a priori l 2 error estimates for finite element methods for nonlinear diffusion equations with memory this paper studies finite element approximations to the solutions of the nonlinear diffusion equations with memory an elliptic projection with memory associated with our equations is defined and then used in the derivations of optimal error estimates for semidiscrete and crank nicolson finite element approximations

convergence and nonlinear stability of the lagrange galerkin method for the navier stokes equations the lagrange galerkin method is a numerical technique for solving convection dominated diffusion problems based on combining a special discretisation of the lagrangian material derivative along particle trajectories with a galerkin finite element method we present optimal error estimates for the lagrange galerkin mixed finite element approximation of the navier stokes equations in a velocity pressure formulation the method is shown to be nonlinearly stable

a 3d non newtonian fluid structure interaction model for blood flow in arteries the mathematical modelling and numerical simulation of the human cardiovascular system is playing nowadays an important role in the comprehension of the genesis and development of cardiovascular diseases in this paper we deal with two problems of 3d modelling and simulation in this field which are very often neglected in the literature on the one hand blood flow in arteries is characterized by travelling pressure waves due to the interaction of blood with the vessel wall on the other hand blood exhibits non newtonian properties like shear thinning viscoelasticity and thixotropy the present work is concerned with the coupling of a generalized newtonian fluid accounting for the shear thinning behaviour of blood with an elastic structure describing the vessel wall to capture the pulse wave due to the interaction between blood and the vessel wall we provide an energy estimate for the coupling and compare the numerical results with those obtained with an equivalent fluid structure interaction model using a newtonian fluid

su 3 richardson gaudin models three level systems we present the exact solution of the richardson gaudin models associated with the su 3 lie algebra the derivation is based on a gaudin algebra valid for any simple lie algebra in the rational trigonometric and hyperbolic cases for the rational case additional cubic integrals of motion are obtained whose number is added to that of the quadratic ones to match as required from the integrability condition the number of quantum degrees of freedom of the model we discuss different su 3 physical representations and elucidate the meaning of the parameters entering in the formalism by considering a bosonic mapping limit of one of the su 3 copies we derive new integrable models for three level systems interacting with two bosons these models include a generalized tavis cummings model for three level atoms interacting with two modes of the quantized electric field

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

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

bootstrap inference for instrumental variable models with many weak instruments this study s main contribution is to theoretically analyze the application of bootstrap methods to instrumental variable models when the available instruments may be weak and the number of instruments goes to infinity with the sample size we demonstrate that a standard residual based bootstrap procedure cannot consistently estimate the distribution of the limited information maximum likelihood estimator or fuller 1977 estimator under many many weak instrument sequence the primary reason is that the standard procedure fails to capture the instrument strength in the sample adequately in addition we consider the restricted efficient re bootstrap of davidson and mackinnon 2008 2010 2014 that generates bootstrap data under the null restricted and uses an efficient estimator of the coefficient of the reduced form equation efficient we find that the re bootstrap is also invalid however it effectively mimics more key features in the limiting distributions of interest and thus is less distorted in finite samples than the standard bootstrap procedure finally we propose modified bootstrap procedures that provide a valid distributional approximation for the two estimators with many many weak instruments a monte carlo experiment shows that hypothesis testing based on the asymptotic normal approximation can have severe size distortions in finite samples instead our modified bootstrap procedures greatly reduce these distortions

on a higher order accurate fully discrete galerkin approximation to the navier stokes equations we consider approximating the solution of the initial and boundary value problem for the navier stokes equations in bounded twoand three dimensional domains using a nonstandard galerkin finite element method for the space discretization and the third order accurate three step backward differentiation method coupled with extrapolation for the nonlinear terms for the time stepping the resulting scheme requires the solution of one linear system per time step plus the solution of five linear systems for the computation of the required initial conditions all these linear systems have the same matrix the resulting approximations of the velocity are shown to have optimal rate of convergence in l2 under suitable restrictions on the discretization parameters of the problem and the size of the solution in an appropriate function space

numerical simulations of shear dependent viscoelastic flows with a combined finite element finite volume method a hybrid combined finite element finite volume method has been developed for the numerical simulation of shear dependent viscoelastic flow problems governed by a generalized oldroyd b model with a non constant viscosity function the method is applied to the 4 1 planar contraction benchmark problem to investigate the influence of the viscosity effects on the flow and results are compared with those found in the literature for creeping oldroyd b flows for a range of weissenberg numbers the method is also applied to flow in a smooth stenosed channel it is shown that the qualitative behavior of the flow is influenced by the rheological properties of the fluid namely its viscoelastic and inertial effects as well as the shear thinning viscosity these results appear in the framework of a preliminary study of the numerical simulation of steady and pulsatile blood flows in two dimensional stenotic vessels using this hybrid finite element finite volume method

convergence analysis of a projection semi implicit coupling scheme for fluid structure interaction problems in this paper we provide a convergence analysis of a projection semi implicit scheme for the simulation of fluid structure systems involving an incompressible viscous fluid the error analysis is performed on a fully discretized linear coupled problem a finite element approximation and a semi implicit time stepping strategy are respectively used for space and time discretization the fluid is described by the stokes equations the structure by the classical linear elastodynamics equations linearized elasticity plate or shell models and all changes of geometry are neglected we derive an error estimate in finite time and we prove that the time discretization error for the coupling scheme is at least sqrt delta t finally some numerical experiments that confirm the theoretical analysis are presented

minimum distance approach to inference with many instruments abstract i analyze a linear instrumental variables model with a single endogenous regressor and many instruments i use invariance arguments to construct a new minimum distance objective function with respect to a particular weight matrix the minimum distance estimator is equivalent to the random effects estimator of chamberlain and imbens 2004 and the estimator of the coefficient on the endogenous regressor coincides with the limited information maximum likelihood estimator this weight matrix is inefficient unless the errors are normal and i construct a new more efficient estimator based on the optimal weight matrix finally i show that when the minimum distance objective function does not impose a proportionality restriction on the reduced form coefficients the resulting estimator corresponds to a version of the bias corrected two stage least squares estimator i use the objective function to construct confidence intervals that remain valid when the proportionality restriction is violated

poisson hopf limit of quantum algebras the poisson hopf analogue of an arbitrary quantum algebra uz g is constructed by introducing a one parameter family of quantizations uz g depending explicitly on and by taking the appropriate 0 limit the q poisson analogues of the su 2 algebra are discussed and the novel case is introduced the q serre relations are also extended to the poisson limit this approach opens the perspective for possible applications of higher rank q deformed hopf algebras in semiclassical contexts

regular article direct simulations of 2d fluid particle flows in biperiodic domains we propose a method to simulate the motion of 2d rigid particles in a viscous incompressible fluid within the arbitrary lagrangian eulerian framework momentum equations for both the fluid and the particles are discretized and a coupled variational formulation is established by introducing an appropriate finite element approximation a symmetric linear system is obtained this system is solved by an inexact uzawa algorithm the main interest of such simulations lies in the average behaviour of a high number of particles we therefore introduced a biperiodic formulation of the problem which makes it possible to represent many body mixtures at a reasonable computational cost in order to model realistic situations an extra term must be added to the pressure this extra term is shown to be the lagrange multiplier associated with the vertical volume conservation constraint we developed an appropriate unstructured mesh generator so that the biperiodicity of the fields can be treated in a strong sense the question of particle contact is addressed and a simple technique to overcome numerical problems is proposed the influence of periodic lengths is investigated through different simulations the same case is simulated for different sizes of the window and the behaviour of some space averaged quantities is studied

multi level spectral galerkin method for the navier stokes problem i spatial discretization a multi level spectral galerkin method for the two dimensional non stationary navier stokes equations is presented the method proposed here is a multiscale method in which the fully nonlinear navier stokes equations are solved only on a low dimensional space subsequent approximations are generated on a succession of higher dimensional spaces j 2 j by solving a linearized navier stokes problem around the solution on the previous level error estimates depending on the kinematic viscosity 0 1 are also presented for the j level spectral galerkin method the optimal accuracy is achieved when we demonstrate theoretically that the j level spectral galerkin method is much more efficient than the standard one level spectral galerkin method on the highest dimensional space

on the transport diffusion algorithm and its applications to the navier stokes equations this paper deals with an algorithm for the solution of diffusion and or convection equations where we mixed the method of characteristics and the finite element method globally it looks like one does one step of transport plus one step of diffusion or projection but the mathematics show that it is also an implicit time discretization of thepde in lagrangian form we give an error bound h t h h t in the interesting case that holds also for the navier stokes equations even when the reynolds number is infinite euler equation

alternative approximations to the distributions of instrumental variable estimators the paper considers the ols the iv and two method of moments estimators mm and mmk of the coefficients of a single equation where the explanatory variables are correlated with the disturbance term the mm and mmk estimators are generalizations of the liml and limlk estimators respectively multivariate first order approximations to the distributions are derived under normality using a parameter sequence where the number of instruments increases as the number of observations increases numerical results show these approximations are more accurate compared to large sample approximations even if the number of instruments is small the moments of the multivariate limit distributions of the mm and mmk estimators can be consistently estimated under a variety of parameter sequences including the large sample sequence the new approximate confidence regions perform well in terms of exact levels compared to traditional ones the iv estimator of the coefficient of a single explanatory endogenous variable is interpreted as a shrinkage estimator which is dominated in practical cases by the mm and mmk estimators in terms of nearness to the true value in the sense of pitman

on the shear thinning and viscoelastic effects of blood flow under various flow rates the aim of this paper is to describe and discuss the results of numerical comparative study performed in order to demonstrate and quantify some of the most relevant non newtonian characteristics of blood flow in medium sized blood vessels namely its shear thinning and viscoelastic behavior the models studied in this work are the classical newtonian and oldroyd b models as well as their generalized shear thinning modifications numerical tests are performed on three dimensional geometries namely an idealized axisymmetric stenosis and a realistic stenosed carotid bifurcation reconstructed from medical images the numerical solution of the system of governing equations is obtained by a finite volume method on a structured grid model sensitivity tests are achieved with respect to the characteristic flow rate to evaluate its impact on the observed non newtonian effects

finite element error estimation for quasi newtonian fluid structure interaction problems we consider a monolithic scheme for fluid structure interaction problems involving an incompressible quasi newtonian fluid the monolithic formulation is obtained using the arbitrary lagrangian eulerian ale method with matching conditions at the fluid structure interface the stability and error analysis are performed for the finite element approximation finally some numerical experiments that confirm the theoretical analysis are presented

optimal error estimates of the legendre petrov galerkin method for the korteweg de vries equation in this paper the legendre petrov galerkin method for the korteweg de vries equation with nonperiodic boundary conditions is analyzed the nonlinear term is computed with the legendre spectral method and some pseudospectral methods respectively optimal error estimates in l2 norm are obtained for both semidiscrete and fully discrete schemes the method is also applicable to some 2m 1 th order differential equations

testing overidentifying restrictions with many instruments and heteroskedasticity this paper gives a test of overidentifying restrictions that is robust to many instruments and heteroskedasticity it is based on a jackknife version of the overidentifying test statistic correct asymptotic critical values are derived for this statistic when the number of instruments grows large at a rate up to the sample size it is also shown that the test is valid when the number of instruments is fixed and there is homoskedasticity this test improves on recently proposed tests by allowing for heteroskedasticity and by avoiding assumptions on the instrument projection matrix this paper finds in monte carlo studies that the test is more accurate and less sensitive to the number of instruments than the hausman sargan or gmm tests of overidentifying restrictions

classical yang baxter equations and quantum integrable systems quantum integrable models associated with nondegenerate solutions of classical yang baxter equations related to the simple lie algebras are investigated these models are diagonalized for rational and trigonometric solutions in the cases of sl n gl n o n and sp n algebras the analogy with the quantum inverse scattering method is demonstrated

numerical analysis of a modified finite element nonlinear galerkin method a fully discrete modified finite element nonlinear galerkin method is presented for the two dimensional equation of navier stokes type the spatial discretization is based on two finite element spaces xh and xh defined on a coarse grid with grid size h and a fine grid with grid size h h respectively the time discretization is based on the euler explicit scheme with respect to the nonlinear term we analyze the stability and convergence rate of the method comparing with the standard finite element galerkin method and the nonlinear galerkin method this method can admit a larger time step under the same convergence rate of same order hence this method can save a large amount of computational time finally we provide some numerical tests on this method the standard finite element galerkin method and the nonlinear galerkin method which are in a good agreement with the theoretical analysis

the long time behavior of finite element approximations of solutions of semilinear parabolic problems error estimates for finite element approximations of the solutions to semilinear parabolic problems are proved under the hypothesis that the exact solution is asymptotically stable as t to infty error estimates of optimal order that hold uniformly on the unbounded time interval 0 leqq t infty are obtained both semidiscrete and completely discrete approximations are considered

an effective fluid structure interaction formulation for vascular dynamics by generalized robin conditions in this work we focus on the modeling and numerical simulation of the fluid structure interaction mechanism in vascular dynamics we first propose a simple membrane model to describe the deformation of the arterial wall which is derived from the koiter shell equations and is applicable to an arbitrary geometry secondly we consider a reformulation of the fluid structure problem in which the newly derived membrane model thanks to its simplicity is embedded into the fluid equations and will appear as a generalized robin boundary condition the original problem is then reduced to the solution of subsequent fluid equations defined on a moving domain and may be achieved with a fluid solver only we also derive a stability estimate for the resulting numerical scheme finally we propose new outflow absorbing boundary conditions which are easy to implement and allow us to reduce significantly the spurious pressure wave reflections that typically appear in artificially truncated computational domains we present several numerical results showing the effectiveness of the proposed approaches

a modified lagrange galerkin method for a fluid rigid system with discontinuous density in this paper we propose a new characteristics method for the discretization of the two dimensional fluid rigid body problem in the case where the densities of the fluid and the solid are different the method is based on a global weak formulation involving only terms defined on the whole fluid rigid domain to take into account the material derivative we construct a special characteristic function which maps the approximate rigid body at the k 1 th discrete time level into the approximate rigid body at k th time convergence results are proved for both semi discrete and fully discrete schemes

the euler implicit explicit scheme for the 2d time dependent navier stokes equations with smooth or non smooth initial data this paper considers the stability and convergence results for the euler implicit explicit scheme applied to the spatially discretized two dimensional 2d time dependent navier stokes equations a galerkin finite element spatial discretization is assumed and the temporal treatment is implicit explict scheme which is implicit for the linear terms and explicit for the nonlinear term here the stability condition depends on the smoothness of the initial data u 0 h i e the time step condition is c 0 in the case of a 2 log h c 0 in the case of a 1 and th 2 c 0 in the case of a 0 for mesh size h and some positive constant c 0 we provide the h 2 stability of the scheme under the stability condition with a 0 1 2 and obtain the optimal h 1 l 2 error estimate of the numerical velocity and the optimal l 2 error estimate of the numerical pressure under the stability condition with a 1 2

convergence of a finite element ale method for the stokes equations in a domain depending on time we consider the approximation of the unsteady stokes equations in a time dependent domain when the motion of the domain is given more precisely we apply the finite element method to an arbitrary lagrangian eulerian ale formulation of the system our main results state the convergence of the solutions of the semi discretized with respect to the space variable and of the fully discrete problems towards the solutions of the stokes system

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

arbitrary lagrangian eulerian method for navier stokes equations with moving boundaries this article deals with the numerical approximation of navier stokes equations in a domain with moving boundaries using the arbitrary lagrangian eulerian ale method we transform the problem from a moving domain to a fixed reference domain through an artificial domain velocity then we apply the characteristic method to solve the navier stokes equation in the fixed domain suitable boundary conditions are used for the interfaces three examples are provided to show the efficiency of the present method

convergence of the lagrange galerkin method for the equations modelling the motion of a fluid rigid system in this paper we consider a lagrange galerkin scheme to approximate a two dimensional fluid rigid body problem the equations of the system are the navier stokes equations in the fluid part coupled with ordinary differential equations for the dynamics of the rigid body in this problem the equations of the fluid are written in a domain whose variation is one of the unknowns we introduce a numerical method based on the use of characteristics and on finite elements with a fixed mesh our main result asserts the convergence of this scheme

nonlinear galerkin methods and mixed finite elements two grid algorithms for the navier stokes equations a nonlinear galerkin method using mixed finite elements is presented for the two dimensional incompressible navier stokes equations the scheme is based on two finite element spaces x h and x h for the approximation of the velocity defined respectively on one coarse grid with grid size h and one fine grid with grid size h ll h and one finite element space m h for the approximation of the pressure nonlinearity and time dependence are both treated on the coarse space we prove that the difference between the new nonlinear galerkin method and the standard galerkin solution is of the order of h 2 both in velocity h 1 omega and pressure l 2 omega norm we also discuss a penalized version of our algorithm which enjoys similar properties

the gauge uzawa finite element method part i the navier stokes equations the gauge uzawa fem is a new first order fully discrete projection method which combines advantages of both the gauge and uzawa methods within a variational framework a time step consists of a sequence of d 1 poisson problems d being the space dimension thereby avoiding both the incompressibility constraint as well as dealing with boundary tangential derivatives as in the gauge method this allows for a simple finite element discretization in space of any order in both two and three dimensions this first part introduces the method for the navier stokes equations of incompressible fluids and shows unconditional stability and error estimates for both velocity and pressure via a variational approach under realistic regularity assumptions several numerical experiments document performance of the gauge uzawa fem and compare it with other projection methods

jackknife instrumental variable estimation with heteroskedasticity we present a new jackknife estimator for instrumental variable inference with unknown heteroskedasticity it weighs observations such that many instruments consistency is guaranteed while the signal component in the data is maintained we show that this results in a smaller signal component in the many instruments asymptotic variance when compared to estimators that neglect a part of the signal to achieve consistency both many strong instruments and many weak instruments asymptotic distributions are derived using high level assumptions that allow for instruments with identifying power that varies between explanatory variables standard errors are formulated compactly we review briefly known estimators and show in particular that our symmetric jackknife estimator performs well when compared to the hlim and hful estimators of hausman et al in monte carlo experiments

galerkin methods for nonlinear parabolic integrodifferential equations with nonlinear boundary conditions galerkin methods are analyzed for the nonlinear parabolic integrodiflerential equation u t nabla cdot left a u nabla u int 0 t b t u x s nabla u x s ds right f u in omega times 0 t t 0 omega subset r d d leqq 3 subject to the nonlinear boundary condition a u frac partial u partial v int 0 t b t u x s frac partial u partial v x s ds g u on s t partial omega times 0 t and the usual initial condition optimal order error estimates are derived in l 2 omega norm for the continuous crank nicolson and modified crank nicolson galerkin approximations as usual the latter will yield a system of linear algebraic equations to be solved at each level

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

a level set formulation of eulerian interface capturing methods for incompressible fluid flows a level set formulation is derived for incompressible immiscible navier stokes equations separated by a free surface the interface is identified as the zero level set of a smooth function eulerian finite difference methods based on this level set formulation are proposed these methods are robust and efficient and are capable of computing interface singularities such as merging and reconnection numerical experiments are presented to demonstrate the effectiveness of the methods

a fictitious domain method for external incompressible viscous flow modeled by navier stokes equations abstract in this article we discuss a fictitious domain method for the numerical solutions of three dimensional elliptic problems with dirichlet boundary conditions and also of the navier stokes equations modeling incompressible viscous flow the methodology for the navier stokes equations described here takes a systematic advantage of time discretization by operator splitting in order to treat separately advection imbedding and incompressibility due to the decoupling fast elliptic solvers can be used to treat the incompressibility condition even if the original problem is taking place on a nonregular geometry the resulting methodology is applied to two dimensional unsteady external incompressible viscous flow problems and three dimensional stokes problems

optimal error estimate of the penalty finite element method for the time dependent navier stokes equations a fully discrete penalty finite element method is presented for the two dimensional time dependent navier stokes equations the time discretization of the penalty navier stokes equations is based on the backward euler scheme the spatial discretization of the time discretized penalty navier stokes equations is based on a finite element space pair x h m h which satisfies some approximate assumption an optimal error estimate of the numerical velocity and pressure is provided for the fully discrete penalty finite element method when the parameters e at and h are sufficiently small

fully discrete error estimation for a quasi newtonian fluid structure interaction problem we consider an incompressible quasi newtonian fluid structure interaction fsi problem formulated in a monolithic framework where the matching conditions at the moving interface are satisfied the fully discretized fsi system is discussed with detailed analysis for the stability and error estimate as well as numerical experiments that confirm the theoretical results

convergence analysis of a finite element projection lagrange galerkin method for the incompressible navier stokes equations this paper provides a convergence analysis of a fractional step method to compute incompressible viscous flows by means of finite element approximations in the proposed algorithm the convection the diffusion and the incompressibility are treated in three different substeps the convection is treated first by means of a lagrange galerkin technique whereas the diffusion and the incompressibility are treated separately in two subsequent substeps by means of a projection method it is shown that provided the time step delta t is of cal o h d 4 where h is the meshsize and d is the space dimension 2 leq d leq 3 the proposed method yields for finite time t an error of cal o h l 1 delta t in the l2 norm for the velocity and an error of cal o h l delta t in the h1 norm or the l2 norm for the pressure where l is the polynomial degree of the approximate velocity

stability and geometric conservation laws for ale formulations the aim of this paper is to investigate a model ale scheme with respect to various possible choices of time discretizations for each time scheme we investigate the relationships between stability and the so called geometric conservation laws gcl we shall see that gcl condition proves neither necessary nor sufficient for stability in doing so we review some known theoretical results and we prove some new stability results for space time ale discretizations some new error estimates are also presented several numerical experiments confirm the theory

generalized n level jaynes cummings and dicke models classical rational r matrices and algebraic bethe ansatz we construct integrable n level generalizations of jaynes cummings and dicke models corresponding to the simple reductive lie algebras of rank n we show that for each such lie algebra there exist many integrable jaynes cummings and dicke type models each of which is associated with the reductive subalgebras containing cartan subalgebra and is obtained via reduction from jaynes cummings or dicke type models with a maximal number of bosons we diagonalize the constructed jaynes cummings and dicke type hamiltonians in the physically most interesting case of using a nested algebraic bethe ansatz

convergence and stability of finite element nonlinear galerkin method for the navier stokes equations in this article we present a new fully discrete finite element nonlinear galerkin method which are well suited to the long time integration of the navier stokes equations spatial discretization is based on two grid finite element technique time discretization is based on euler explicit scheme with variable time step size moreover we analyse the boundedness convergence and stability condition of the finite element nonlinear galerkin method our discussion shows that the time step constraints of the method depend only on the coarse grid parameter h and the time step constraints of the finite element galerkin method depend on the fine grid parameter h h under the same convergence accuracy

unconditional stability and long term behavior of transient algorithms for the incompressible navier stokes and euler equations abstract this paper examines the long term behavior dissipativity and unconditional nonlinear stability properties of time integration algorithms for the incompressible navier stokes equations including both direct schemes and fractional step projection methods the algorithms are termed nonlinear unconditionally stable if in the absence of a forcing term but for arbitrary initial conditions the computed kinetic energy decreases for arbitrary step sizes i e l 2 stability such an a priori stability estimate is a characteristic feature of the navier stokes system similarly the algorithms are said to exhibit asymptotic t independent long term dissipative behavior if as the continuum flow generated by the navier stokes equations the algorithmic flow also exhibits an absorbing set and a maximal attractor both direct and fractional step methods are described which inherit these fundamental properties of the navier stokes system for any time step size moreover a subclass of algorithms which retain these strong notions of nonlinear stability and long term dissipative behavior is identified which in addition has the remarkable property of being linear within the time step the key implication is that no iterations are required to compute the solution within a time step a specific member of this class is shown to possess the same absorbing set as the continuum navier stokes system a second order accurate unconditionally stable method is also identified which retains the property of linearity within a time step numerical analysis and computational aspects involved in the implementation of these methods are addressed in detail and illustrated in representative numerical simulations

consistent estimation with a large number of weak instruments this paper analyzes the conditions under which consistent estimation can be achieved in instrumental variables iv regression when the available instruments are weak and the number of instruments k n goes to infinity with the sample size we show that consistent estimation depends importantly on the strength of the instruments as measured by r the rate of growth of the so called concentration parameter and also on k n in particular when k n the concentration parameter can grow even if each individual instrument is only weakly correlated with the endogenous explanatory variables and consistency of certain estimators can be established under weaker conditions than have previously been assumed in the literature hence the use of many weak instruments may actually improve the performance of certain point estimators more specifically we find that the limited information maximum likelihood liml estimator and the bias corrected two stage least squares b2sls estimator are consistent when k n r n 0 while the two stage least squares 2sls estimator is consistent only if k n r n 0 as n these consistency results suggest that liml and b2sls are more robust to instrument weakness than 2sls

a space time galerkin least squares finite element formulation of the navier stokes equations for moving domain problems a space time galerkin least squares finite element formulation of the navier stokes equations is presented for the analysis of free surface flows moving spatial configurations and deforming fluid structure interfaces the variational equation is based on the time discontinuous galerkin method employing the physical entropy variables the space time elements are oriented in time to accommodate the spatial deformations if the elements are oriented along the particle paths the formulation is lagrangian and if they are fixed in time it is eulerian consequently this formulation is analogous to the arbitrary lagrangian eulerian ale technique a novel mesh rezoning strategy is presented to orient the elements in time and adapt the fluid mesh to the changing spatial configuration numerical results are presented to show the performance of the method