reduced basis error bound computation of parameter dependent navier stokes equations by the natural norm approach this work focuses on the a posteriori error estimation for the reduced basis method applied to partial differential equations with quadratic nonlinearity and affine parameter dependence we rely on natural norms local parameter dependent norms to provide a sharp and computable lower bound of the inf sup constant we prove a formulation of the brezzi rappaz raviart existence and uniqueness theorem in the presence of two distinct norms this allows us to relax the existence condition and to sharpen the field variable error bound we also provide a robust algorithm to compute the sobolev embedding constants involved in the error bound and in the inf sup lower bound computation we apply our method to a steady natural convection problem in a closed cavity with a grashof number varying from 10 to 10 7

local projection stabilization for the oseen problem and its interpretation as a variational multiscale method we propose to apply the recently introduced local projection stabilization to the numerical computation of the oseen equation at high reynolds number the discretization is done by nested finite element spaces using a priori error estimation techniques we prove the convergence of the method the a priori estimates are independent of the local peclet number and give a sufficient condition for the size of the stabilization parameters in order to ensure optimality of the approximation when the exact solution is smooth moreover we show how this method may be cast in the framework of variational multiscale methods we indicate what modeling assumptions must be made to use the method for large eddy simulations

a bias correction method for identification of linear dynamic errors in variables models this paper considers the problem of identifying linear systems where the input is observed in white noise but the output is observed in colored noise which also includes process disturbances an efficient method is developed which can perform unbiased parameter estimation without utilizing a prefilter the developed method is characterized by attractive features direct use of the observed data without prefiltering no need to evaluate autocorrelation functions for the input noise no need to identify a high order augmented system and provision of a direct unbiased estimate of the system parameters without parameter extraction computer simulations are presented to illustrate its superior performance including its significantly reduced computational complexity

the stability in _ and _ of the projection onto finite element function spaces on etablit la stabilite de la l 2 projection sur quelques espaces a elements finis v h consideree comme une application dans l p et w p 1 1 p sous des hypotheses de regularite faibles

on the error analysis of stabilized finite element methods for the stokes problem for a family of stabilized mixed finite element methods for the stokes equations a complete a priori and a posteriori error analysis is given

common randomness in information theory and cryptography i secret sharing as the first part of a study of problems involving common randomness at distance locations information theoretic models of secret sharing generating a common random key at two terminals without letting an eavesdropper obtain information about this key are considered the concept of key capacity is defined single letter formulas of key capacity are obtained for several models and bounds to key capacity are derived for other models

secret key generation for a pairwise independent network model we consider secret key generation for a pairwise independent network model in which every pair of terminals observes correlated sources that are independent of sources observed by all other pairs of terminals the terminals are then allowed to communicate publicly with all such communication being observed by all the terminals the objective is to generate a secret key shared by a given subset of terminals at the largest rate possible with the cooperation of any remaining terminals secrecy is required from an eavesdropper that has access to the public interterminal communication a single letter formula for secret key capacity brings out a natural connection between the problem of secret key generation and a combinatorial problem of maximal packing of steiner trees in an associated multigraph an explicit algorithm is proposed for secret key generation based on a maximal packing of steiner trees in a multigraph the corresponding maximum rate of steiner tree packing is thus a lower bound for the secret key capacity when only two of the terminals or when all the terminals seek to share a secret key the mentioned algorithm achieves secret key capacity in which case the bound is tight

brief paper accuracy analysis of bias eliminating least squares estimates for errors in variables systems the bias eliminating least squares bels method is one of the consistent estimators for identifying dynamic errors in variables systems in this paper we investigate the accuracy properties of the bels estimates an explicit expression for the normalized asymptotic covariance matrix of the estimated parameters is derived and supported by some numerical examples

galerkin finite element methods with symmetric pressure stabilization for the transient stokes equations stability and convergence analysis we consider the stability and convergence analysis of pressure stabilized finite element approximations of the transient stokes equation the analysis is valid for a class of symmetric pressure stabilization operators but also for standard inf sup stable velocity pressure spaces without stabilization provided the initial data are chosen as a specific method dependent ritz projection we get unconditional stability and optimal convergence for both pressure and velocity approximations in natural norms for arbitrary interpolations of the initial data a condition between the space and time discretization parameters has to be verified in order to guarantee pressure stability

on the stability of the reduced basis method for stokes equations in parametrized domains we present an application of reduced basis method for stokes equations in domains with affine parametric dependence the essential components of the method are i the rapid convergence of global reduced basis approximations galerkin projection onto a space wn spanned by solutions of the governing partial differential equation at n selected points in parameter space ii the off line on line computational procedures decoupling the generation and projection stages of the approximation process the operation count for the on line stage in which given a new parameter value we calculate an output of interest depends only on n typically very small and the parametric complexity of the problem the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation design optimization and real time control particular attention is given i to the pressure treatment of incompressible stokes problem ii to find an equivalent inf sup condition that guarantees stability of reduced basis solutions by enriching the reduced basis velocity approximation space with the solutions of a supremizer problem iii to provide algebraic stability of the problem by reducing the condition number of reduced basis matrices using an orthonormalization procedure applied to basis functions iv to reduce computational costs in order to allow real time solution of parametrized problem

subspace identification of bilinear and lpv systems for open and closed loop data in this paper we present a novel algorithm to identify lpv systems with affine parameter dependence operating under open and closed loop conditions a factorization is introduced which makes it possible to form a predictor that predicts the output which is based on past inputs outputs and scheduling data the predictor contains the lpv equivalent of the markov parameters using this predictor ideas from closed loop lti identification are developed to estimate the state sequence from which the lpv system matrices can be constructed a numerically efficient implementation is presented using the kernel method it turns out that if structure is present in the scheduling sequence the computational complexity reduces even more

on really locking free mixed finite element methods for the transient incompressible stokes equations inf sup stable mixed methods for the steady incompressible stokes equations that relax the divergence constraint are often claimed to deliver locking free discretizations however this relaxation leads to a pressure dependent contribution in the velocity error which is proportional to the inverse of the viscosity thus giving rise to a different locking phenomenon however a recently proposed modification of the right hand side alone leads to a discretization that is really locking free i e its velocity error converges with optimal order and is independent of the pressure and the smallness of the viscosity in this contribution we extend this approach to the transient incompressible stokes equations where besides the right hand side also the velocity time derivative requires an improved space discretization semidiscrete and fully discrete a priori velocity and pressure error estimates are derived which show remarkable robustness properties two numerical examples illustrate the superior accura

reduced basis approximation of parametrized optimal flow control problems for the stokes equations this paper extends the reduced basis method for the solution of parametrized optimal control problems presented in negri et al 2013 to the case of noncoercive elliptic equations such as the stokes equations we discuss both the theoretical properties with particular emphasis on the stability of the resulting double nested saddle point problems and on aggregated error estimates and the computational aspects of the method then we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three dimensional flow through boundary control demonstrating the effectivity of the methodology

on the stability of the l 2 projection in h 1 ω we prove the stability in h1 of the l2 projection onto a family of finite element spaces of conforming piecewise linear functions satisfying certain local mesh conditions we give explicit formulae to check these conditions for a given finite element mesh in any number of spatial dimensions in particular stability of the l2 projection in h1 holds for locally quasiuniform geometrically refined meshes as long as the volume of neighboring elements does not change too drastically

on a multiscale approach to the transient stokes problem dynamic subscales and anisotropic space time discretization abstract in this article we analyze some residual based stabilization techniques for the transient stokes problem when considering anisotropic time space discretizations we define an anisotropic time space discretization as a family of time space partitions that does not satisfy the condition h 2 c t with c uniform with respect to h and t standard residual based stabilization techniques are motivated by a multiscale approach approximating the effect of the subscales onto the large scales one of the approximations is to consider the subscales quasi static neglecting their time derivative it is well known that these techniques are unstable for anisotropic time space discretizations we show that the use of dynamic subscales where the subscales time derivatives are not neglected solves the problem and prove optimal convergence and stability results that are valid for anisotropic time space discretizations also the improvements related to the use of orthogonal subscales are addressed

on the public communication needed to achieve sk capacity in the multiterminal source model the focus of this paper is on the public communication required for generating a maximal rate secret key sk within the multiterminal source model of csiszar and narayan building on the prior work of tyagi for the two terminal scenario we derive a lower bound on the communication complexity r text sk defined to be the minimum rate of public communication needed to generate a maximal rate sk it is well known that the minimum rate of communication for omniscience denoted by r text co is an upper bound on r text sk for the class of pairwise independent network pin models defined on uniform hypergraphs we show that a certain type mathcal s condition which is verifiable in polynomial time guarantees that our lower bound on r text sk meets the r text co upper bound thus the pin models satisfying our condition are r text sk maximal indicating that the upper bound r text sk le r text co holds with equality this allows us to explicitly evaluate r text sk for such pin models we also give several examples of pin models that satisfy our type mathcal s condition finally we prove that for an arbitrary multiterminal source model a stricter version of our type mathcal s condition implies that communication from all terminals omnivocality is needed for establishing an sk of maximum rate for three terminal source models the converse is also true omnivocality is needed for generating a maximal rate sk only if the strict type mathcal s condition is satisfied however for the source models with four or more terminals counterexamples exist showing that the converse does not hold in general

a least squares petrov galerkin finite element method for the stationary navier stokes equations in this paper a galerkin least squares type finite element method is proposed and analyzed for the stationary navier stokes equations the method is consistent and stable for any combination of discrete velocity and pressure spaces without requiring a babuska brezzi stability condition the existence uniqueness and convergence at optimal rate of the discrete solution is proved in the case of sufficient viscosity or small data

the role of vector autoregressive modeling in predictor based subspace identification subspace identification for closed loop systems has been recently studied by several authors a class of new and consistent closed loop subspace algorithms is based on identification of a predictor model in a way similar as prediction error methods pem do experimental evidence suggests that these methods have a behavior which is very close to pem in certain examples the asymptotical statistical properties of one of these methods have been studied recently allowing to show i its relation with cca and ii that cramer rao lower bound is not reached in general very little however is known concerning their relative performance in this paper we shall discuss the link between these predictor based methods to this purpose we exploit the role which vector auto regressive with exogenous input models play in all these algorithms the results of this paper provide a unifying framework under which all these algorithms can be viewed also the link with varx modeling have important implications as to computational complexity is concerned leading to very computationally attractive implementations we also hope that this framework and in particular the relation with varx modeling followed by model reduction will turn out to be useful in future developments of subspace identification such as the quest for efficient procedures and the statistical analysis with finite data

residual based stabilized higher order fem for advection dominated problems abstract we reconsider the numerical solution of linear ized advection diffusion reaction problems using higher order finite elements together with stabilized galerkin methods of streamline diffusion type supg and with shock capturing stabilization the analysis improves the a priori analysis in our previous paper t knopp g lube g rapin stabilized finite element methods with shock capturing for advection diffusion problems comput methods appl mech engrg 191 2002 2997 3013 the theoretical results are supported by some numerical experiments

analysis of finite element approximation of evolution problems in mixed form this paper deals with the finite element approximation of evolution problems in mixed form following d boffi f brezzi and l gastaldi math comp 69 2000 pp 121 140 we handle separately two types of problems a model for the first case is the heat equation in mixed form while the time dependent stokes problem fits within the second one for either case we give sufficient conditions for a good approximation in the natural functional spaces the results are not obvious in the first situation in this case the well known conditions for the well posedness and convergence of the corresponding steady problem are not sufficient for the good approximation of the time dependent problem this issue is demonstrated with a numerical counter example and justified analytically

secret key agreement by public discussion from common information the problem of generating a shared secret key s by two parties knowing dependent random variables x and y respectively but not sharing a secret key initially is considered an enemy who knows the random variable z jointly distributed with x and y according to some probability distribution p sub xyz can also receive all messages exchanged by the two parties over a public channel the goal of a protocol is that the enemy obtains at most a negligible amount of information about s upper bounds on h s as a function of p sub xyz are presented lower bounds on the rate h s n as n to infinity are derived for the case in which x x sub 1 x sub n y y sub 1 y sub n and z z sub 1 z sub n result from n independent executions of a random experiment generating x sub i y sub i and z sub i for i 1 n it is shown that such a secret key agreement is possible for a scenario in which all three parties receive the output of a binary symmetric source over independent binary symmetric channels even when the enemy s channel is superior to the other two channels

supg reduced order models for convection dominated convection diffusion reaction equations abstract this paper presents a streamline upwind petrov galerkin supg reduced order model rom based on proper orthogonal decomposition pod this rom is investigated theoretically and numerically for convection dominated convection diffusion reaction problems the supg finite element method was used on realistic meshes for computing the snapshots leading to some noise in the pod data numerical analysis is used to propose the scaling of the stabilization parameter for the supg rom two approaches are used one based on the underlying finite element discretization and the other one based on the pod truncation the resulting supg roms and the standard galerkin rom g rom are studied numerically for many settings the results obtained with the supg roms are more accurate finally one of the choices for the stabilization parameter is recommended

a posteriori error estimators for stabilized p1 nonconforming approximation of the stokes problem in this paper we derive and analyze some a posteriori error estimators for the stabilized p1 nonconforming approximation of the stokes problem involving the strain tensor this will be done by decomposing the numerical error in a proper way into conforming and nonconforming contributions the error estimator for the nonconforming error is obtained in the standard way and the implicit error estimator for the conforming error is derived by applying the equilibrated residual method a crucial part of this work is construction of approximate normal stresses on interelement boundaries which will serve as equilibrated neumann data for local stokes problems it turns out that such normal stresses can be simply computed by local weak residuals of the discrete system plus jumps of the velocity solution and that a stronger equilibration condition is satisfied to ensure solvability of local stokes problems we also derive a simple explicit error estimator based on the nonsymmetric tensor recovery of the normal stress error numerical results are provided to illustrate the performance of our error estimators

reduced basis method for multi parameter dependent steady navier stokes equations applications to natural convection in a cavity this work focuses on the approximation of parametric steady navier stokes equations by the reduced basis method for a particular instance of the parameters under consideration we are able to solve the underlying partial differential equations compute an output and give sharp error bounds the computations are split into an offline part where the values of the parameters are not yet identified but only given within a range of interest and an online part where the problem is solved for an instance of the parameters the offline part is expensive and is used to build a reduced basis and prepare all the ingredients mainly matrix vector and scalar products but also eigenvalue computations necessary for the online part which is fast we provide a model problem describing natural convection phenomena in a laterally heated cavity characterized by three parameters grashof and prandtl numbers and the aspect ratio of the cavity we show the feasibility and efficiency of the a posteriori error estimation by the natural norm approach considering several test cases by varying two different parameters the gain in terms of cpu time with respect to a parallel finite element approximation is of three magnitude orders with an acceptable indeed less than 0 1 error on the selected outputs

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

a bias correction method for indirect identification of closed loop systems a novel least squares like method is developed to deal with the bias problem in indirect identification of closed loop systems with coloured disturbances it is shown that combined with a bias correction procedure this method can give rise to consistent parameter estimates by fully and efficiently using the given information about the regulator simulation results are also included for illustration

change of multivariate mutual information from local to global we study the change of multivariate mutual information among a set of random variables when some common randomness is added to or removed from a subset of the random variables this is formulated more precisely as two new multiterminal secret key agreement problems that respectively ask how one can increase the secrecy capacity efficiently by adding common randomness to a small subset of users and how one can simplify the source model by removing redundant common randomness that does not contribute to the secrecy capacity characterizations and strongly polynomial time computations are derived for the rates of change maximum usable increment and redundancy these results can be applied to study the communication complexity for secret key agreement

strong laws of large numbers under weak assumptions with application the employment of strong laws of large numbers is instrumental to the analysis of system estimation and identification strategies however the vast bulk of such laws as presented in the wider literature assume independence or at least uncorrelatedness of random components and these assumptions are quite restrictive from an engineering point of view by way of contrast the paper shows how to establish strong laws for possibly nonstationary random processes with very general dependence structure a brief example is provided that illustrates the utility of the strong law of large numbers presented

stabilized reduced basis methods for parametrized steady stokes and navier stokes equations abstract it is well known in the reduced basis approximation of saddle point problems that the galerkin projection on the reduced space does not guarantee the inf sup approximation stability even if a stable high fidelity method was used to generate snapshots for problems in computational fluid dynamics the lack of inf sup stability is reflected by the inability to accurately approximate the pressure field in this context inf sup stability is usually recovered through the enrichment of the velocity space with suitable supremizer functions the main goal of this work is to propose an alternative approach which relies on the residual based stabilization techniques customarily employed in the finite element literature such as brezzi pitkaranta franca hughes streamline upwind petrov galerkin galerkin least square in the spirit of offline online reduced basis computational splitting two such options are proposed namely offline only stabilization and offline online stabilization these approaches are then compared to and combined with the state of the art supremizer enrichment approach numerical results are discussed highlighting that the proposed methodology allows to obtain smaller reduced basis spaces i e neglecting supremizer enrichment for which a modified inf sup stability is still preserved at the reduced order level

packing steiner trees a cutting plane algorithm and computational results in this paper we describe a cutting plane algorithm for the steiner tree packing problem we use our algorithm to solve some switchbox routing problems of vlsi design and report on our computational experience this includes a brief discussion of separation algorithms a new lp based primal heuristic and implementation details the paper is based on the polyhedral theory for the steiner tree packing polyhedron developed in our companion paper this issue and meant to turn this theory into an algorithmic tool for the solution of practical problems

recovery based error estimator for stabilized finite element methods for the stokes equation abstract a recovery based error estimator is proposed and analyzed for stabilized p 1 p 0 continuous linear velocity constant pressure finite element approximations to the stokes equation reliability and efficiency of the estimator are established for various stabilized methods for several test problems numerical results show that our estimator is more accurate than the classical residual error estimator

a finite element formulation for the stokes problem allowing equal velocity pressure interpolation abstract in this paper we study a variational formulation of the stokes problem that accommodates the use of equal velocity pressure finite element interpolations the motivation of this method relies on the analysis of a class of fractional step methods for the navier stokes equations for which it is known that equal interpolations yield good numerical results the reason for this turns out to be the difference between two discrete laplacian operators computed in a different manner the formulation of the stokes problem considered here aims to reproduce this effect from the analysis of the finite element approximation of the problem we obtain stability and optimal error estimates using velocity pressure interpolations satisfying a compatibility condition much weaker than the inf sup condition of the standard formulation in particular this condition is fulfilled by the most common equal order interpolations

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

perfect omniscience perfect secrecy and steiner tree packing we consider perfect secret key generation for a pairwise independent network model in which every pair of terminals share a random binary string with the strings shared by distinct terminal pairs being mutually independent the terminals are then allowed to communicate interactively over a public noiseless channel of unlimited capacity all the terminals as well as an eavesdropper observe this communication the objective is to generate a perfect secret key shared by a given set of terminals at the largest rate possible and concealed from the eavesdropper first we show how the notion of perfect omniscience plays a central role in characterizing perfect secret key capacity second a multigraph representation of the underlying secrecy model leads us to an efficient algorithm for perfect secret key generation based on maximal steiner tree packing this algorithm attains capacity when all the terminals seek to share a key and in general attains at least half the capacity third when a single helper terminal assists the remaining user terminals in generating a perfect secret key we give necessary and sufficient conditions for the optimality of the algorithm also a weak helper is shown to be sufficient for optimality

determining optimal rates for communication for omniscience this paper considers the communication for omniscience problem a set of users observe a discrete memoryless multiple source and want to recover the entire multiple source via noise free broadcast communications we study the problem of how to determine an optimal rate vector that attains omniscience with the minimum sum rate the total number of communications the results cover both asymptotic and non asymptotic models where the transmission rates are real and integral respectively we propose a modified decomposition algorithm mda and a sum rate increment algorithm sia for the asymptotic and non asymptotic models respectively both of which determine the value of the minimum sum rate and a corresponding optimal rate vector in polynomial time for the coordinate saturation capacity algorithm a nesting algorithm in mda and sia we propose to implement it by a fusion method and show by experimental results that this fusion method contributes to a reduction in computation complexity finally we show that the separable convex minimization problem over the optimal rate vector set in the asymptotic model can be decomposed by the fundamental partition the optimal partition of the user set that determines the minimum sum rate so that the problem can be solved more efficiently

secrecy capacities for multiple terminals we derive single letter characterizations of strong secrecy capacities for models with an arbitrary number of terminals each of which observes a distinct component of a discrete memoryless multiple source with unrestricted and interactive public communication permitted between the terminals a subset of these terminals can serve as helpers for the remaining terminals in generating secrecy according to the extent of an eavesdropper s knowledge three kinds of secrecy capacity are considered secret key sk private key pk and wiretap secret key wsk capacity the characterizations of the sk and pk capacities highlight the innate connections between secrecy generation and multiterminal source coding without secrecy requirements a general upper bound for wsk capacity is derived which is tight in the case when the eavesdropper can wiretap noisy versions of the components of the underlying multiple source provided randomization is permitted at the terminals these secrecy capacities are seen to be achievable with noninteractive communication between the terminals the achievability results are also shown to be universal

a posteriori error estimators for the stokes equations we present two a posteriori error estimators for the mini element discretization of the stokes equations one is based on a suitable evaluation of the residual of the finite element solution the other one is based on the solution of suitable local stokes problems involving the residual of the finite element solution both estimators are globally upper and locally lower bounds for the error of the finite element discretization numerical examples show their efficiency both in estimating the error and in controlling an automatic self adaptive mesh refinement process the methods presented here can easily be generalized to the navier stokes equations and to other discretization schemes

a new error analysis for discontinuous finite element methods for linear elliptic problems the standard a priori error analysis of discontinuous galerkin methods requires additional regularity on the solution of the elliptic boundary value problem in order to justify the galerkin orthogonality and to handle the normal derivative on element interfaces that appear in the discrete energy norm in this paper a new error analysis of discontinuous galerkin methods is developed using only the h k weak formulation of a boundary value problem of order 2k this is accomplished by replacing the galerkin orthogonality with estimates borrowed from a posteriori error analysis and by using a discrete energy norm that is well defined for functions in h k

time dependent subscales in the stabilized finite element approximation of incompressible flow problems abstract in this paper we analyze a stabilized finite element approximation for the incompressible navier stokes equations based on the subgrid scale concept the essential point is that we explore the properties of the discrete formulation that results allowing the subgrid scales to depend on time this apparently natural idea avoids several inconsistencies of previous formulations and also opens the door to generalizations

continuous interior penalty finite element method for oseen s equations in this paper we present an extension of the continuous interior penalty method of douglas and dupont interior penalty procedures for elliptic and parabolic galerkin methods in computing methods in applied sciences lecture notes in phys 58 springer verlag berlin 1976 pp 207 216 to oseen s equations the method consists of a stabilized galerkin formulation using equal order interpolation for pressure and velocity to counter instabilities due to the pressure velocity coupling or due to a high local reynolds number we add a stabilization term giving l2 control of the jump of the gradient over element faces edges in two dimensions to the standard galerkin formulation boundary conditions are imposed in a weak sense using a consistent penalty formulation due to nitsche we prove energy type a priori error estimates independent of the local reynolds number and give some numerical examples recovering the theoretical results

variance reduction in covariance based realization algorithm with application to closed loop data abstract the covariance based realization algorithm cobra one branch of subspace methods enables the estimation of multivariable models using a large number of data points due to the use of finite size covariance matrices in addition the covariance pre processing allows cobra to ignore any high order noise dynamics and focus on the estimation of the low order deterministic model however subspace methods and cobra in particular are not maximum likelihood methods in this paper an in depth study on the statistical behavior of the noise effects is conducted an approach is provided to reduce the variance of an estimate obtained by cobra via the choice of optimal row and column weighting matrices for closed loop implementation of cobra a two stage procedure is proposed with the estimate on an intermediate instrument at the first stage a least length perturbation of a scalar accuracy function is used to obtain an analytic solution for the optimal weighting matrices the resulting instruments produced by the first stage are used for the identification at the second stage to extract the plant model simulation examples are given to illustrate the efficiency of the proposed two stage cobra method on the basis of closed loop data and compared with other subspace methods

a posteriori error estimation for stabilized mixed approximations of the stokes equations the practical implementation of the lowest order pl p0 linear velocity constant pressure finite element method for the steady state incompressible navier stokes equations is addressed in this work three different types of a posteriori error indicator are introduced and each is shown to be equivalent to the discretization error our numerical results show that these indicators can be used to drive an adaptive refinement process which is specially tailored to create grids which conform to the requirements of the local stabilization it is also shown that the indicators provide an effective method for detecting local singularities in the flow solution

error analysis of some galerkin least squares methods for the elasticity equations the recent technique of stabilizing mixed finite element methods by augmenting the galerkin formulation with least squares terms calculated separately on each element is considered the error analysis is performed in a unified manner yielding improved results for some methods introduced earlier in addition a new formulation is introduced and analyzed method is used within two different contexts the first is in connection with the plain strain or three dimensional problems near the incompressible limit for which the poisson ratio equals one half it is well known that for these problems a standard lower order displacement finite element method will break down by now it is also well known how a working method can be obtained a new unknown the pressure is introduced and discretized with a finite element space different from that used for the displacements the finite element method obtained falls into the class of saddlepoint problems for which there is a general theory developed by brezzi and babuska 5 7 the application of this theory shows that the method converges optimally if the discrete spaces for the displacement and pressure satisfy a stability condition for a particular choice of displacement and pressure approximations it can be a difficult task to verify this babuska brezzi or inf sup condition during the last decade this problem has been intensively studied and the performances of many combinations are now known cf 18 and 23 26 for some recent extensions in addition there exists a general technique utilizing bubble functions by which a stable method can

a unified framework for a posteriori error estimation for the stokes problem in this paper a unified framework for a posteriori error estimation for the stokes problem is developed it is based on h 1 0 omega d conforming velocity reconstruction and underline boldsymbol h mathrm div omega conforming locally conservative flux stress reconstruction it gives guaranteed fully computable global upper bounds as well as local lower bounds on the energy error in order to apply this framework to a given numerical method two simple conditions need to be checked we show how to do this for various conforming and conforming stabilized finite element methods the discontinuous galerkin method the crouzeix raviart nonconforming finite element method the mixed finite element method and a general class of finite volume methods the tools developed and used include a new simple equilibration on dual meshes and the solution of local poisson type neumann problems by the mixed finite element method numerical experiments illustrate the theoretical developments

stabilized finite element methods for the generalized oseen problem the numerical solution of the non stationary incompressible navierstokes model can be split into linearized auxiliary problems of oseen type we present in a unique way different stabilization techniques of finite element schemes on isotropic meshes first we describe the state of the art for the classical residual based supg pspg method then we discuss recent symmetric stabilization techniques which avoid some drawbacks of the classical method these methods are closely related to the concept of variational multiscale methods which seems to provide a new approach to large eddy simulation finally we give a critical comparison of these methods

analysis of the pspg method for the transient stokes problem abstract we propose a new analysis for the pspg method applied to the transient stokes problem stability and convergence are obtained under different conditions on the discretization parameters depending on the approximation used in space for the pressure we prove optimal stability and convergence only in the case of piecewise affine approximation under the standard condition on the time step finally we show that the stability problems of the pspg method can be circumvented using an appropriate discrete reconstruction of the laplace operator

certified reduced basis methods for parametrized saddle point problems we present reduced basis approximations and associated rigorous a posteriori error bounds for parametrized saddle point problems first we develop new a posteriori error estimates that unlike earlier approaches provide upper bounds for the errors in the approximations of the primal variable and the lagrange multiplier separately the proposed method is an application of brezzi s theory for saddle point problems to the reduced basis context and exhibits significant advantages over existing methods second based on an analysis of brezzi s theory we compare several options for the reduced basis approximation space from the perspective of approximation stability and computational cost finally we introduce a new adaptive sampling procedure for saddle point problems constructing approximation spaces that are stable and compared to earlier approaches computationally much more efficient the method is applied to a stokes flow problem in a two dimensional channel with a parametrized rectangular obstacle

a stabilized nitsche cut finite element method for the oseen problem abstract we provide the numerical analysis for a nitsche based cut finite element formulation for the oseen problem which has been originally presented for the incompressible navier stokes equations by schott and wall 2014 and allows the boundary of the domain to cut through the elements of an easy to generate background mesh the formulation is based on the continuous interior penalty cip method of burman et al 2006 which penalizes jumps of velocity and pressure gradients over inter element faces to counteract instabilities arising for high local reynolds numbers and the use of equal order interpolation spaces for the velocity and pressure since the mesh does not fit the boundary dirichlet boundary conditions are imposed weakly by a stabilized nitsche type approach the addition of cip like ghost penalties in the boundary zone allows to prove that our method is inf supstable and to derive optimal order a priori error estimates in an energy type norm irrespective of how the boundary cuts the underlying mesh all applied stabilization techniques are developed with particular emphasis on low and high reynolds numbers two and three dimensional numerical examples corroborate the theoretical findings finally the proposed method is applied to solve the transient incompressible navier stokes equations on a complex geometry

on some time marching schemes for the stabilized finite element approximation of the mixed wave equation abstract in this paper we analyze time marching schemes for the wave equation in mixed form the problem is discretized in space using stabilized finite elements on the one hand stability and convergence analyses of the fully discrete numerical schemes are presented using different time integration schemes and appropriate functional settings on the other hand we use fourier techniques also known as von neumann analysis in order to analyze stability dispersion and dissipation numerical convergence tests are presented for various time integration schemes polynomial interpolations for the spatial discretization stabilization methods and variational forms to analyze the behavior of the different schemes considered a 1d wave propagation problem is solved

edge stabilization for the generalized stokes problem a continuous interior penalty method in this note we introduce and analyze a stabilized finite element method for the generalized stokes equation stability is obtained by adding a least squares penalization of the gradient jumps acro

optimal low order finite element methods for incompressible flow abstract in this paper we consider the characterization of optimal stabilisation parameters associated with mixed finite element approximations of stokes flow we show how the optimal parameter in terms of the approximating power of the method is related to the parameter value which minimises the condition number of the associated schur complement system for the pressure field we illustrate the tightness of our abstract theoretical results in the cases of the q 1 p 0 quadrilateral and p 1 p 1 triangular elements

reduced basis approximation and a posteriori error estimation for stokes flows in parametrized geometries roles of the inf sup stability constants in this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady stokes flows in affinely parametrized geometries focusing on the role played by the brezzi s and babuska s stability constants the crucial ingredients of the methodology are a galerkin projection onto a low dimensional space of basis functions properly selected an affine parametric dependence enabling to perform competitive offline online splitting in the computational procedure and a rigorous a posteriori error estimation on field variables the combinatiofn of these three factors yields substantial computational savings which are at the basis of an efficient model order reduction ideally suited for real time simulation and many query contexts e g optimization control or parameter identification in particular in this work we focus on i the stability of the reduced basis approximation based on the brezzi s saddle point theory and the introduction of a supremizer operator on the pressure terms ii a rigorous a posteriori error estimation procedure for velocity and pressure fields based on the babuska s inf sup constant including residuals calculations iii the computation of a lower bound of the stability constant and iv different options for the reduced basis spaces construction we present some illustrative results for both interior and external steady stokes flows in parametrized geometries representing two parametrized classical poiseuille and couette flows a channel contraction and a simple flow control problem around a curved obstacle

closed loop identification revisited identification of systems operating in closed loop has long been of prime interest in industrial applications the problem offers many possibilities and also some fallacies and a wide variety of approaches have been suggested many quite recently the purpose of the current contribution is to place most of these approaches in a coherent framework thereby showing their connections and display similarities and differences in the asymptotic properties of the resulting estimates the common framework is created by the basic prediction error method and it is shown that most of the common methods correspond to different parameterizations of the dynamics and noise models the so called indirect methods e g are indeed direct methods employing noise models that contain the regulator the asymptotic properties of the estimates then follow from the general theory and take different forms as they are translated to the particular parameterizations we also study a new projection approach to closed loop identification with the advantage of allowing approximation of the open loop dynamics in a given and user chosen frequency domain norm even in the case of an unknown nonlinear regulator

recursive algorithms for identification in closed loop a unified approach and evaluation a unified presentation of recursive algorithms for plant model identification in closed loop is given from the basic formulation of the problem of finding the plant model that gives the best predictor for the closed loop system two families of algorithms using either a reparameterized predictor for the closed loop or a plant predictor operating on filtered data are presented and their asymptotic properties are examined validation tests for the models identified in closed loop are proposed a comparative evaluation of the various algorithms in simulation and on real time experiments concludes the paper

stabilized reduced basis method for parametrized advection diffusion pdes the aim of this master thesis is to study and develop a stabilized reduced basis method suitable for the approximation of the solution of parametrized advection diffusion pdes with high peclet number that is roughly the ratio between the advection coefficient and the diffusion one advection diffusion equations are very important in many engineering applications because they are used to model for example heat transfer phenomena or the diffusion of pollutants in the atmosphere in such applications we often need very fast evaluations of the approximated solution depending on some input parameters this happens for example in the case of real time simulation moreover we need rapid evaluations also if we have to perform repeated approximation of the solution for different input parameters an important case of this many query situation is represented by some optimization problems in which the objective function to optimize depends on the parameters through the solution of a pde the reduced basis rb method meets our need for rapidity and it is also able to guarantee the reliability of the solution thanks to sharp a posteriori error bounds we can find in literature many works about the application of the rb method to advection diffusion problems but they mainly deal with equations in which the peclet number is low the need for stabilization arise from the fact that the finite element fe approximated solution that the rb method aims to recover shows strong instability problems that have to be fixed in this work we want to go further in the study of the stabilization of the rb method for advection dominated problem in both steady and unsteady case as regards the steady case we first compare two possible stabilization strategies by testing them on some test problems in order to design an efficient stabilized reduced basis method we will then test this method using the piecewise quadratic fe approximation as reference solution instead of the usual piecewise linear one we extend the method designed for the steady case to the time dependent case and we will carry out some numerical tests

a posteriori error estimates of stabilization of low order mixed finite elements for incompressible flow in this paper we derive a posteriori error estimates for the stabilization of low order mixed finite element methods for the stokes equations by defining different projection estimators we prove that up to higher order perturbation terms the estimators yield global upper and lower bounds on the error of stabilized finite element methods in numerical tests each error estimator is shown to be equivalent to the discretization error it is also shown that the adaptive strategy based on both projection estimators is efficient to detect local singularities in the flow problems

refined a posteriori error estimation for classical and pressure robust stokes finite element methods recent works showed that pressure robust modifications of mixed finite element methods for the stokes equations outperform their standard versions in many cases this is achieved by divergence free reconstruction operators and results in pressure independent velocity error estimates which are robust with respect to small viscosities in this paper we develop a posteriori error control which reflects this robustness the main difficulty lies in the volume contribution of the standard residual based approach that includes the l 2 norm of the right hand side however the velocity is only steered by the divergence free part of this source term an efficient error estimator must approximate this divergence free part in a proper manner otherwise it can be dominated by the pressure error to overcome this difficulty a novel approach is suggested that uses arguments from the stream function and vorticity formulation of the navier stokes equations the novel error estimators only take the hbox curl of the right hand side into account and so lead to provably reliable efficient and pressure independent upper bounds in case of a pressure robust method in particular in pressure dominant situations this is also confirmed by some numerical examples with the novel pressure robust modifications of the taylor hood and mini finite element methods

a bias corrected estimator for nonlinear systems with output error type model structures parametric identification of linear time invariant lti systems with output error oe type of noise model structures has a well established theoretical framework different algorithms like instrumental variables based approaches or prediction error methods pems have been proposed in the literature to compute a consistent parameter estimate for linear oe systems although the prediction error method provides a consistent parameter estimate also for nonlinear output error noe systems it requires to compute the solution of a nonconvex optimization problem therefore an accurate initialization of the numerical optimization algorithms is required otherwise they may get stuck in a local minimum and as a consequence the computed estimate of the system might not be accurate in this paper we propose an approach to obtain in a computationally efficient fashion a consistent parameter estimate for output error systems with polynomial nonlinearities the performance of the method is demonstrated through a simulation example

supremizer stabilization of pod galerkin approximation of parametrized steady incompressible navier stokes equations in this work we present a stable proper orthogonal decomposition pod galerkin approximation for parametrized steady incompressible navier stokes equations with low reynolds number supremizers solutions are added to the reduced velocity space in order to obtain a stable reduced order system considering in particular the fulfillment of an inf sup condition the stability analysis is first carried out from a theoretical standpoint then confirmed by numerical tests performed on a parametrized two dimensional backward facing step flow

a bias correction method for closed loop identification of linear parameter varying systems abstract due to safety constraints and unstable open loop dynamics system identification of many real world processes often requiresgathering data from closed loop experiments in this paper we present a bias correction scheme for closed loop identification of linear parameter varying input output lpv io models which aims at correcting the bias caused by the correlation between the input signal exciting the process and output noise the proposed identification algorithm provides a consistent estimate of the open loop model parameters when both the output signal and the scheduling variable are corrupted by measurement noise the effectiveness of the proposed methodology is tested in two simulation case studies

stabilized finite element method for the transient navier stokes equations based on a pressure gradient projection abstract in this paper we present a stabilized finite element formulation for the transient incompressible navier stokes equations the main idea is to introduce as a new unknown of the problem the projection of the pressure gradient onto the velocity space and to add to the incompresibility equation the difference between the laplacian of the pressure and the divergence of this new vector field this leads to a pressure stabilization effect that allows the use of equal interpolation for both velocities and pressures in the case of the transient equations we consider the possibility of treating the pressure gradient projection either implicitly or explicity in the first case the number of unknowns of the problem is substantially increased with respect to the standard galerkin formulation nevertheless iterative techniques may be used in order to uncouple the calculation of the pressure gradient projection from the rest of unknowns velocity and pressure when this vector field is treated explicitly the increment of computational cost of the stabilized formulation with respect to the galerkin method is very low we provide a stability estimate for the case of the simple backward euler time integration scheme for both the implicit and the explicit treatment of the pressure gradient projection

analysis of a streamline diffusion finite element method for the stokes and navier stokes equations for the stokes equations with convection and the incompressible navier stokes equations the authors analyze a streamline diffusion finite element method that is capable of balancing both the convection and the pressure thus allowing the use of arbitrary pairs of velocity pressure spaces for the linear problem the authors obtain for all mesh peclet numbers optimal error estimates in natural norms including in particular the l 2 norm of the pressure the same holds for the nonlinear problem which close to a regular branch of solutions i e the linearized operator is an isomorphism of the norm of the inverse of which still depends on the reynolds number consequently the dependence of the error constants on the reynolds number is not completely resolved in this case

brief on the relation between a bias eliminated least squares bels and an iv estimator in closed loop identification a bias correction method for closed loop identification introduced in the literature as the bias eliminated least squares bels method zheng feng automatica 31 1995 1019 is shown to be equivalent to a basic instrumental variable estimator applied to a predictor for the closed loop system this predictor is a function of the plant parameters and the known controller corresponding to the related method using a least squares criterion the method is referred to as the tailor made iv method for closed loop identification the indicated equivalence greatly facilitates the understanding and the analysis of the bels method

a minimal stabilisation procedure for mixed finite element methods stabilisation methods are often used to circumvent the difficulties associated with the stability of mixed finite element methods stabilisation however also means an excessive amount of dissipation or the loss of nice conservation properties it would thus be desirable to reduce these disadvantages to a minimum we present a general framework not restricted to mixed methods that permits to introduce a minimal stabilising term and hence a minimal perturbation with respect to the original problem to do so we rely on the fact that some part of the problem is stable and should not be modified sections 2 and 3 present the method in an abstract framework section 4 and 5 present two classes of stabilisations for the inf sup condition in mixed problems we present many examples most arising from the discretisation of flow problems section 6 presents examples in which the stabilising terms is introduced to cure coercivity problems

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100