a new mixed finite element for the stokes and elasticity problems the stokes problem is approximated by a mixed finite element method using a new finite el ement which has properties analogous to the finite volume methods namely the local conservation of the momentum and the mass estimates of optimal order are derived for the errors in the velocity the pressure and the gradient of the velocity this new finite element also works for the elasticity problem and all estimates are valid uniformly with respect to the compressibility finally some numerical results for the incompressible navier stokes equations are presented

a continuous interior penalty method for viscoelastic flows in this paper we consider a finite element discretization of the oldroyd b model of viscoelastic flows the method uses standard continuous polynomial finite element spaces for velocities pressures and stresses inf sup stability and stability for convection dominated flows are obtained by adding a term penalizing the jump of the solution gradient over element faces to increase robustness when the deborah number is high we add a nonlinear artificial viscosity of shock capturing type the method is analyzed on a linear model problem and optimal a priori error estimates are proven that are independent of the solvent viscosity eta s finally we demonstrate the performance of the method on some known benchmark cases

multilevel time series models with applications to repeated measures data the analysis of repeated measures data can be conducted efficiently using a two level random coefficients model a standard assumption is that the within individual level 1 residuals are uncorrelated in some cases especially where measurements are made close together in time this may not be reasonable and this additional correlation structure should also be modelled a time series model for such data is proposed which consists of a standard multilevel model for repeated measures data augmented by an autocorrelation model for the level 1 residuals first and second order autoregressive models are considered in detail together with a seasonal component both discrete and continuous time are considered and it is shown how the autocorrelation parameters can themselves be structured in terms of further explanatory variables the models are fitted to a data set consisting of repeated height measurements on children

conditions for superconvergence of hdg methods for stokes flow we provide an a priori error analysis of a wide class of finite element methods for the stokes equations the methods are based on the velocity gradient velocity pressure formulation of the equations and include new and old mixed and hybridizable discontinuous galerkin methods we show how to reduce the error analysis to the verification of some properties of an elementwise defined projection and of the local spaces defining the methods we also show that the projection of the errors only depends on the approximation properties of the projection we then provide sufficient conditions for the superconvergence of the projection of the error in the approximate velocity we give many examples of these methods and show how to systematically construct them from similar methods for the diffusion equation

modelling balanced longitudinal data maximum likelihood estimation and analysis of variance for linear models assuming a within experimental units covariance structure that incorporates errors of measurement serial correlation and variation between units results on explicit estimation of regression parameters are used to simplify maximum likelihood estimation of covariance parameters the use of an analysis of variance table as a simpler alternative to likelihood inference is illustrated with two examples

review and complements on mixed hybrid finite element methods for fluid flows mixed and hybrid finite element methods for the resolution of a wide range of linear and nonlinear boundary value problems linear elasticity stokes problem navier stokes equations boussinesq equations etc have known a great development in the last few years these methods allow simultaneous computation of the original variable and its gradient both of them being equally accurate moreover they have local conservation properties conservation of the mass and the momentum as in the finite volume methods the purpose of this paper is to give a review on some mixed finite elements developed recently for the resolution of stokes and navier stokes equations and the linear elasticity problem further developments for a quasi newtonian flow obeying the power law are presented

analysis of non singular solutions of a mixed navier stokes formulation abstract a mixed finite element method is used for the numerical solution of the stationary navier stokes equations in this formulation the pressure the velocity and its gradient are the most relevant unknowns an existence and uniqueness results for the finite element solution together with the convergence results are proved near a non singular solution optimal error estimates and numerical results are presented

inf sup conditions for twofold saddle point problems necessary and sufficient conditions for existence and uniqueness of solutions are developed for twofold saddle point problems which arise in mixed formulations of problems in continuum mechanics this work extends the classical saddle point theory to accommodate nonlinear constitutive relations and the twofold saddle structure application to problems in incompressible fluid mechanics employing symmetric tensor finite elements for the stress approximation is presented

a discontinuous petrov galerkin method with lagrangian multipliers for second order elliptic problems we present a discontinuous petrov galerkin dpg method for the finite element discretization of second order elliptic boundary value problems the novel approach emanates from a one element weak formulation of the differential problem this procedure which is typical of discontinuous galerkin dg methods is based on introducing variables defined in the interior and on the boundary of the element the interface variables are suitable lagrangian multipliers that enforce interelement continuity of the solution and of its normal derivative thus providing the proper connection between neighboring elements the internal variables can be eliminated in favor of the interface variables using static condensation to end up with a system of reduced size in the sole lagrangian multipliers a stability and convergence analysis of the novel formulation is carried out and its connection with mixed hybrid and dg methods is explored numerical tests on several benchmark problems are included to validate the convergence performance and the flux conservation properties of the dpg method

reml estimation asymptotic behavior and related topics the restricted maximum likelihood reml estimates of dispersion parameters variance components in a general non normal mixed model are defined as solutions of the reml equations in this paper we show the reml estimates are consistent if the model is asymptotically identifiable and infinitely informative under the location invariant class and are asymptotically normal a n if in addition the model is asymptotically nondegenerate the result does not require normality or boundedness of the rank p of design matrix of fixed effects moreover we give a necessary and sufficient condition for asymptotic normality of gaussian maximum likelihood estimates mle in non normal cases as an application we show for all unconfounded balanced mixed models of the analysis of variance the reml anova estimates are consistent and are also a n provided the models are nondegenerate the mle are consistent a n if and only if certain constraints on p are satisfied

a new mixed finite element method for the stokes problem we propose a new mixed formulation of the stokes problem where the extra stress tensor is considered based on such a formulation a mixed finite element is constructed and analyzed this new finite element has properties analogous to the finite volume methods namely the local conservation of the momentum and the mass optimal error estimates are derived for the numerical implementation of this finite element a hybrid form is presented this work is a first step towards the treatment of viscoelastic fluid flows by mixed finite element methods

formulation and estimation of dynamic models using panel data abstract this paper presents a statistical analysis of time series regression models for longitudinal data with and without lagged dependent variables under a variety of assumptions about the initial conditions of the processes being analyzed the analysis demonstrates how the asymptotic properties of estimators of longitudinal models are critically dependent on the manner in which samples become large by expanding the number of observations per person holding the number of people fixed or by expanding the number of persons holding the number of observations per person fixed the paper demonstrates which parameters can and cannot be identified from data produced by different sampling plans

finite volume methods for two dimensional incompressible flows with complex boundaries abstract the paper discusses possible ways of developing accurate and efficient finite volume methods for complex incompressible flows the issues of boundary fitted grid generation choice of coupled or uncoupled procedures cartesian or grid aligned velocity components staggered or non staggered variable arrangement discretization methods solution algorithms and convergence acceleration by multigrid methods are addressed an example of a finite volume method for general two dimensional flows is described in some detail and applications of this method to a variety of flows are presented

a note on modelling the covariance structure of repeated measurements geary 1989 biometrics 45 1183 1195 generalized the repeated measurements models used by wilson hebel and sherwin 1981 biometrics 37 553 565 and mansour nordheim and rutledge 1985 biometrics 41 287 294 in this note it is shown analytically that geary s generalization is not suitable because of difficulties in estimating the generalizing parameter this verifies the simulation based results of geary

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

on universally easy classes for np complete problems we explore the natural question of whether all np complete problems have a common restriction under which they are polynomially solvable more precisely we study what languages are universally easy in that their intersection with any np complete problem is in p universally polynomial or at least no longer np complete universally simplifying in particular we give a polynomial time algorithm to determine whether a regular language is universally easy while our approach is language theoretic the results bear directly on finding polynomial time solutions to very broad and useful classes of problems

a dual mixed hybrid formulation for fluid mechanics problems mathematical analysis and application to semiconductor process technology in this paper we propose a dual mixed hybrid formulation capable of treating under a unified framework both compressible and incompressible problems in continuum mechanics a theoretical analysis of the method is carried out and optimal error estimates are derived for both mixed and hybrid variables the potentialities of the novel approach are exploited in the computation of the stress field required in the simulation of the thermal oxidation process in semiconductor technology the numerical formulation is validated both on model problems in continuum mechanics and on a realistic example of the thermal oxidation process in a local oxidation structure

kernel regression estimation using repeated measurements data abstract the estimation of growth curves has been studied extensively in parametric situations here we consider the nonparametric estimation of an average growth curve suppose that there are observations from several experimental units each following the regression model y xi f xj e j 1 n where e1 e n are correlated zero mean errors and 0 x1 xn 1 are fixed constants we study some of the properties of a kernel estimator of f x asymptotic and finite sample results concerning the mean squared error of the estimator are obtained in particular the influence of correlation on the bandwidth minimizing mean squared error is discussed a data based method for selecting the bandwidth is illustrated in a data analysis most previous research on kernel regression estimators has involved uncorrelated errors we investigate how dependence of the errors changes the behavior of a kernel estimator our theorems concerning the asymptotic mean squared error show that the estimator cannot be consistent un

a mixed discontinuous galerkin method with symmetric stress for brinkman problem based on the velocity pseudostress formulation abstract the brinkman equations can be regarded as a combination of the stokes and darcy equations which model transitions between the fast flow in channels governed by stokes equations and the slow flow in porous media governed by darcy s law the numerical challenge for this model is the designing of a numerical scheme which is stable for both the stokes dominated high permeability and the darcy dominated low permeability equations in this paper we solve the brinkman model in n dimensions n 2 3 by using the mixed discontinuous galerkin mdg method which meets this challenge this mdg method is based on the pseudostress velocity formulation and uses a discontinuous piecewise polynomial pair p k 1 s p k k 0 where the stress field is symmetric the main unknowns are the pseudostress and the velocity whereas the pressure is easily recovered through a simple postprocessing a key step in the analysis is to establish the parameter robust inf sup stability through specific parameter dependent norms at both continuous and discrete levels therefore the stability results presented here are uniform with respect to the permeability thanks to the parameter robust stability analysis we obtain optimal error estimates for the stress in broken h div norm and velocity in l 2 norm furthermore the l 2 error estimate for pseudostress is derived under certain conditions finally numerical experiments are provided to support the theoretical results and to show the robustness accuracy and flexibility of the mdg method

prediction and estimation of growth curves with special covariance structures abstract the model considered here is a generalized multivariate analysis of variance model useful especially for many types of growth curve problems including biological growth and technology substitutions it is defined as yp n xp m m rar n p n where is unknown and x and a are known design matrices of ranks m p and r n respectively further the columns of are independent p variate normal with mean vector 0 and common covariance matrix in general p is the number of time or spatial points observed on each of the n cases m 1 is the degree of polynomial and r is the number of groups this article focuses mainly on predicting future observations including partially observed vectors and future values on a given number of cases using their past observations these prediction problems as well as the estimation of parameters are considered for two parsimonious covariance structures that are very important in practice the results are illustrated with three real data sets som

estimation and hypothesis testing for collections of autoregressive time series summary the analysis of a number of independent first order autoregressive time series is considered in a normal theory context a model is studied which allows for nonstationary and nonidentical distribution of the series caused by both fixed effect and random effect components

modelling the covariance structure of repeated measurements models for repeated measurements used by wilson hebel and sherwin 1981 biometrics 37 553565 and mansour nordheim and rutledge 1985 biometrics 41 287 294 are considered these two models are generalized by the a p e k model obtained by introducing an extra parameter k a more general class of models described by kenward unpublished ph d thesis university of reading 1981 is briefly discussed simulation results are presented in which model parameters are estimated by maximum likelihood and likelihood ratios are used as criteria for choosing between models a set of blood pressure data is used to illustrate model fitting

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

estimation of dynamic models with error components abstract observations on n cross section units at t time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit different assumptions about the initial conditions are a initial state fixed b initial state random c the unobserved individual effect independent of the unobserved dynamic process with the initial value fixed and d the unobserved individual effect independent of the unobserved dynamic process with initial value random asymptotic properties of the maximum likelihood and covariance estimators are obtained when t and when n the relationship between the pseudo and conditional maximum likelihood estimators is clarified a simple consistent estimator that is independent of the initial conditions and the way in which t or n is also suggested

a new mixed formulation for elasticity we propose a new mixed variational formulation for the equations of linear elasticity it does not require symmetric tensors and consequently is easy to discretize by adapting mixed finite elements developed for scalar second order elliptic equations

maximum likelihood estimation in a two way analysis of variance with correlated errors in one classification summary a two way analysis of variance model with correlated errors in one classification is discussed it is assumed that the p measurements in each row have a general covariance matrix e the maximum likelihood estimates of the row and column parameters as well as of the covariance matrix are obtained and their asymptotic distribution are discussed finally the likelihood ratio test statistics for the various hypotheses in a two way layout are given

a mixed formulation of boussinesq equations analysis of nonsingular solutions this paper is concerned with the mixed formulation of the boussinesq equations in two dimensional domains and its numerical approximation the paper deals first with existence and uniqueness results as well as the description of the regularity of any solution the problem is then approximated by a mixed finite element method where the gradient of the velocity and the gradient of the temperature quantities of practical importance are introduced as new unknowns an existence result for the finite element solution and convergence results are proved near a nonsingular solution quasi optimal error estimates are finally presented

nested analysis of variance with autocorrelated errors summary in this paper we consider the problem where there is a randomized experimental design with several successive time measurements on each experimental unit one approach to the analysis of such data is to treat time as the subplot treatment and to use a split plot analysis of variance alternatively the problem may be considered in a more general multivariate framework here we recognize the timeinduced correlations and apply an autoregressive time series modelling approach estimation and testing are addressed two examples are presented to illustrate the practicality of our procedure some extensions are also considered briefly frequently data arise from a randomized experimental design where several successive measurements over time are made on each experimental unit there are many examples such as the following i in medical trials observations may be taken on each subject at regular time intervals ii in wildlife radio telemetry studies the distance moved by each animal may be tracked during successive periods of a day iii in plant animal experiments observations may be taken on the same plant animal as it grows and changes over time in all cases there will be a correlation between observations taken on the same experimental unit at different time points it is also likely that there is a decay in the correlation with increasing time lags in other words observations on the same experimental unit which are close together should be more highly correlated than those that are far apart in time this is contrary to the assumption of constant correlation between all time points subplots within a unit whole plot made by the traditional split plot analysis an alternative approach is to consider a general multivariate analysis of variance manova model which assumes an arbitrary covariance matrix for the observations see timm 1980 however we believe that the multivariate model is overparametrized and also it cannot easily incorporate missing values therefore we consider a time series modelling approach to the problem which serves as a compromise we now present the time series model that we consider for analyzing such data we denote the variable under study by the letter y with two subscripts where the first subscript refers to the individual experimental units and the second subscript refers to the successive measurements for the particular individual we assume that n individuals are selected at random and that measurements are taken at ti consecutive time points on the ith individual we consider a linear model r