mixed finite element method for dirichlet boundary control problem governed by elliptic pdes in this paper we study the finite element approximation of dirichlet boundary control problems governed by elliptic pdes based on a mixed variational scheme we establish a mixed finite element approximation to the underlying optimal control problem we consider the optimal control problems posed on both polygonal and general smooth domains and we derive a priori error estimates for optimal control state and adjoint state the optimal and quasi optimal error estimates are obtained for problems on polygonal and smooth domains respectively numerical experiments are provided to confirm our theoretical results

treating inhomogeneous essential boundary conditions in finite element methods and the calculation of boundary stresses finite element approximations of the stokes and navier stokes equations with in homogeneous essential boundary conditions are considered boundary conditions are enforced weakly by introducing lagrange multipliers optimal error estimates including some for the stress vector on the boundary are derived under minimal regularity assumptions on the data particular attention is paid to the analysis of a practical choice of finite element spaces for which the lagrange multiplier calculation uncouples from that for the velocity and pressure the results are also applicable to general second order elliptic systems

semidiscrete finite element approximations of a linear fluid structure interaction problem semidiscrete finite element approximations of a linear fluid structure interaction problem are studied first results concerning a divergence free weak formulation of the interaction problem are reviewed next semidiscrete finite element approximations are defined and the existence of finite element solutions is proved with the help of an auxiliary discretely divergence free formulation a discrete inf sup condition is verified and the existence of a finite element pressure is established strong a priori estimates for the finite element solutions are also derived then by passing to the limit in the finite element approximations the existence of a strong solution is demonstrated and semidiscrete error estimates are obtained

calculation of global optimal initial and boundary perturbations for the linearised incompressible navier stokes equations this study considers numerical methods for computation of optimal boundary and initial perturbations to incompressible flows similar to previous work constrained lagrangian functionals are built and gradient optimisation methods are applied to optimise perturbations that maximise the energy of perturbations in the computational domain at a given time horizon unlike most of the previous work in this field we consider both optimal initial and boundary condition problems and demonstrate how each can be transformed into an eigenvalue problem it is demonstrated analytically and numerically that both optimisation and eigenvalue approaches converge to the same outcome even though the optimisation approach may converge more slowly owing to the large number of inflection points in a case study these tools are used to calculate optimal initial and boundary perturbations to the batchelor vortex it is observed that when the flow is asymptotically stable the optimal inflow perturbation is similar to the most unstable local eigenmode while when the flow is stable weakly unstable the spatial distribution of the optimal inflow perturbation is similar to the local optimal initial perturbation

strong stochastic bounds for the stationary distribution of a class of multicomponent performability models we consider a class of models for multicomponent systems in which components can break down and be repaired in a dependent manner and where breakdown and repair times can be arbitrarily distributed the problem of calculating the equilibrium distribution and from this the expected performability for these models is intractable unless certain assumptions are made about breakdowns and repairs in this paper we show that the performability of multicomponent systems that do not satisfy these rules can be bounded by tractable modifications our results are proved by stochastic comparability arguments and a markov reward technique which is of interest in itself as it enables one to prove that the equilibrium distribution of one process can be bounded by that of another even when the sample paths of the process are not this is illustrated by an example

constrained dirichlet boundary control in l 2 for a class of evolution equations optimal dirichlet boundary control based on the very weak solution of a parabolic state equation is analyzed this approach allows us to consider the boundary controls in l 2 which has advantages over approaches which consider control in sobolev spaces involving fractional derivatives pointwise constraints on the boundary are incorporated by the primal dual active set strategy its global and local superlinear convergences are shown a discretization based on space time finite elements is proposed and numerical examples are included

approximations of very weak solutions to boundary value problems standard weak solutions to the poisson problem on a bounded domain have square integrable derivatives which limits the admissible regularity of inhomogeneous data the concept of solution may be further weakened in order to define solutions when data is rough such as for inhomogeneous dirichlet data that is only square integrable over the boundary such very weak solutions satisfy a nonstandard variational form u v g v a galerkin approximation combined with an approximation of the right hand side g defines a finite element approximation of the very weak solution applying conforming linear elements leads to a discrete solution equivalent to the text book finite element solutionto the poisson problem in which the boundary data is approximated by l2 projections the l2 convergence rate of the discrete solution is o hs for some s in 0 1 2 that depends on the shape of the domain assuming a polygonal two dimensional or polyhedral three dimensional domain without slits and only square integr

directional derivatives of oblique reflection maps given an oblique reflection map and functions documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document psi chi in mathcal d lim end document the space of k valued functions that have finite left and right limits at every point the directional derivative documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document nabla chi gamma psi end document of along evaluated at is defined to be the pointwise limit as documentclass aastex usepackage amsbsy usepackage amsfonts u

an energy space finite element approach for elliptic dirichlet boundary control problems in this paper we present a finite element analysis for a dirichlet boundary control problem where the dirichlet control is considered in a convex closed subspace of the energy space h 1 2 gamma h 1 2 as an equivalent norm in h 1 2 gamma h 1 2 we use the energy norm induced by the so called steklov poincare operator which realizes the dirichlet to neumann map and which can be implemented by using standard finite element methods the presented stability and error analysis of the discretization of the resulting variational inequality is based on the mapping properties of the solution operators related to the primal and adjoint boundary value problems and their finite element approximations some numerical results are given which confirm on one hand the theoretical estimates but on the other hand indicate the differences when modelling the control in l 2 gamma l 2

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

on the pathwise optimal bernoulli routing policy for homogeneous parallel servers a long standing conjecture on the optimal bernoulli routing policy is proven to be true for the case of equal exponential service times it is shown that splitting equally among the queues minimizes the departure times in a stochastic pathwise sense a new technique is used showing that certain distributional properties related to schur convexity propagate forward in time

poisson arrivals see time averages in many stochastic models particularly in queueing theory poisson arrivals both observe see a stochastic process and interact with it in particular cases and or under restrictive assumptions it has been shown that the fraction of arrivals that see the process in some state is equal to the fraction of time the process is in that state in this paper we present a proof of this result under one basic assumption the process being observed cannot anticipate the future jumps of the poisson process

error analysis for a finite element approximation of elliptic dirichlet boundary control problems we consider the galerkin finite element approximation of an elliptic dirichlet boundary control model problem governed by the laplacian operator the analytical setting of this problem uses l 2 controls and a very weak formulation of the state equation however the corresponding finite element approximation uses standard continuous trial and test functions for this approximation we derive a priori error estimates of optimal order which are confirmed by numerical experiments the proofs employ duality arguments and known results from the l p error analysis for the finite element dirichlet projection

on the regularity of the solutions of dirichlet optimal control problems in polygonal domains a linear quadratic dirichlet control problem governed by an elliptic equation posed on a possibly nonconvex polygonal domain is analyzed detailed regularity results are provided in classical sobolev slobodetski spaces in particular it is proved that in the presence of pointwise control constraints the optimal control is continuous despite the nonconvexity of the domain

on the accuracy of the simple peak hour approximation for markovian queues we empirically explore the accuracy of the simple stationary peak hour approximation spha for estimating peak hour performance in multiserver queuing systems with exponential service times and periodic sinusoidal poisson arrival processes we show that the spha is very good for a range of parameter values corresponding to a reasonably broad spectrum of real systems however we do find and document that there are many situations in which this approximation will be very inaccurate we postulate and then support empirically a set of hypotheses that link the accuracy of the spha and the related point wise stationary approximation psa to key parameter values and model characteristics we also present results on the time dependent behavior of these systems as a function of key parameters finally we present results which indicate that our findings developed for models with sinusoidal input streams may apply to a much broader range of markovian models with more general cyclic inputs

comparison of semimartingales and levy processes in this paper we derive comparison results for terminal values of d dimensional special semimartingales and also for finite dimensional distributions of multivariate levy processes the comparison is with respect to nondecreasing increasing convex increasing directionally convex and increasing supermodular functions we use three different approaches in the first approach we give sufficient conditions on the local predictable characteristics that imply ordering of terminal values of semimartingales this generalizes some recent convex comparison results of exponential models in math finance 8 1998 93 126 finance stoch 4 2000 209 222 proc steklov inst math 237 2002 73 113 finance stoch 10 2006 222 249 in the second part we give comparison results for finite dimensional distributions of levy processes with infinite levy measure in the first step we derive a comparison result for markov processes based on a monotone separating transition kernel by a coupling argument we get an application to the comparison of compound poisson processes these comparisons are then extended by an approximation argument to the ordering of levy processes with infinite levy measure the third approach is based on mixing representations which are known for several relevant distribution classes we discuss this approach in detail for the comparison of generalized hyperbolic distributions and for normal inverse gaussian processes

the physics of the m t g symbol queue we establish some general structural results and derive some simple formulas describing the time dependent performance of the mt g queue with a nonhomogeneous poisson arrival process we know that for appropriate initial conditions the number of busy servers at time t has a poisson distribution for each t our results show how the time dependent mean function m depends on the time dependent arrival rate function and the service time distribution for example when is quadratic the mean m t coincides with the pointwise stationary approximation t e s where s is a service time except for a time lag and a space shift it is significant that the well known insensitivity property of the stationary m g model does not hold for the nonstationary mt g model the time dependent mean function m depends on the service time distribution beyond its mean the service time stationary excess distribution plays an important role when is decreasing before time t m t is increasing in the service time

on finite element approximations of problems having inhomogeneous essential boundary conditions abstract the analysis and implementation of finite element methods for problems with inhomogeneous essential boundary conditions are considered the results are given for linear second order elliptic partial differential equations and for the nonlinear stationary navier stokes equations for certain easily implemented boundary treatments optimal error estimates and numerical examples are provided for problems posed on polyhedral domains

the transient solution of time dependent m m 1 queues the transient behavior of time dependent m m 1 queues is studied the boundary probability function pi sub 0 t which is the probability that the queue is empty at time t is shown with analyticity arguments to satisfy a volterra type integral equation the boundary integral equation is derived and a numerical algorithm is used to solve the integral equation and to find the expected queue size from pi sub 0 t the approach can be applied to many other types of time dependent queues examples are given

probabilistic models of database locking solutions computational algorithms and asymptotics modelisation de l effet des conflits sur les transactions dans une base de donnees et on obtient des formules exactes pour les mesures de performances a l equilibre et des algorithmes efficaces pour leur calcul

monotonicity in generalized semi markov processes we establish stochastic monotonicity of the event epoch sequences of generalized semi markov processes through the structure of the generalized semi markov schemes on which they are based our main condition states roughly that the occurrence of more events in the short run never leads to the activation of less events in the long run we consider monotonicity with respect to two types of inputs clock times which translate to e g service and interarrival times in queueing systems and structural parameters which translate to e g buffer size number of servers and job population for the second type of comparison we replace a structural change with an equivalent change in clock times to reduce the comparison to one of the first type when applied to queueing systems our results yield new comparisons and also unify several existing results previously established using special properties of individual systems

a robust finite element method for nonhomogeneous dirichlet problems in domains with curved boundaries in this paper the authors consider a simple finite element method on an approximately polygonal domain using linear elements the dirichlet data are transferred in a natural way and the resulting linear system can be solved using multigrid techniques their analysis takes into account the change in domain and data transfer and optimal error estimates are obtained that are robust in the regularity of the boundary data provided they are at least square integrable it is proved that the natural extension of this finite element approximation to the original domain is optimal order accurate

generalizations and accelerations of lions nonoverlapping domain decomposition method for linear elliptic pde in this paper a one parameter generalization of lions nonoverlapping domain decomposition method for linear elliptic pdes is proposed and studied the generalized methods are shown to be descent direction methods for minimizing an interface bias functional iteration convergence of both the continuous and finite element versions of the proposed methods is established it is theoretically and numerically demonstrated that for generic choices of the parameter the generalized methods converge faster than lions original method algorithms are given and numerical results are presented

weak boundary penalization for dirichlet boundary control problems governed by elliptic equations abstract this paper concerns the finite element approximation of dirichlet boundary control problems governed by elliptic equations different from the existing literatures in which standard finite element method mixed finite element method or robin penalization method are used to deal with the underlying problems we adopt an alternative penalization approach introduced by nitsche called weak boundary penalization compared with the above methods our discrete scheme not only keeps consistency and avoids penalization error but also can be analyzed and computed conveniently as neumann boundary control problems based on the weak boundary penalization method we establish a finite element approximation to the dirichlet boundary control problems and derive the a priori error estimates for the control state and adjoint state numerical experiments are provided to confirm our theoretical results

time dependent queues a single server queue is considered having exponentially distributed inter arrival and service times with slowly changing time dependent rates lambda varepsilon t and mu varepsilon t the parameter varepsilon is the ratio of an average inter arrival time to the time over which the rates change appreciably so it is small therefore an asymptotic solution valid for varepsilon small is constructed for the time dependent queue length probability distribution it consists of five typical parts corresponding to five typical time periods they are the initial period the period of light traffic when lambda mu 1 the saturation transition period when lambda mu increases through unity the oversaturation period when lambda mu starts out greater than unity and then decreases below unity and the transition period at the end of oversaturation when the queue returns to the light traffic condition by combining the solutions for these five intervals the solution fo

stochastic comparisons for non markov processes a technique is developed for comparing a non markov process to a markov process on a general state space with many possible stochastic orderings two such comparisons with a common markov process yield a comparison between two non markov processes the technique which is based on stochastic monotonicity of the markov process yields stochastic comparisons of the limiting distributions and the marginal distributions at single time points but not the joint distributions these stochastic comparisons are obtained under the condition that the one step transition probabilities in discrete time or infinitesimal transition rates in continuous time are appropriately ordered uniformly in the extra information needed to add to the state to make the non markov process markov the technique is illustrated by establishing an inequality in traffic theory concerning the blocking in multi server service facilities when each customer requires service from several facilities simultaneously

two time scale markov chains and applications to quasi birth death queues aiming at reduction of complexity this work is concerned with two time scale markov chains and applications to quasi birth death queues asymptotic expansions of probability vectors are constructed and justified lumping all states of the markov chain in each subspace into a single state an aggregated process is shown to converge to a continuous time markov chain whose generator is an average with respect to the stationary measures then a suitably scaled sequence is shown to converge to a switching diffusion process extensions of the results are presented together with examples of quasi birth death queues

stochastic convexity and concavity of markov processes in this paper we consider the temporal stochastic convexity and concavity properties of markov processes x t t s in discrete time then s n 0 1 2 or in continuous time then s 0 that is we obtain conditions on the process x t t s which imply that the expectation ef x t is a monotone convex concave function of t whenever f is a monotone convex concave function the theory is illustrated through some examples after giving some background we define monotonicity and then obtain some general results concerning stochastic convexity and concavity of markov processes by using the notion of monotone operators we then introduce a method for identifying monotone operators and we discuss the relationship between our results concerning temporal convexity and other results in the literature in particular we center our attention on a notion of stochastic concavity in this respect we show that a result of shaked and shanthikumar is incorrect and we prove two alternativ

asymptotic analysis of the time dependent m m 1 queue using operator analytic techniques we develop a nonstationary markovian queueing theory starting with the mt mt 1 queue we employ an asymptotic approach quite different from the usual large time analysis instead we uniformly accelerate the queue length process that is we divide the arrival and service rate by a common parameter e then for a fixed time interval we consider the asymptotics for the distribution mean and variance of the queue length process as e goes to zero the effects of e can be quite different for the given time interval this gives us a dynamic asymptotic behavior for the queue length process we can formulate a time dependent traffic intensity parameter that determines when the process is asymptotically stable and when it is asymptotically unstable

performance bounds for nonhomogeneous queues this paper considers nonhomogeneous m t m t 1 queues which can model systems such as communications networks for such systems bounds on moment generating functions and on the tail distribution of the queue process are obtained these bounds are useful for characterizing the quality of service a system can provide to its users an approach utilizing the theory of differential equations is adapted the bounds given in this paper are tighter than those previously available in fact the bounds can be made arbitrarily tight given sufficient computational effort

filtered monte carlo by a filtered monte carlo estimator we mean one whose constituent parts summands or integral increments are conditioned on an increasing family of fields unbiased estimators of this type are suggested by compensator identities replacing a point process integrator with its intensity gives rise to one class of examples exploiting levy s formula gives rise to another we establish variance inequalities complementing compensator identities among estimators that are stieltjes stochastic integrals we show that filtering reduces variance if the integrand and the increments of the integrator have conditional positive correlation we also provide more primitive hypotheses that ensure this condition making use of stochastic monotonicity properties our most detailed conditions apply in a markov setting where monotone up down and convex generators play a central role we give examples as an application of our results we compare certain estimators that do and do not exploit the property that poisson arr

stochastic orderings for markov processes on partially ordered spaces the purpose of this paper is to develop a unified theory of stochastic ordering for markov processes on countable partially ordered state spaces when such a space is not totally ordered it can induce a wide range of stochastic orderings none of which are equivalent to sample path comparisons similar comparison theorems are also developed for non markov processes that are functions of markov processes and for time inhomogeneous markov processes such alternative orderings can be quite useful when analyzing multi dimensional stochastic models such as queueing networks

treating a single stiff second order ode directly abstract the stability of direct methods for second order systems is examined the methods suggested by krogh are generalized bdf methods the control of stepsize to ensure stability is examined and criteria for deciding when to switch between methods are discussed

error estimates for the numerical approximation of dirichlet boundary control for semilinear elliptic equations we study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control the control is the trace of the state on the boundary of the domain which is assumed to be a convex polygonal open set in mathbb r 2 piecewise linear finite elements are used to approximate the control as well as the state we prove that the error estimates are of order o h 1 1 p for some p 2 which is consistent with the w 1 1 p p gamma regularity of the optimal control

the pointwise stationary approximation for m 1 m 1 s green kolesar and svoronos in press and green and kolesar in press use numerical methods to investigate the behavior of multiserver markov queues with a poisson arrival process having a sinusoidal arrival rate for this model they propose an approximation for long run average performance measures called the pointwise stationary approximation psa which consists of an appropriate weighted average of the performance measure that would result at each point in time if the system were stationary with the arrival rate that applies at that point in time in this paper we verify their conjecture that psa is asymptotically correct as the service and arrival rates increase with the instantaneous traffic intensity held fixed corresponding to long arrival rate cycles we actually establish both pointwise and average versions of this result for general time dependent birth and death processes

analysis of a robust finite element approximation for a parabolic equation with rough boundary data the approximation of parabolic equations with nonhomogeneous dirichlet boundary data by a numerical method that consists of finite elements for the space discretization and the backward euler time discretization is studied the boundary values are assumed in a least squares sense it is shown that this method achieves an optimal rate of convergence for rough only l2 boundary data and for smooth data as well the results of numerical computations which confirm the robust theoretical error estimates are also presented

error bounds for perturbing nonexponential queues a general framework is provided to derive analytic error bounds for the effect of perturbations and inaccuracies of nonexponential service or arrival distributions in single and multiserver queues the general framework is worked out in detail for the three types of finite or infinite buffer queues gi g 1 n m g c n andgi m c n first for the standardgi g 1 n queue it is illustrated how the general error bound result can lead to error bounds for different performance measures like the throughput mean queue length and stationary queue length distribution next for them g c n queue an error bound and monotonicity result are established for the throughput m g c n queues can so be compared even when hazard rates are not ordered finally for thegi m c n queue a similar result is obtained with a perturbation of the interarrival time distribution the error bound results are supported by asymptotic expressions for them m c n queue and numerical results for thegi g 1 n queue

componentwise bounds for nearly completely decomposable markov chains using stochastic comparison and reordering this paper presents an improved version of a componentwise bounding algorithm for the state probability vector of nearly completely decomposable markov chains and on an application it provides the first numerical results with the type of algorithm discussed the given two level algorithm uses aggregation and stochastic comparison with the strong stochastic st order in order to improve accuracy it employs reordering of states and a better componentwise probability bounding algorithm given st upper and lower bounding probability vectors results in sparse storage show that there are cases in which the given algorithm proves to be useful

solving nonstiff higher order odes directly by the direct integration method the variable order and stepsize direct integration di method for solving systems of nonstiff higher order odes directly is reviewed mention is also made of the current inroads in solving stiff higher order odes directly the advantages of the di method over the corresponding adams method when used to solve the same problem as a first order system are pointed out numerical results are presented comparing the two methods in terms of execution times for each tolerance used and execution times for each solution of the same range of accuracy

finite element approximation of dirichlet boundary control for elliptic pdes on two and three dimensional curved domains we consider the variational discretization of elliptic dirichlet optimal control problems with constraints on the control the underlying state equation which is considered on smooth two and three dimensional domains is discretized by linear finite elements taking into account domain approximation the control variable is not discretized we obtain optimal error bounds for the optimal control in two and three space dimensions and prove a superconvergence result in two dimensions provided that the underlying mesh satisfies some additional condition we confirm our analytical findings by numerical experiments

the pointwise stationary approximation for queues with nonstationary arrivals we empirically explore the accuracy of an easily computed approximation for long run average performance measures such as expected delay and probability of delay in multiserver queueing systems with exponential service times and periodic sinusoidal poisson arrival processes the pointwise stationary approximation is computed by integrating over time that is taking the expectation of the formula for the stationary performance measure with the arrival rate that applies at each point in time this approximation which has been empirically confirmed as a tight upper bound of the true value is shown to be very accurate for a range of parameter values corresponding to a reasonably broad spectrum of real systems

strong approximations for time dependent queues a time dependent mt mt 1 queue alternates through periods of under over and critical loading we derive period dependent pathwise asymptotic expansions for its queue length within the framework of strong approximations our main results include time dependent fluid approximations supported by a functional strong law of large numbers and diffusion approximations supported by a functional central limit theorem this complements and extends previous work on asymptotic expansions of the queue length transition probabilities