formulation and analysis of a parameter free stabilized finite element method we present and study a parameter free stabilized finite element method for the scalar advection diffusion equation edge element lifting of diffusive edge fluxes defines the stabilization the amount of edge diffusion varies with the edge peclet number and adapts to solution features without mesh dependent parameters we prove that the method is first order accurate in the advective limit numerical studies confirm the theoretical estimates

selection of important variables and determination of functional form for continuous predictors in multivariable model building in developing regression models data analysts are often faced with many predictor variables that may influence an outcome variable after more than half a century of research the best way of selecting a multivariable model is still unresolved it is generally agreed that subject matter knowledge when available should guide model building however such knowledge is often limited and data dependent model building is required we limit the scope of the modelling exercise to selecting important predictors and choosing interpretable and transportable functions for continuous predictors assuming linear functions stepwise selection and all subset strategies are discussed the key tuning parameters are the nominal p value for testing a variable for inclusion and the penalty for model complexity respectively we argue that stepwise procedures perform better than a literature based assessment would suggest concerning selection of functional form for continuous predictors the principal competitors are fractional polynomial functions and various types of spline techniques we note that a rigorous selection strategy known as multivariable fractional polynomials mfp has been developed no spline based procedure for simultaneously selecting variables and functional forms has found wide acceptance results of fp and spline modelling are compared in two data sets it is shown that spline modelling while extremely flexible can generate fitted curves with uninterpretable wiggles particularly when automatic methods for choosing the smoothness are employed we give general recommendations to practitioners for carrying out variable and function selection while acknowledging that further research is needed we argue why mfp is our preferred approach for multivariable model building with continuous covariates

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

solution of toeplitz normal equations by sine transform based preconditioning abstract the normal equations constructed by a toeplitz matrix are studied in order to find a suitable preconditioner related to the discrete sine transform new results are given about the structure of the product of two toeplitz matrices which allow the cgn method to achieve a superlinear rate of convergence this preconditioner outperforms the circulant one for the iterative solution of toeplitz least squares problems such strategy can also be applied to nonsymmetric linear systems a block generalization is discussed

an overall strategy based on regression models to estimate relative survival and model the effects of prognostic factors in cancer survival studies relative survival provides a measure of the proportion of patients dying from the disease under study without requiring the knowledge of the cause of death we propose an overall strategy based on regression models to estimate the relative survival and model the effects of potential prognostic factors the baseline hazard was modelled until 10 years follow up using parametric continuous functions six models including cubic regression splines were considered and the akaike information criterion was used to select the final model this approach yielded smooth and reliable estimates of mortality hazard and allowed us to deal with sparse data taking into account all the available information splines were also used to model simultaneously non linear effects of continuous covariates and time dependent hazard ratios this led to a graphical representation of the hazard ratio that can be useful for clinical interpretation estimates of these models were obtained by likelihood maximization we showed that these estimates could be also obtained using standard algorithms for poisson regression

solving the inverse eigenvalue problem via the eigenvalue matrix abstract a numerical algorithm for the inverse eigenvalue problem for symmetric matrices is developed based on continually updating the eigenvector matrix using plane rotations a fundamental tool in the algorithm is a matrix formed from the rayleigh quotients of the eigenvectors with respect to each of the basis matrices involved with the basis orthonormalized with respect to the frobenius inner product two criteria of closeness to a solution are defined either of which makes it possible to monitor progress towards a solution the computational questions involved in this approach are examined in detail numerical examples are given for toeplitz and centrosymmetric tridiagonal matrices the new algorithm is much more robust than newton s method

spectral and computational properties of band symmetric toeplitz matrices abstract we are investigating spectral properties of band symmetric toeplitz matrices bst matrices by giving a suitable representation of a bst matrix we achieve separation results and multiplicity conditions for the eigenvalues of a 7 r 5 diagonal bst matrix and also structural properties of the eigenvectors we give eigenvalue bounds for a 2k 1 diagonal bst matrix and also necessary and sufficient conditions for positive definiteness which are easy to check the same conditions apply in the case of block bst matrices either with full blocks or with bst blocks we exhibit fast computational methods for the evaluation of the determinant and the characteristic polynomial of a bst matrix either for sequential or for parallel computations two algorithms based on the bisection technique and newton s method are shown to be very fast for computing the eigenvalues of a 7 or 5 diagonal bst matrix

causal diagrams for empirical research summary the primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject matter information in particular the paper develops a principled nonparametric framework for causal inference in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data if so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions otherwise the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

the inverse eigenvalue problem for real symmetric toeplitz matrices we show that every set of n real numbers is the set of eigenvalues of an n x n real symmetric toeplitz matrix the matrix has a certain additional regularity the argument based on the topological degree is nonconstructive at t bell laboratories murray hill new jersey 07974 e mail address hjlfresearch att com this content downloaded from 157 55 39 29 on tue 12 apr 2016 08 53 54 utc all use subject to http about jstor org terms

boundary lagrange multipliers in finite element methods error analysis in natural norms a finite element procedure for circumventing the babuska brezzi condition in mixed formulations with lagrange multipliers defined on the boundary is presented residual terms constructed from the euler lagrange equations are added to the classical galerkin formulation in order to attain coercivity in a mesh dependent norm convergence is proven for the primal variable and the multiplier in the natural mesh independent norm of the problem generalizing results of a previous paper

convergence analyses of galerkin least squares methods for symmetric advective diffusive forms of the stokes and incompressible navier stokes equations abstract symmetric advective diffusive forms of the stokes and incompressible navier stokes equations are presented the galerkin least squares method for advective diffusive equations is used for both systems and is related to other stabilized methods previously studied the presentation reveals that the convergence analysis for advective diffusive equations as applied before to a linearized form of the compressible navier stokes equations carries over in a straightforward manner to the stokes problem and to a linearized form of the incompressible navier stokes equations

studies of domain based formulations for computing exterior problems of acoustics a strategy must be devised to compute solutions over domains which are unbounded exact impedance conditions at an artificial external boundary are specified by the dtn method yielding an equivalent problem that is suitable for domain based computation the dtn boundary condition is non reflective giving rise to exact and thereby unique solutions the truncated dtn operator which is employed in practice fails to inhibit the reflection of higher modes so that non unique solutions may occur at their harmonics simple expressions determine a sufficient number of terms in the truncated operator for unique solutions at any given wave number there are three characteristic length scales in the computational problem the radius of the artificial boundary the geometry of the body represented by the internal boundary and the mesh size

a new control volume finite element method for the stable and accurate solution of the drift diffusion equations on general unstructured grids abstract we present a new control volume finite element method with multi dimensional scharfetter gummel upwinding cvfem sg for the drift diffusion equations the method combines a conservative formulation of the carrier density continuity equations with an edge element lifting of the one dimensional scharfetter gummel edge currents into curl conforming elemental currents these elemental currents combine the upwind effect from all element edges and enable accurate computation of the flux on arbitrary surfaces inside the elements in so doing we obtain a formulation that is stable and accurate on general unstructured finite element grids this approach sets our formulation apart from other methods which require the control volumes to be topologically dual to the primal grid numerical studies of the cvfem sg for a suite of scalar advection diffusion test problems confirm the accuracy and the robustness of the new formulation simulations of a pn diode and an n channel mosfet device demonstrate the performance of the method for the fully coupled drift diffusion system

comparison between splines and fractional polynomials for multivariable model building with continuous covariates a simulation study with continuous response in observational studies many continuous or categorical covariates may be related to an outcome various spline based procedures or the multivariable fractional polynomial mfp procedure can be used to identify important variables and functional forms for continuous covariates this is the main aim of an explanatory model as opposed to a model only for prediction the type of analysis often guides the complexity of the final model spline based procedures and mfp have tuning parameters for choosing the required complexity to compare model selection approaches we perform a simulation study in the linear regression context based on a data structure intended to reflect realistic biomedical data we vary the sample size variance explained and complexity parameters for model selection we consider 15 variables a sample size of 200 1000 and r 2 0 2 0 8 is the scenario with the smallest largest amount of information for assessing performance we consider prediction error correct and incorrect inclusion of covariates qualitative measures for judging selected functional forms and further novel criteria from limited information a suitable explanatory model cannot be obtained prediction performance from all types of models is similar with a medium amount of information mfp performs better than splines on several criteria mfp better recovers simpler functions whereas splines better recover more complex functions for a large amount of information and no local structure mfp and the spline procedures often select similar explanatory models

a new algebra of toeplitz plus hankel matrices and applications we introduce a new simultaneously diagonalizable real algebra a of symmetrical centrosymmetrical matrices having a toeplitz plus hankel structure we give the corresponding orthonormal basis of eigenvectors which are alternately symmetrical and skewsymmetrical vectors an application is the construction of a symmetrical toeplitz plus centrosymmetrical hankel matrix of equal row sums having a prescribed real spectrum this matrix can be used as the starting matrix for symmetrical centrosymmetrical isospectral flows in particular for the isospectral flow corresponding to the construction of a regular toeplitz matrix having prescribed eigenvalues moreover if a is a noise representation of an unknown matrix in a of rank k then we give a procedure to approximate a by a matrix in a of rank k

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

isospectral flows and the inverse eigenvalue problem for toeplitz matrices abstract the inverse eigenvalue problem for toeplitz matrices itep concerning the reconstruction of a symmetric toeplitz matrix from prescribed spectral data is considered to numerically construct such a matrix the approach introduced by chu in siam rev 40 1 1998 1 39 is followed he proposed to solve the itep by using an isospectral flow whose equilibria are symmetric toeplitz matrices in this paper we study the previous isospectral flow for reversed times and we obtain some formal properties of the solution the case n 3 for itep is analytically investigated by following an approach different from the one in chu siam rev 40 1 1998 1 39 we prove that the flow globally converges to a regular toeplitz matrix starting from a tridiagonal symmetric and centro symmetric matrix numerical experiments confirm the above results and suggest their extension in higher dimension

strengthening analytical thinking for observational studies the stratos initiative the validity and practical utility of observational medical research depends critically on good study design excellent data quality appropriate statistical methods and accurate interpretation of results statistical methodology has seen substantial development in recent times unfortunately many of these methodological developments are ignored in practice consequently design and analysis of observational studies often exhibit serious weaknesses the lack of guidance on vital practical issues discourages many applied researchers from using more sophisticated and possibly more appropriate methods when analyzing observational studies furthermore many analyses are conducted by researchers with a relatively weak statistical background and limited experience in using statistical methodology and software consequently even standard analyses reported in the medical literature are often flawed casting doubt on their results and conclusions an efficient way to help researchers to keep up with recent methodological developments is to develop guidance documents that are spread to the research community at large these observations led to the initiation of the strengthening analytical thinking for observational studies stratos initiative a large collaboration of experts in many different areas of biostatistical research the objective of stratos is to provide accessible and accurate guidance in the design and analysis of observational studies the guidance is intended for applied statisticians and other data analysts with varying levels of statistical education experience and interests in this article we introduce the stratos initiative and its main aims present the need for guidance documents and outline the planned approach and progress so far we encourage other biostatisticians to become involved

numerical solution of isospectral flows in this paper we are concerned with the problem of solving numerically isospectral flows these flows are characterized by the differential equation l b l l l 0 l 0 where l 0 is a d x d symmetric matrix b l is a skew symmetric matrix function of l and b l is the lie bracket operator we show that standard runge kutta schemes fail in recovering the main qualitative feature of these flows that is isospectrality since they cannot recover arbitrary cubic conservation laws this failure motivates us to introduce an alternative approach and establish a framework for generation of isospectral methods of arbitrarily high order

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

multiple imputation for an incomplete covariate that is a ratio we are concerned with multiple imputation of the ratio of two variables which is to be used as a covariate in a regression analysis if the numerator and denominator are not missing simultaneously it seems sensible to make use of the observed variable in the imputation model one such strategy is to impute missing values for the numerator and denominator or the log transformed numerator and denominator and then calculate the ratio of interest we call this passive imputation alternatively missing ratio values might be imputed directly with or without the numerator and or the denominator in the imputation model we call this active imputation in two motivating datasets one involving body mass index as a covariate and the other involving the ratio of total to high density lipoprotein cholesterol we assess the sensitivity of results to the choice of imputation model and as an alternative explore fully bayesian joint models for the outcome and incomplete ratio fully bayesian approaches using winbugs were unusable in both datasets because of computational problems in our first dataset multiple imputation results are similar regardless of the imputation model in the second results are sensitive to the choice of imputation model sensitivity depends strongly on the coefficient of variation of the ratio s denominator a simulation study demonstrates that passive imputation without transformation is risky because it can lead to downward bias when the coefficient of variation of the ratio s denominator is larger than about 0 1 active imputation or passive imputation after log transformation is preferable 2013 the authors statistics in medicine published by john wiley sons ltd

centrosymmetric isospectral flows and some inverse eigenvalue problems this paper is concerned with the solution of some structured inverse eigenvalue problems in the class of centrosymmetric matrices for this aim isospectral flows evolving in the space of centrosymmetric matrices are considered to numerically construct a symmetric toeplitz matrix or a persymmetric hankel matrix from prescribed eigenvalues we establish a link between the two problems and we investigate the use of simultaneously diagonalizable algebra based on sine transform linear algebra appl 52 53 1983 992 to choose the starting centrosymmetric matrices for the isospectral flows some numerical tests show that our approach can tackle both problems when the solvability is guaranteed and it can give good insights when the existence of the solution is not guaranteed

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

bubble functions prompt unusual stabilized finite element methods a second order linear scalar differential equation including a zero th order term is approximated using first the standard galerkin method enriched with bubble functions static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations the method is generalized to allow for a convection operator in the equation this work may be employed as a starting point for simulation of nonlinear equations governing turbulence phenomena flows with chemical reactions and other important problems

analysis of algebraic flux correction schemes a family of algebraic flux correction afc schemes for linear boundary value problems in any space dimension is studied these methods main feature is that they limit the fluxes along each one of the edges of the triangulation and we suppose that the limiters used are symmetric for an abstract problem the existence of a solution existence and uniqueness of the solution of a linearized problem and an a priori error estimate are proved under rather general assumptions on the limiters for a particular but standard in practice choice of the limiters it is shown that a local discrete maximum principle holds the theory developed for the abstract problem is applied to convection diffusion reaction equations where in particular an error estimate is derived numerical studies show its sharpness

isospectral flows preserving some centrosymmetric structures abstract let g be a simple undirected graph no loops no multiple edges on n vertices let s n be the set of real symmetric matrices of order n a matrix a a i j s n is said to be a matrix on g if a i j 0 whenever i j and the vertices i j of g are not joined by an edge of g we recall that if f is a skew symmetric operator on s n then the solution a t of d a d t a f a a 0 a 0 s n maintains the spectrum of a0 the matrix a s n is said to be centrosymmetric if jaj a where j is the matrix with ones on the secondary diagonal and zeros elsewhere centrosymmetric matrices are symmetric about the secondary diagonal centrosymmetric matrices appear in fields such as finite element analysis we construct an isospectral flow on a graph g with the property that if a0 is centrosymmetric so is a t and discuss the limit of a t as t

numerical solution of the inverse eigenvalue problem for real symmetric toeplitz matrices h j landau has recently given a nonconstructive proof of an existence theorem for the inverse eigenvalue problem for real symmetric toeplitz rst matrices this paper presents a procedure for the numerical solution of this problem the procedure is based on an implementation of newton s method that exploits landau s theorem and other special spectral properties of rst matrices with this version of newton s method together with the strategy proposed for applying it the method appears to be globally convergent however this is not proved

generalized survival models for correlated time to event data our aim is to develop a rich and coherent framework for modeling correlated time to event data including 1 survival regression models with different links and 2 flexible modeling for time dependent and nonlinear effects with rich postestimation we extend the class of generalized survival models which expresses a transformed survival in terms of a linear predictor by incorporating a shared frailty or random effects for correlated survival data the proposed approach can include parametric or penalized smooth functions for time time dependent effects nonlinear effects and their interactions the maximum penalized marginal likelihood method is used to estimate the regression coefficients and the variance for the frailty or random effects the optimal smoothing parameters for the penalized marginal likelihood estimation can be automatically selected by a likelihood based cross validation criterion for models with normal random effects gauss hermite quadrature can be used to obtain the cluster level marginal likelihoods the akaike information criterion can be used to compare models and select the link function we have implemented these methods in the r package rstpm2 simulating for both small and larger clusters we find that this approach performs well through 2 applications we demonstrate 1 a comparison of proportional hazards and proportional odds models with random effects for clustered survival data and 2 the estimation of time varying effects on the log time scale age varying effects for a specific treatment and two dimensional splines for time and age

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

methods for dealing with time dependent confounding longitudinal studies where data are repeatedly collected on subjects over a period are common in medical research when estimating the effect of a time varying treatment or exposure on an outcome of interest measured at a later time standard methods fail to give consistent estimators in the presence of time varying confounders if those confounders are themselves affected by the treatment robins and colleagues have proposed several alternative methods that provided certain assumptions hold avoid the problems associated with standard approaches they include the g computation formula inverse probability weighted estimation of marginal structural models and g estimation of structural nested models in this tutorial we give a description of each of these methods exploring the links and differences between them and the reasons for choosing one over the others in different settings

comparison of some finite element methods for solving the diffusion convection reaction equation abstract in this paper we describe several finite element methods for solving the diffusion convection reaction equation none of them is new although the presentation is non standard in an effort to emphasize the similarities and differences between them in particular it is shown that the classical supg method is very similar to an explicit version of the characteristic galerkin method whereas the taylor galerkin method has a stabilization effect similar to a sub grid scale model which is in turn related to the introduction of bubble functions

unitary integrators and applications to continuous orthonormalization techniques in this paper the issue of integrating matrix differential systems whose solutions are unitary matrices is addressed such systems have skew hermitian coefficient matrices in the linear case and a

joint estimation of time dependent and non linear effects of continuous covariates on survival in order to yield more flexible models the cox regression model lambda t x lambda 0 t exp betax has been generalized using different non parametric model estimation techniques one generalization is the relaxation of log linearity in x lambda t x lambda 0 t exp r x another is the relaxation of the proportional hazards assumption lambda t x lambda 0 t exp beta t x these generalizations are typically considered independently of each other we propose the product model lambda t x lambda 0 t exp beta t r x which allows for joint estimation of both effects and investigate its properties the functions describing the time dependent beta t and non linear r x effects are modelled simultaneously using regression splines and estimated by maximum partial likelihood likelihood ratio tests are proposed to compare alternative models simulations indicate that both the recovery of the shapes of the two functions and the size of the tests are reasonably accurate provided they are based on the correct model by contrast type i error rates may be highly inflated and the estimates considerably biased if the model is misspecified applications in cancer epidemiology illustrate how the product model may yield new insights about the role of prognostic factors

a numerical method of structure preserving model updating problem and its perturbation theory a method is presented to update a special finite element fe analytical model based on matrix approximation theory with spectral constraint at first the model updating problem is treated as a matrix approximation problem dependent on the spectrum data from vibration test and modal parameter identification the optimal approximation is the first modified solution of fe model an algorithm is given to preserve the sparsity of the model by multiple correction the convergence of the algorithm is investigated and perturbation of the modified solution is analyzed finally a numerical example is provided to confirm the convergence of the algorithm and perturbation theory

testing for improvement in prediction model performance authors have proposed new methodology in recent years for evaluating the improvement in prediction performance gained by adding a new predictor y to a risk model containing a set of baseline predictors x for a binary outcome d we prove theoretically that null hypotheses concerning no improvement in performance are equivalent to the simple null hypothesis that y is not a risk factor when controlling for x h0 p d 1 x y p d 1 x therefore testing for improvement in prediction performance is redundant if y has already been shown to be a risk factor we also investigate properties of tests through simulation studies focusing on the change in the area under the roc curve auc an unexpected finding is that standard testing procedures that do not adjust for variability in estimated regression coefficients are extremely conservative this may explain why the auc is widely considered insensitive to improvements in prediction performance and suggests that the problem of insensitivity has to do with use of invalid procedures for inference rather than with the measure itself to avoid redundant testing and use of potentially problematic methods for inference we recommend that hypothesis testing for no improvement be limited to evaluation of y as a risk factor for which methods are well developed and widely available analyses of measures of prediction performance should focus on estimation rather than on testing for no improvement in performance copyright 2013 john wiley sons ltd

one step semi explicit methods based on the cayley transform for solving isospectral flows abstract this note deals with the numerical solution of the matrix differential system y b t y y y 0 y0 t 0 where y0 is a real constant symmetric matrix b maps symmetric into skew symmetric matrices and b t y y is the lie bracket commutator of b t y and y i e b t y y b t y y yb t y the unique solution of 1 is isospectral that is the matrix y t preserves the eigenvalues of y0 and is symmetric for all t see 1 5 isospectral methods exploit the flaschka formulation of 1 in which y t is written as y t u t y0ut t for t 0 where u t is the orthogonal solution of the differential system u b t uy0ut u u 0 i t 0 see 5 here a numerical procedure based on the cayley transform is proposed and compared with known isospectral methods

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

sine transform based preconditioners for symmetric toeplitz systems abstract the optimal circulant preconditioner for a given matrix a is defined to be the minimizer of c a f over the set of all circulant matrices c here f is the frobenius norm optimal circulant preconditioners have been proved to be good preconditioners in solving toeplitz systems with the preconditioned conjugate gradient method in this paper we construct an optimal sine transform based preconditioner which is defined to be the minimizer of b a f over the set of matrices b that can be diagonalized by sine transforms we will prove that for general n by n matrices a these optimal preconditioners can be constructed in o n 2 real operations and in o n real operations if a is toeplitz we will also show that the convergence properties of these optimal sine transform preconditioners are the same as that of the optimal circulant ones when they are employed to solve toeplitz systems numerical examples are given to support our convergence analysis

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