adaptive poromechanics computations based on a posteriori error estimates for fully mixed formulations of biot s consolidation model abstract this paper is concerned with the analysis of coupled mixed finite element methods applied to the biot s consolidation model we consider two mixed formulations that use the stress tensor and darcy velocity as primary variables as well as the displacement and pressure the first formulation is with a symmetric stress tensor while the other enforces the symmetry of the stress weakly through the introduction of a lagrange multiplier the well posedness of the two formulations is shown through galerkin s method and suitable a priori estimates the two formulations are then discretized with the backward euler scheme in time and with two mixed finite elements in space we present next a general and unified a posteriori error analysis which is applicable for any flux and stress conforming discretization our estimates are based on h 1 conforming reconstruction of the pressure and a suitable h 1 d conforming reconstruction of the displacement both are continuous and piecewise affine in time these reconstructions are used to infer a guaranteed and fully computable upper bound on the energy type error measuring the differences between the exact and the approximate pressure and displacement the error components resulting from the spatial and the temporal discretization are distinguished they are then used to design an adaptive space time algorithm numerical experiments illustrate the efficiency of our estimates and the performance of the adaptive algorithm

lq regulator design method for system with delay based on spectral decomposition of the hamiltonian a design method to construct an lq regulator for a system with time delay is proposed it is based on a new technique for composing the solution of an infinite dimensional riccati equation using the spectral decomposition of the hamiltonian this design method has the feature that the closed loop poles can be calculated a priori from the open loop poles and one scalar design parameter so that we can choose the parameter to obtain an optimal control law which results in the desired degree of exponential stability of the closed loop system

dynamic programming for optimal control problems with delays in the control variable we study a class of optimal control problems with state constraint where the state equation is a differential equation with delays in the control variable this class of problems arises in some economic applications in particular in optimal advertising problems the optimal control problem is embedded in a suitable hilbert space and the associated hamilton jacobi bellman hjb equation is considered in this space it is proved that the value function is continuous with respect to a weak norm and that it solves in the viscosity sense the associated hjb equation the main results are the proof of a directional c 1 regularity for the value function and the feedback characterization of optimal controls

regular linear systems governed by neutral fdes the aim of this paper is to prove that a class of distributed parameter systems governed by neutral fdes provides regular linear systems employing the well established theory of representation transfer function and feedback of these later we then give new representations of the state and the output function of the neutral systems

structure and stability of finite dimensional approximations for functional differential equations this paper deals with the structural and stability properties of the averaging approximation scheme for linear retarded functional differential equations both in the discrete and in the continuous time case the structure of the approximating systems is shown to be analogous to the structure of the underlying retarded equation moreover it is shown that the approximating systems are exponentially stable in a uniform sense if the original system is asymptotically stable

brief paper maximum principle for the stochastic optimal control problem with delay and application in this paper we consider an optimal control problem for the stochastic system described by stochastic differential equations with delay we obtain the maximum principle for the optimal control of this problem by virtue of the duality method and the anticipated backward stochastic differential equations our results can be applied to a production and consumption choice problem the explicit optimal consumption rate is obtained

guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity we obtain fully computable a posteriori error estimators for the energy norm of the error in second order conforming and nonconforming finite element approximations in planar elasticity these estimators are completely free of unknown constants and give a guaranteed numerical upper bound on the norm of the error the estimators are shown to also provide local lower bounds up to a constant and higher order data oscillation terms numerical examples are presented illustrating the theory and confirming the effectiveness of the estimator

stress and flux reconstruction in biots poro elasticity problem with application to a posteriori error analysis we derive equilibrated reconstructions of the darcy velocity and of the total stress tensor for biots poro elasticity problem both reconstructions are obtained from mixed finite element solutions of local neumann problems posed over patches of elements around mesh vertices the darcy velocity is reconstructed using raviartthomas finite elements and the stress tensor using arnoldwinther finite elements so that the reconstructed stress tensor is symmetric both reconstructions have continuous normal component across mesh interfaces using these reconstructions we derive a posteriori error estimators for biots poro elasticity problem and we devise an adaptive spacetime algorithm driven by these estimators the algorithm is illustrated on test cases with analytical solution on the quarter five spot problem and on an industrial test case simulating the excavation of two galleries

a local a posteriori error estimator based on equilibrated fluxes we present and analyze a new a posteriori error estimator for lowest order conforming finite elements it is based on raviart thomas finite elements and can be obtained locally by a postprocessing technique involving for each vertex a local subproblem associated with a dual mesh under certain regularity assumptions on the right hand side we obtain an error estimator where the constant in the upper bound for the true error tends to one replacing the conforming finite element solution by a postprocessed one the error estimator is asymptotically exact the local equivalence between our estimator and the standard residual based error estimator is established numerical results illustrate the performance of the error estimator

numerical algorithms for optimal controls for nonlinear stochastic systems with delays the markov chain approximation numerical methods were extended to general controlled nonlinear and reflected diffusions with delays in a recent monograph where many types of ideal algorithms were developed and convergence proved any combination of the path control and reflection terms can be delayed if the control and or reflection terms are delayed then the memory requirements with naive algorithms can be huge recasting the problem in terms of a wave equation yields algorithms with considerably reduced memory needs the reference concentrated on theoretical issues here we are concerned with adapting the ideal to applications and present data showing that the method can work well

state space theory of linear time invariant systems with delays in state control and observation variables ii abstract part i of this paper studies a coupled mathematical system which provides a good model for important families of linear time invariant hereditary systems delay differential equations integro differential equations volterra stieltjes integral equations functional differential equations of retarded and neutral types etc appropriate states are constructed and associated semigroups and abstract differential equations are obtained in part ii we emphasize the structural operator approach as in delfour and manitius control operators are added to the coupled mathematical system allowing delays in the control variables again structural operators are introduced to define the state and obtain abstract differential equations without delays in the control variable as in the work of vinter and kwong finally observation operators are added which allow for delays in the observation variable and delayed control variables in the observation equation again a new state and a state equations are constructed in such a way that no delay appears in the new observation operator thus generalizing the construction of a pritchard and d salamon

paper linear optimal control of systems with state and control variable delays in this paper we announce a new rigorous state space formulation for systems with delays in state and control variables this is used to solve the linear quadratic optimal control problem over both finite and infinite time horizons in each case abstract operational riccati equations are derived to characterize the feedback gains this paper extends recent results of vinter and kwong

guaranteed a posteriori error estimator for mixed finite element methods of linear elasticity with weak stress symmetry in this paper we propose an a posteriori error estimator for the mixed finite element methods of the linear elasticity problem with the symmetry condition weakly imposed on the stress tensor the error estimator is constructed by making a proper decomposition of the stress error and using an argument similar to the hypercircle method it is shown that the resulting estimator yields a guaranteed upper bound on the stress error which relies on computable upper bounds of the constants in the first and second korn inequalities we also establish the local lower bound by using the discrete friedrichs inequality our approach is equivalent to the helmholtz decomposition of the stress error but requires assumptions neither on the regularity of the solution nor the geometry of the domain numerical results are provided to illustrate the efficiency of our error estimator

robust stabilization of uncertain time delay systems via combined internal external approach a robust stabilization problem is discussed for time delay systems by introducing an indefinite riccati type operator equation for time delay systems a design method for a stabilizing control law robust against parametric uncertainties which occur in lumped parameter elements and in all types of delay element is obtained in the derivation of the control law a combined approach is taken an internal approach based on a lyapunov type operator equation is combined with an external approach based on the small gain theorem this enables the uncertainties of time delay systems to be dealt with in a unified way

reliable a posteriori error control for nonconforming finite element approximation of stokes flow we derive computable a posteriori error estimates for the lowest order nonconforming crouzeix raviart element applied to the approximation of incompressible stokes flow the estimator provides an explicit upper bound that is free of any unknown constants provided that a reasonable lower bound for the inf sup constant of the underlying problem is available in addition it is shown that the estimator provides an equivalent lower bound on the error up to a generic constant

a posteriori error estimates for mixed fem in elasticity a residue based reliable and efficient error estimator is established for finite element solutions of mixed boundary value problems in linear planar elasticity the proof of the reliability of the estimator is based on helmholtz type decompositions of the error in the stress variable and a duality argument for the error in the displacements the efficiency follows from inverse estimates the constants in both estimates are independent of the lame constant lambda and so locking phenomena for lambda to infty are properly indicated the analysis justifies a new adaptive algorithm for automatic mesh refinement

h norm and invariant manifolds of systems with state delays abstract the problem of finding bounds on the h norm of systems with a finite number of point delays and distributed delay is considered sufficient conditions for the system to possess an h norm which is less or equal to a prescribed bound are obtained in terms of riccati partial differential equations rpde s we show that the existence of a solution to the rpde s is equivalent to the existence of a stable manifold of the associated hamiltonian system for small delays the existence of the stable manifold is equivalent to the existence of a stable manifold of the ordinary differential equations that govern the flow on the slow manifold of the hamiltonian system this leads to an algebraic finite dimensional criterion for systems with small delays

the cone of distance matrices abstract the geometry of the cone of euclidean distance matrices edms is analyzed using a new characterization of an edm the facial structure and the angle that edms of embedding dimension one make with the center ray are found this result follows from a complete analysis of the critical points of the distance function in frobenius norm from the matrix e consisting of zero diagonal and ones elsewhere to the edms of embedding dimension one

korn s inequalities and their applications in continuum mechanics korn s inequalities have played a central role in the development of linear elasticity not only in connection with the basic theoretical issues such as existence and uniqueness but also in a variety of applications the korn inequalities and other related inequalities for integrals of quadratic functionals also arise in the analysis of viscous incompressible fluid flow the dimensionless optimal constants appearing in these inequalities the korn constants depend only on the shape of the domains of concern information on the geometric dependence of these constants is essential in applications in this review article we summarize the major results on korn s inequalities for bounded domains in two and three dimensions with emphasis on results concerning the korn constants some applications in continuum mechanics are also described

equilibrated residual error estimator for edge elements reliable a posteriori error estimates without generic constants can be obtained by a comparison of the finite element solution with a feasible function for the dual problem a cheap computation of such functions via equilibration is well known for scalar equations of second order we simplify and modify the equilibration such that it can be applied to the curl curl equation and edge elements the construction is more involved for edge elements since the equilibration has to be performed on subsets with different dimensions for this reason raviart thomas elements are extended in the spirit of distributions

error estimate procedure in the finite element method and applications statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models the error on constitutive law for these fields yields an expression of the finite element error moreover the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy

output regulation of nonlinear systems with delay abstract output regulation of retarded type nonlinear systems is considered regulator equations are derived which generalize francis byrnes isidori equations to the case of systems with delay it is shown that under standard assumptions the regulator problem is solvable if and only if these equations are solvable in the linear case the solution of these equations is reduced to linear matrix equations an example of a delayed van der pol equation illustrates the efficiency of the results

an evolution equation approach to nonautonomous linear systems with state input and output delays we propose a new approach which brings nonautonomous linear systems with state input and output delays in the line with the standard theory of nonautonomous linear systems to this purpose we establish using the concept of lebesgue extensions a new variation of constants formula for nonhomogenous delay equations from this we deduce another new one for nonautonomous linear systems with state and input delays inspiriting from this formula we show that a given delay system determines a nonautonomous absolutely regular linear system with the same input and output spaces as of the delay system our abstract results will be applied to investigate the existence and the uniqueness of the solutions for a class of nonautonomous neutral equations in banach spaces

characterization of kernel functions associated with operator algebraic riccati equations for linear delay systems abstract in infinite time quadratic control and stochastic filtering problems for linear delay systems operator algebraic riccati equations play a very important role however since these are abstract operator equations it is very useful in analyzing their structure to be able to characterize the kernel functions associated with the solutions of the operator riccati equations the kernel functions are given by the unique solution of a set of coupled differential equations by comparing these kernel equations with similar ones available in the literature it is shown that this characterization result is somewhat stronger than previously known results possible extentions to systems with control observation as well as state delays are also pointed out

approximating lyapunov exponents and sacker sell spectrum for retarded functional differential equations we consider lyapunov exponents and sacker sell spectrum for linear nonautonomous retarded functional differential equations posed on an appropriate hilbert space a numerical method is proposed to approximate such quantities based on the reduction to finite dimension of the evolution family associated to the system to which a classic discrete qr method is then applied the discretization of the evolution family is accomplished by a combination of collocation and generalized fourier projection a rigorous error analysis is developed to bound the difference between the computed stability spectra and the exact stability spectra the efficacy of the results is illustrated with some numerical examples

a framework for obtaining guaranteed error bounds for finite element approximations we give an overview of our recent progress in developing a framework for the derivation of fully computable guaranteed posteriori error bounds for finite element approximation including conforming non conforming mixed and discontinuous finite element schemes whilst the details of the actual estimator are rather different for each particular scheme there is nonetheless a common underlying structure at work in all cases we aim to illustrate this structure by treating conforming non conforming and discontinuous finite element schemes in a single framework in taking a rather general viewpoint some of the finer details of the analysis that rely on the specific properties of each particular scheme are obscured but in return we hope to allow the reader to see the wood despite the trees

optimal controls and their discontinuities in quadratic problems of delay systems we construct and study quadratic optimal controls in delay systems of neutral type in these systems we allow functional lags in the derivative the state the control and in the cost index we point out that typically optimal controls of time lag systems are discontinuous discontinuities might occur as a consequence of delays in the control action and of the neutrality of the system we exhibit computed examples of jumps in optimal controls whose origins are in each of the two types our techniques are based on the method of steps which we generalize to fit systems with functional lags the work includes an analysis of r n controllability in time lag systems

the infinite time quadratic control problem for linear systems with state and control delays an evolution equation approach we show how a linear differential delay equation with delays in the control can be reformulated as an evolution equation with bounded input operator as a simple application we solve an infinite time quadratic cost control problem for the delay differential equation we also point out how our results even when specialized to the case where delays in the control disappear extend results previously published in the literature

basic reproduction ratios for almost periodic compartmental models with time delay abstract the theory of basic reproduction ratio r 0 is established for a large class of almost periodic and time delayed compartmental population models we first present some dynamical properties for linear almost periodic functional differential systems by using the product space and evolution semigroup approach we then prove that r 0 1 has the same sign as the exponential growth bound of an associated linear system as an application we apply the developed theory to an almost periodic seir model with an incubation period and obtain a threshold result on its global dynamics in terms of r 0 finally we present some numerical simulations numerical simulations indicate that prolonging the length of incubation period is beneficial for the control of the disease in addition a simple model shows that the basic reproduction ratio may be underestimated or overestimated if an almost periodic coefficient is approximated by a periodic one

locking free adaptive mixed finite element methods in linear elasticity mixed finite element methods such as peers or the bdms methods are designed to avoid locking for nearly incompressible materials in plane elasticity in this paper we establish a robust adaptive mesh refining algorithm that is rigorously based on a reliable and efficient a posteriori error estimate numerical evidence is provided for the independence of the constants in the a posteriori error bounds and for the efficiency of the adaptive mesh refining algorithm proposed

residual flux based a posteriori error estimates for finite volume and related locally conservative methods we derive in this paper a posteriori error estimates for discretizations of convection diffusion reaction equations in two or three space dimensions our estimates are valid for any cell centered finite volume scheme and in a larger sense for any locally conservative method such as the mimetic finite difference covolume and other we consider meshes consisting of simplices or rectangular parallelepipeds and also provide extensions to nonconvex cells and nonmatching interfaces we allow for the cases of inhomogeneous and anisotropic diffusion dispersion tensors and of convection dominance the estimates are established in the energy semi norm for a locally postprocessed approximate solution preserving the conservative fluxes and are of residual type they are fully computable all occurring constants are evaluated explicitly and locally efficient give a local lower bound on the error times an efficiency constant so that they can serve both as indicators for adaptive refinement and for the actual control of the error they are semi robust in the sense that the local efficiency constant only depends on local variations in the coefficients and becomes optimal as the local peclet number gets sufficiently small numerical experiments confirm their accuracy

nonlinear eigenvector algorithms for local optimization in multivariate data analysis abstract many multivariate statistical procedures such as principal component canonical correlation correspondence and discriminant analysis are based on the solution of a certain matrix approximation problem one of the most important being the reduced rank approximation its solution hinges on the singular value or the eigendecomposition of a certain matrix therefore numerical techniques to determine eigenvalues and eigenvectors play an important role in these statistical applications furthermore various modifications generalizations or refinements of the classical methods lead to some sort of nonlinear eigenproblem with no immediate unique solution however the nonlinear eigenvector approach has proved to be quite effective in solving these types of constrained optimization problems in diverse fields of multivariate data analysis since a general analysis of the properties and performance of the nonlinear eigenvector algorithm seems to be long overdue this paper collects the common features in the applications mentioned above and gives an overview from a superior perspective it unifies the treatment by contrasting the nonlinear eigenvector algorithm with the well known inverse iteration iteratively reweighted least squares and majorization algorithms extracts the mathematical tools basically from convex analysis and matrix algebra needed for the convergence proofs and discusses convergence properties

observability and related structural results for linear hereditary systems new results on the theory of observability and deterministic observers for linear time invariant systems with delays are presented the results have been established only for the case of point delays which are commensurable however most of the results can be generalized to the situation with distributed delays and to the ease with non commensurate delays

optimal scaling by alternating length constrained nonnegative least squares with application to distance based analysis an important feature of distance based principal components analysis is that the variables can be optimally transformed for monotone spline transformation a nonnegative least squares problem with a length constraint has to be solved in each iteration as an alternative algorithm to lawson and hanson 1974 we propose the alternating length constrained non negative least squares alc nnls algorithm which minimizes the nonnegative least squares loss function over the parameters under a length constraint by alternatingly minimizing over one parameter while keeping the others fixed several properties of the new algorithm are discussed a monte carlo study is presented which shows that for most cases in distance based principal components analysis alc nnls performs as good as the method of lawson and hanson or sometimes even better in terms of the quality of the solution

a posteriori error estimates for lowest order mixed finite element discretizations of convection diffusion reaction equations we establish residual a posteriori error estimates for lowest order raviart thomas mixed finite element discretizations of convection diffusion reaction equations on simplicial meshes in two or three space dimensions the upwind mixed scheme is considered as well and the emphasis is put on the presence of an inhomogeneous and anisotropic diffusion dispersion tensor and on a possible convection dominance global upper bounds for the approximation error in the energy norm are derived where in particular all constants are evaluated explicitly so that the estimators are fully computable our estimators give local lower bounds for the error as well and they hold from the cases where convection or reaction are not present to convection or reaction dominated problems we prove that their local efficiency depends only on local variations in the coefficients and on the local peclet number moreover the developed general framework allows for asymptotic exactness and full robustness with respect to inhomogeneities and anisotropies the main idea of the proof is a construction of a locally postprocessed approximate solution using the mean value and the flux in each element known in the mixed finite element method and a subsequent use of the abstract framework arising from the primal weak formulation of the continuous problem numerical experiments confirm the guaranteed upper bound and excellent efficiency and robustness of the derived estimators

closed loop properties of the infinite time linear quadratic optimal regulator for systems with delays the infinite time linear quadratic optimal control problem for systems with delays is discussed from the viewpoint of closed loop properties the kalman equation and the circle condition for the optimal closed loop control law are derived and the optimal closed loop poles are characterized via the hamiltonian matrix

structure theory and duality for time varying retarded functional differential equations on etudie les equations differentielles fonctionnelles a retard variant dans le temps dans le cadre de l espace etat c des fonctions continues et de l espace produit r n l p dans l espace c on considere deux concepts d etat l etat donne par la fonction initiale et l etat donne par le terme de forcage la theorie de dualite est basee sur ces 2 concepts on utilise explicitement deux operateurs structuraux f t et g t

circle condition and stability margin of the optimal regulator for systems with delays robustness properties of the optimal regulator for systems with delays in the state are characterized first a nyquist stability criterion is developed and the circle condition of the optimal regulator is derived on the basis of these results the stability margin of the optimal regulator is evaluated as by lehtomaki el al 1981 and it is shown finally that the stability margin is equal to that in the finite dimensional case

a hybrid high order locking free method for linear elasticity on general meshes abstract we devise an arbitrary order locking free method for linear elasticity the method relies on a pure displacement primal formulation and leads to a symmetric positive definite system matrix with compact stencil the degrees of freedom are vector valued polynomials of arbitrary order k 1 on the mesh faces so that in three space dimensions the lowest order scheme only requires 9 degrees of freedom per mesh face the method can be deployed on general polyhedral meshes the key idea is to reconstruct the symmetric gradient and divergence inside each mesh cell in terms of the degrees of freedom by solving inexpensive local problems the discrete problem is assembled cell wise using these operators and a high order stabilization bilinear form locking free error estimates are derived for the energy norm and for the l 2 norm of the displacement with optimal convergence rates of order k 1 and k 2 respectively for smooth solutions on general meshes the theoretical results are confirmed numerically and the cpu cost is evaluated on both standard and polygonal meshes

a posteriori error analysis for locally conservative mixed methods in this work we present a theoretical analysis for a residual type error estimator for locally conservative mixed methods this estimator was first introduced by braess and verfurth for the raviart thomas mixed finite element method working in mesh dependent norms we improve and extend their results to cover any locally conservative mixed method under minimal assumptions in particular avoiding the saturation assumption made by braess and verfurth our analysis also takes into account discontinuous coefficients with possibly large jumps across interelement boundaries the main results are applied to the p1 nonconforming finite element method and the interior penalty discontinuous galerkin method as well as the mixed finite element method

guaranteed a posteriori error estimator for mixed finite element methods of elliptic problems abstract in this work we analyze a posteriori error estimator for a general class of mixed finite element methods of elliptic problems which guarantees an upper bound on the vector error thus extending the recent result obtained for the lowest order triangular raviart thomas mixed finite element method in m ainsworth a posteriori error estimation for lowest order raviart thomas mixed finite elements siam j sci comput 30 2007 08 189 204 the error estimator is constructed through a variant of stenberg s postprocessing procedure and the guaranteed upper bound is readily established by making use of the argument similar to the hypercircle method however the proof of the lower bound given in the above reference does not seem to apply to other kinds of mixed elements so we employ a different technique using the discrete friedrichs inequality to establish the lower bound of the error estimator

a posteriori error estimation for lowest order raviart thomas mixed finite elements for the lowest order raviart thomas mixed finite element we derive an a posteriori error estimator that provides actual guaranteed computable upper bounds on the error in the flux variable regardless of jumps in the material coefficients across interfaces moreover the estimator is efficient in that it provides a local lower bound on the error up to a constant that is independent of the solution and the local mesh size the estimator may be evaluated at virtually no additional cost compared to the evaluation of the finite element approximation itself

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

error indicators for mixed finite elements in 2 dimensional linear elasticity abstract we establish a posteriori error indicators for mixed finite elements in plane elasticity the error estimators refer to residuals of the strong equations and to jumps of the displacements on interelement boundaries for the bdm elements of lowest order the error indicators are computed with displacement fields which are obtained by a postprocessing procedure numerical examples show that adaptive mesh refinements based on these estimators lead to very efficient algorithms

differentiability and convergence rates of approximating semigroups for retarded functional differential equations in this paper the averaging approximations i e semidiscrete finite difference scheme for linear retarded functional differential equations are considered in the context of the semigroups on the hilbert space r n times l 2 it is shown that the approximating semigroups are all differentiable uniformly with respect to the index n determining the mesh size this fact makes it possible to prove the existence of a uniform exponential decay or growth rate for the approximating semigroups which can be made arbitrarily close to the decay respectively growth rate of the original semigroup more importantly the uniform differentiability makes it possible to establish convergence rates that improve with time and to prove the convergence of the approximating semigroups in the uniform operator topology the dependence of the convergence rate on the initial conditions and system parameters is also established

the best euclidian fit to a given distance matrix in prescribed dimensions abstract in this paper we determine the euclidean distance matrix which is closest to a given not necessarily euclidian one we admit a wide class of appropriate matrix norms as measures of closeness majorization results on sums of eigenvalues of symmetric matrices serve as basic tools

towards discrete velte decompositions and narrow bounds for inf sup constants abstract for the velte decomposition of the function space h 1 0 into three orthogonal subspaces the possibility of discrete equivalents is investigated and some first results are derived for conforming finite element methods for the difference approximation on a staggered grid a full description of the discrete velte decomposition is given in the continuous case we consider the connection of the velte decomposition to an orthogonal decomposition of the pressure space and to the inf sup stability condition of the stokes problem some bounds for inf sup constants in the continuous two dimensional case and numerous discrete inf sup constants have been computed

mixed finite element methods for linear elasticity with weakly imposed symmetry in this paper we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approxima tions to both stresses and displacements the methods are based on a modified form of the hellinger reissner variational principle that only weakly imposes the symmetry condition on the stresses although this approach has been previously used by a number of authors a key new ingredient here is a constructive derivation of the elasticity complex starting from the de rham complex by mimicking this construction in the discrete case we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of the de rham complex these elements appear to be simpler than the ones previously derived for example we construct stable discretizations which use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

a posteriori error estimators for mixed finite element methods in linear elasticity three a posteriori error estimators for peers and bdms elements in linear elasticity are presented one residual error estimator and two estimators based on the solution of auxiliary local problems with different boundary conditions all of them are reliable and efficient with respect to the standard norm and furthermore robust for nearly incompressible materials

a family of mixed finite elements for the elasticity problem a new mixed finite element formulation for the equations of linear elasticity is considered in the formulation the variables approximated are the displacement the unsymmetric stress tensor and the rotation the rotation act as a lagrange multiplier introduced in order to enforce the symmetry of the stress tensor based on this formulation a new family of both two and three dimensional mixed methods is defined optimal error estimates which are valid uniformly with respect to the poisson ratio are derived finally a new postprocessing scheme for improving the displacement is introduced and analyzed

a posteriori error estimation for discontinuous galerkin finite element approximation it is shown that the interelement discontinuities in a discontinuous galerkin finite element approximation are subordinate to the error measured in the broken h 1 seminorm one consequence is that the dg norm of the error is equivalent to the broken energy seminorm computable a posteriori error bounds are obtained for the error measured in both the dg norm and the broken energy seminorm and are shown to be efficient in the sense that they also provide lower bounds up to a constant and higher order data oscillation terms the estimators are completely free of unknown constants and provide guaranteed numerical bounds for the error

stabilization of discrete time systems with multiplicative noise and multiple delays in the control variable this paper focuses on the stabilization problem of discrete time systems with multiplicative noise and multiple delays in the control variable first a transformation is constructed to convert the original system into a delay free system with its input matrix containing future noise next the finite horizon linear quadratic regulation problem for the delay free system subject to a constraint on the control is investigated we provide the necessary and sufficient condition for the problem having a unique solution and the optimal feedback control using riccati type difference equations finally we show that the original system can be stabilized in the mean square sense if and only if the set of solutions to the riccati type difference equations is convergent this further yields the fact that the system under consideration can be stabilized if and only if the algebraic riccati type equations have a unique solution such that a specific matrix is positive definite

unified primal formulation based a priori and a posteriori error analysis of mixed finite element methods we derive in this paper a unified framework for a priori and a posteriori error analysis of mixed finite element discretizations of second order elliptic problems it is based on the classical primal weak formulation the postprocessing of the potential proposed in t arbogast and z chen on the implementation of mixed methods as nonconforming methods for second order elliptic problems math comp 64 1995 943 972 and the discrete friedrichs inequality our analysis in particular avoids any explicit use of the uniform discrete inf sup condition and in a straightforward manner and under minimal necessary assumptions known convergence and superconvergence results are recovered the same framework then turns out to lead to optimal a posteriori energy error bounds in particular estimators for all families and orders of mixed finite element methods on grids consisting of simplices or rectangular parallelepipeds are derived they give a guaranteed and fully computable upper bound on the energy error represent error local lower bounds and are robust under some conditions on the diffusion dispersion tensor they are thus suitable for both overall error control and adaptive mesh refinement moreover the developed abstract framework and a posteriori error estimates are quite general and apply to any locally conservative method we finally prove that in parallel and simultaneously in converse to galerkin finite element methods under some circumstances the weak solution is the orthogonal projection of the postprocessed mixed finite element approximation onto the h 1 0 space and also establish several links between mixed finite element approximations and some generalized weak solutions

infinite dimensional linear systems with unbounded control and observation a functional analytic approach abstract the object of these notes is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators on the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem the implications of the theory for large classes of functional and partial differential equations are discussed in detail keywords representation of infinite dimensional systems semigroups boundary control feedback linear quadratic control

mixed finite elements for elasticity there have been many efforts dating back four decades to develop stable mixed finite elements for the stress displacement formulation of the plane elasticity system this requires the development of a compatible pair of finite element spaces one to discretize the space of symmetric tensors in which the stress field is sought and one to discretize the space of vector fields in which the displacement is sought although there are number of well known mixed finite element pairs known for the analogous problem involving vector fields and scalar fields the symmetry of the stress field is a substantial additional difficulty and the elements presented here are the first ones using polynomial shape functions which are known to be stable we present a family of such pairs of finite element spaces one for each polynomial degree beginning with degree two for the stress and degree one for the displacement and show stability and optimal order approximation we also analyze some obstructions to the construction of such finite element spaces which account for the paucity of elements available

an integral equation approach to the singular values of a system with distributed output delays abstract we present a state space approach for the analysis of the hankel singular values of a system with output delays and we derive asymptotic estimates for them

riccati equation solution for controllers with continuous delays abstract we reduce the solution of a riccati equation for infinite time linear quadratic controllers with continuous delays and n state variables to the problem of finding scalar parameter values for an integral kernel whose form is completely specified to simplify the exposition the reduction is described only for a special case involving 2 dimensional state variables but the method is entirely general an abstract formulation of vinter and kwong is used throughout