the true but uncomputable likelihood estimator numerical results illustrate its properties

brief paper finite time control of discrete time linear systems analysis and design conditions in this paper we deal with some finite time control problems for discrete time time varying linear systems first we provide necessary and sufficient conditions for finite time stability these conditions require either the computation of the state transition matrix of the system or the solution of a certain difference lyapunov inequality then we address the design problem the proposed conditions allow us to find output feedback controllers which stabilize the closed loop system in the finite time sense all these conditions can be expressed in terms of lmis and therefore are numerically tractable as shown in the example included in the paper

filtered likelihood for point processes abstract point processes are widely used in finance and economics to model the timing of defaults market transactions unemployment spells births and a range of other events we develop and analyze likelihood estimators for the parameters of a marked point process and incompletely observed explanatory factors that influence the arrival intensity and mark distribution we establish an approximation to the likelihood and analyze the convergence and large sample properties of the associated estimators numerical results illustrate the behavior of our estimators

budget dependent convergence rate of stochastic approximation convergence rate results are derived for a stochastic optimization problem where a performance measure is minimized with respect to a vector parameter t assuming that a gradient estimator is available and that both the bias and the variance of the estimator are known functions of the budget devoted to its computation the gradient estimator is employed in conjunction with a stochastic approximation sa algorithm our interest is to figure out how to allocate the total available computational budget to the successive sa iterations the effort is devoted to solving the asymptotic version of this problem by finding the convergence rate of sa toward the optimizer first as a function of the number of iterations and then as a function of the total computational effort as a result the optimal rate of increase of the computational budget per iteration can be found explicit expressions for the case where the computational budget devoted to an iteration is a polynomial in the iteration number and where the bias and variance of the gradient estimator are polynomials of the computational budget are derived applications include the optimization of steady state simulation models with likelihood ratio perturbation analysis or finite difference gradient estimators optimization of infinite horizon models with discounting optimization of functions of several expectations and so on several examples are discussed our results readily generalize to general root finding problems

adaptive ofdm synchronization algorithms based on discrete stochastic approximation this paper presents discrete stochastic approximation algorithms dsa for time synchronization in orthogonal frequency division multiplexing ofdm systems it is shown that the discrete stochastic approximation algorithms can be effectively used to achieve a significant reduction in computational complexity compared to brute force maximum likelihood ml methods for ofdm synchronization the most important property of the proposed algorithms is their recursive self learning capability most of the computational effort is spent at the global or a local optimizer of the objective function the convergence of the algorithms is analyzed an adaptive version of the discrete stochastic approximation algorithm is also presented for tracking time varying time delays and frequency offsets in time selective fading channels detailed numerical examples illustrate the performance gains of these dsa based synchronization algorithms

two level method based on finite element and crank nicolson extrapolation for the time dependent navier stokes equations a fully discrete two level finite element method the two level method is presented for solving the two dimensional time dependent navier stokes problem the method requires a crank nicolson extrapolation solution u h tau 0 p h tau 0 on a spatial time coarse grid j h tau 0 and a backward euler solution u h tau p h tau on a space time fine grid j h tau the error estimates of optimal order of the discrete solution for the two level method are derived compared with the standard crank nicolson extrapolation method the one level method based on a space time fine grid j h tau the two level method is of the error estimates of the same order as the one level method in the h1 norm for velocity and the l2 norm for pressure however the two level method involves much less work than the one level method

asymptotics of likelihood ratio derivative estimators in simulations of highly reliable markovian systems we discuss the estimation of derivatives of a performance measure using the likelihood ratio method in simulations of highly reliable markovian systems we compare the difficulties of estimating the performance measure and of estimating its partial derivatives with respect to component failure rates as the component failure rates tend to 0 and the component repair rates remain fixed we first consider the case when the quantities are estimated using naive simulation i e when no variance reduction technique is used in particular we prove that in the limit some of the partial derivatives can be estimated as accurately as the performance measure itself this result is of particular interest in light of the somewhat pessimistic empirical results others have obtained when applying the likelihood ratio method to other types of systems however the result only holds for certain partial derivatives of the performance measure when using naive simulation more specifically we can estimate a certain partial

optimal error estimates for semidiscrete galerkin approximations to equations of motion described by kelvin voigt viscoelastic fluid flow model in this paper a finite element galerkin method is applied to equations of motion arising in the kelvin voigt viscoelastic fluid flow model when the forcing function is in l l 2 some a priori estimates for the exact solution which are valid uniformly in time as t and even uniformly in the retardation time an 0 are derived it is shown that the semidiscrete method admits a global attractor further with the help of a priori bounds and sobolev stokes projection optimal error estimates for the velocity in l l 2 and l h 1 norms and for the pressure in l l 2 norm are established since the constants involved in error estimates have an exponential growth in time therefore in the last part of the article under certain uniqueness condition the error bounds are established which are valid uniformly in time finally some numerical experiments are conducted which confirm our theoretical findings

indirect estimation via l w for a large class of queueing systems little s law l w helps provide a variety of statistical estimators for the long run time average queue length l and the long run customer average waiting time w we apply central limit theorem versions of little s law to investigate the asymptotic efficiency of these estimators we show that an indirect estimator for l using the natural estimator for w plus the known arrival rate is more efficient than a direct estimator for l provided that the interarrival and waiting times are negatively correlated thus extending a variance reduction principle for the gi g s model due to a m law and j s carson we also introduce a general framework for indirect estimation which can be applied to other problems besides l w we show that the issue of indirect versus direct estimation is related to estimation using nonlinear control variables we also show under mild regularity conditions that any nonlinear control variable scheme is equivalent to a linear control va

asymptotic formulas for markov processes with applications to simulation the simulation run length required to achieve desired statistical precision for a sample mean in a steady state stochastic simulation experiment is largely determined by the asymptotic variance of the sample mean and to a lesser extent by the second order asymptotics of the variance and the asymptotic bias the asymptotic variance the second order asymptotics of the variance and the asymptotic bias of the sample mean of a function of an ergodic markov process can be expressed in terms of solutions of poisson s equation as indicated by positive recurrent potential theory we review this positive recurrent potential theory giving special attention to continuous time markov chains we provide explicit formulas for birth and death processes and diffusion processes and recursive computational procedures for skip free chains these results can be used to help design simulation experiments after approximating the stochastic process of interest by one of the elementary markov processes considered here

analysis of a sequential regularization method for the unsteady navier stokes equations the incompressibility constraint makes navier stokes equations difficult a reformulation to a better posed problem is needed before solving it numerically the sequential regularization method srm is a reformulation which combines the penalty method with a stabilization method in the context of constrained dynamical systems and has the benefit of both methods in the paper we study the existence and uniqueness for the solution of the srm and provide a simple proof of the convergence of the solution of the srm to the solution of the navier stokes equations we also give error estimates for the time discretized srm formulation

finite element approximation for the viscoelastic fluid motion problem in this article the variational formulation of the two dimensional viscoelastic fluid motion problem and its finite element approximation are considered an local error estimate for the velocity with h1 norm and the pressure with l2 norm is obtained and a uniform error estimate for the velocity and pressure with the above norms is provided if the given data satisfies the uniqueness condition

general multilevel monte carlo methods for pricing discretely monitored asian options abstract we describe general multilevel monte carlo methods that estimate the price of an asian option monitored at m fixed dates for a variety of processes that can be simulated exactly we prove that for the same computational cost our method yields an unbiased estimator with variance lower than the variance of the standard monte carlo estimator by a factor of order m we show how to combine our approach with the milstein scheme for processes driven by scalar stochastic differential equations and with the euler scheme for processes driven by multidimensional stochastic differential equations numerical experiments confirm that our method outperforms the conventional monte carlo algorithm by a factor proportional to m

long time numerical solution of a parabolic equation with memory long time stability and convergence properties of two time discreti zation methods for an integro differential equation of parabolic type are studied the methods are based on the standard backward euler and second order back ward differencing methods the memory term is approximated by a quadrature rule with emphasis on such rules with reduced computational memory require ments discretization of the spatial partial differential operators by the finite element method is also considered

euler implicit explicit iterative scheme for the stationary navier stokes equations in this paper a new uniqueness assumption a2 of the solution for the stationary navier stokes equations is presented under assumption a2 the exponential stability of the solution bar u bar p for the stationary navier stokes equations is proven moreover the euler implicit explicit scheme based on the mixed finite element is applied to solve the stationary navier stokes equations finally the almost unconditionally stability is proven and the optimal error estimates uniform in time are provided for the scheme

a defect correction method for unsteady conduction convection problems ii time discretization in this paper a fully discrete defect correction mixed finite element method mfem for solving the non stationary conduction convection problems in two dimension which is leaded by combining the back euler time discretization with the two step defect correction in space is presented in this method we solve the nonlinear equations with an added artificial viscosity term on a finite element grid and correct these solutions on the same grid using a linearized defect correction technique the stability and the error analysis are derived the theory analysis shows that our method is stable and has a good convergence property some numerical results are also given which show that this method is highly efficient for the unsteady conduction convection problems

error estimates with smooth and nonsmooth data for a finite element method for the cahn hilliard equation a finite element method for the cahn hilliard equation a semilinear parabolic equation of fourth order is analyzed both in a spatially semidiscrete case and in a completely discrete case based on the backward euler method error bounds of optimal order over a finite time interval are obtained for solutions with smooth and nonsmooth initial data a detailed study of the regularity of the exact solution is included the analysis is based on local lipschitz conditions for the nonlinearity with respect to sobolev norms and the existence of a ljapunov functional for the exact and the discretized equations is essential a result concerning the convergence of the attractor of the corresponding approximate nonlinear semigroup upper semicontinuity with respect to the discretization parameters is obtained as a simple application of the nonsmooth data error estimate

ordinary clt and wlln versions of l λw the familiar queueing principle expressed by the formula l w little s law can be interpreted as a relation among strong laws of large numbers sllns here we prove central limit theorem clt and weak law of large numbers wlln versions of l w for example if the sequence of ordered pairs of interarrival times and waiting times is strictly stationary and satisfies a joint clt then the queue length process also obeys a clt with a related limiting distribution in a previous paper we proved a functional central limit theorem version of l w without stationarity by very different arguments the two papers highlight the differences between establishing ordinary limit theorems and their functional limit theorem counterparts

a reduced order extrapolation algorithm based on sfve method and pod technique for non stationary stokes equations in this paper a reduced order extrapolation algorithm roea based on proper orthogonal decomposition pod technique and classical stabilized finite volume element sfve method for non stationary stokes equations is established the error estimates between the roea solutions and the classical sfve solutions and the implementation for solving roea are provided some numerical examples are used to verify that the results of numerical computation are consistent with theoretical conclusions moreover it is shown that roea based on sfve formulation and pod method is feasible and efficient for solving non stationary stokes equations

dirichlet bridge sampling for the variance gamma process pricing path dependent options the authors develop a new monte carlo based method for pricing path dependent options under the variance gamma vg model the gamma bridge sampling method proposed by avramidis et al avramidis a n p l ecuyer p a tremblay 2003 efficient simulation of gamma and variance gamma processes proc 2003 winter simulation conf ieee press piscataway nj 319 326 and ribeiro and webber ribeiro c n webber 2004 valuing path dependent options in the variance gamma model by monte carlo with a gamma bridge j computational finance7 2 81 100 is generalized to a multivariate dirichlet construction bridging simultaneously over all time partition points of the trajectory of a gamma process the generation of the increments of the gamma process given its value at the terminal point is interpreted as a dirichlet partition of the unit interval the increments are generated in a decreasing stochastic order and under the kingman limit have a known distribution thus simulation of a trajectory from the gamma process requires generating only a small number of uniforms avoiding the expensive simulation of beta variates via numerical probability integral inversion the proposed method is then applied in simulating the trajectory of a vg process using its difference of gammas representation it has been implemented in both plain monte carlo and quasi monte carlo environments it is tested in pricing lookback barrier and asian options and is shown to provide consistent efficiency gains compared to the sequential method and the difference of gammas bridge sampling proposed by avramidis and l ecuyer avramidis a n p l ecuyer 2006 efficient monte carlo and quasi monte carlo option pricing under the variance gamma model management sci 52 12 1930 1944

randomized dimension reduction for monte carlo simulations we present a new unbiased algorithm that estimates the expected value of f u via monte carlo simulation where u is a vector of d independent random variables and f is a function of d variables

estimating average production intervals using inventory measurements little s law for partially observable processes this paper proposes an indirect approach to estimate average production intervals the length of time between starting and finishing work on each product using work in process inventory measurements the idea is to apply a modified version of little s law l w from queueing theory to cope with stochastic processes that are not directly observable when the actual amount of completed product to be produced from the current work in process is not known we suggest working with an appropriate expected amount of completed product associated with current work in process taking care to properly account for such features as partial yields changing lot sizes and reconstituted lots this indirect estimation procedure can be applied to computer simulation as well as direct system measurement the approach also can be used to calculate expected values of steady state random variables in mathematical models