an economical finite element approximation of generalized newtonian flows abstract we consider an economical bilinear rectangular mixed finite element scheme on regular mesh for generalized newtonian flows where the viscosity obeys a carreau type law for a pseudo plastic the key issue in the scheme is that the two components of the velocity and the pressure are defined on different meshes optimal error bounds for both the velocity and pressure are obtained by proving a discrete babuska brezzi inf sup condition on the regular quadrangulation finally we perform some numerical experiments including an example in a unit square with exact solutions a backward facing step and a four to one abrupt contraction generalized newtonian flows numerical experiments confirm our error bounds

a new mixed finite element formulation and the mac method for the stokes equations a new mixed finite element method is formulated for the stokes equations in which the two components of the velocity and the pressure are defined on different meshes first order error estimates are obtained for both the velocity and the pressure also the well known mac method is derived from the resulting finite element method

analysis of some mixed finite element methods related to reduced integration we prove error estimates for the following two mixed finite element methods related to reduced integration a method for stokes problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress the main idea of the proof in the case of stokes problem is to combine a weak babuska brezzi type stability estimate for the pressure with a superapproximability property for the velocities a similar technique is used in the case of the plate problem

on the stability of bilinear constant velocity pressure finite elements an analysis of the babuska stability of bilinear constant finite element pairs for viscous flow calculations is given an unstable mode not of the checkerboard type is given for which the stability constant turns out to beo h thus the indicated spaces are not stable in general for numerical calculation

on polynomial matrix spectral factorization by symmetric extraction we revise the 1963 davis algorithm 2 for the spectral factorization of a para hermitian nonnegative polynomial matrix phi by symmetric factor extraction this algorithm is careless about zeros at infinity by introducing the notion of diagonal reducedness of phi we obtain an easy sufficient test for the absence of zeros at infinity we show then how to get phi diagonally reduced by diagonal excess reduction steps similar to the oono and yasuura steps removing all zeros at infinity and then how to remove synunetrically finite zeros while keeping el diagonally reduced hence free of zeros at infinity this results in a revised symmetric extraction spectral factorization algorithm with monotone degree control an example shows the didactical conceptual simplicity of the method appropriate symmetric extraction is discovered by revising and discovering important particular one sided factor extraction properties of polynomial matrices

inner outer factorization for strictly proper transfer matrices considers inner outer factorization for strictly proper transfer matrices we provide characterizations to the solution of this particular factorization problem and develop a computational algorithm to solve it a numerical example is used to illustrate the proposed theory and algorithm

the iterative penalty method for stokes equations using q1 p0 element abstract the iterative penalty method for stokes equations is an effective algorithm in this paper we discuss the bilinear constant velocity pressure element for the stokes equations and present the error estimates for the iterative penalty method using this element the key technique we use is the local checkerboard pattern numerical experiments are given which are consistent with our analysis

finite element methods principles for their selection abstract principles for the selection of a finite element method for a particular problem are discussed these principles are stated in terms of the notion of approximability optimality and stability several examples are discussed in detail as illustrations conclusions regarding the selection of finite element methods are summarized in the final section of the paper

on conforming mixed finite element methods for incompressible viscous flow problems abstract the asymptotic rates of convergence for approximate solutions of linearizations of the stationary navier stokes equations are computationally determined for some specific choices of conforming finite element spaces these rates are computed for norms of physical interest and are compared to available theoretical estimates it is shown that equivalent rates of convergence are achieved by algorithms which differ greatly in their computer storage and time requirements the solution of the discrete system of equations resulting from the finite element discretization is also discussed

on inner outer factorization abstract the calculation of an inner outer factorization of a proper rational matrix by state space methods is considered particular attention is given to the extraction of the inner factor so that a minimal realization is obtained for this factor

inner outer factorization for strictly proper functions with j w axis zeros abstract this paper discussed the inner outer factorization for square real rational matrices which may have zeros on the j axis including infinity a factorization method is given in terms of the descriptor form representation of the rational matrix this method uses the solution of a generalized riccati equation we also propose an efficient computation algorithm for solving the generalized riccati equation

optimal average sample number of the sprt chart for monitoring fraction nonconforming abstract the sequential probability ratio test sprt control chart is a powerful tool for monitoring manufacturing processes it is highly suitable for the applications where testing is destructive or very expensive such as the automobile airbags test this article studies the effect of the average sample number asn i e the average sample size on the chart s performance a design algorithm is proposed to develop the optimal sprt chart for monitoring the fraction nonconforming p of bernoulli processes by optimizing the asn and other charting parameters the average detection speed of the sprt chart is almost doubled it is also found that the optimal sprt chart significantly outperforms the optimal np and binomial cusum charts in terms of average number of defectives and under different combinations of the design specifications it is observed that the sprt chart using a relatively smaller asn and a shorter sampling interval h has a higher overall detection effectiveness

finite element methods of least squares type we consider the application of least squares variational principles to the numerical solution of partial differential equations our main focus is on the development of least squares finite element methods for elliptic boundary value problems arising in fields such as fluid flows linear elasticity and convection diffusion for many of these problems least squares principles offer numerous theoretical and computational advantages in the algorithmic design and implementation of corresponding finite element methods that are not present in standard galerkin discretizations most notably the use of least squares principles leads to symmetric and positive definite algebraic problems and allows us to circumvent stability conditions such as the inf sup condition arising in mixed methods for the stokes and navier stokes equations as a result application of least squares principles has led to the development of robust and efficient finite element methods for a large class of problems of practical importance

analysis of semi staggered finite difference method with application to bingham flows abstract in this paper a finite difference scheme for incompressible flow problems is treated the scheme uses non staggered grid for velocity approximation a special stabilization is introduced to ensure the well posedness and optimal approximation properties of the scheme the stability estimate is proved in the form of a mesh independent bound for the norm of discrete operator inverse the finite difference method is particularly suitable for problems in which velocity vector is involved in additional quantities that enter the system of flow equations as for example in the bingham problem we describe this application in the paper in some detail results of numerical experiments are included that confirm the applicability and optimality of the method

factor screening for simulation with multiple responses sequential bifurcation the goal of factor screening is to find the really important inputs factors among the many inputs that may be changed in a realistic simulation experiment a specific method is sequential bifurcation sb which is a sequential method that changes groups of inputs simultaneously sb is most efficient and effective if the following assumptions are satisfied i second order polynomials are adequate approximations of the input output functions implied by the simulation model ii the signs of all first order effects are known and iii if two inputs have no important first order effects then they have no important second order effects either heredity property this paper examines sb for random simulation with multiple responses outputs called multi response sb msb this msb selects groups of inputs such that within a group all inputs have the same sign for a specific type of output so no cancellation of first order effects occurs to obtain enough replicates replications for correctly classifying a group effect or an individual effect as being important or unimportant msb applies wald s sequential probability ratio test sprt the initial number of replicates in this sprt is also selected efficiently by msb moreover msb includes a procedure to validate the three assumptions of msb the paper evaluates the performance of msb through extensive monte carlo experiments that satisfy all msb assumptions and through a case study representing a logistic system in china the results are very promising

on the performance of semi blind subspace based channel estimation this paper is devoted to the analysis of a semi blind estimation framework in which the standard least squares estimator based on a known training sequence is enhanced by using the statistical structure of the observations more specifically we consider the case of a general time division multiple access tdma frame based receiver equipped with multiple sensors and restrict our attention to second order based subspace methods that are suitable for most standard communication applications due to their moderate computational cost the semi blind channel estimator is obtained as a regularized least squares solution where a blind subspace criterion plays the role of the regularization constraint the main contribution of the paper consists of showing by asymptotic analysis how to optimally tune the balance between the blind criterion and the least squares fit depending on the design parameters of the system simulations show that the proposed solutions are robust and significantly improve the efficiency of the equalization

synthesis of positive real multivariable feedback systems this is a tutorial paper describing the application of infinity norm optimal control theory to the synthesis of sector bounded and positive real multivariable feedback systems the paper gives a concise treatment of the practical aspects of the theory describing how it has been implemented via state space oriented computer algorithms included is a concise summary of the state space approach to infinity norm control developed by doyle and by safonov and verma based on the hankel model reduction theory and incorporating the multivariable hankel results of glover

two stage sensitivity based group screening in computer experiments sophisticated computer codes that implement mathematical models of physical processes can involve large numbers of inputs and screening to determine the most active inputs is critical for understanding the input output relationship this article presents a new two stage group screening methodology for identifying active inputs in stage 1 groups of inputs showing low activity are screened out in stage 2 individual inputs from the active groups are identified inputs are evaluated through their estimated total effect sensitivity indices tsis which are compared with a benchmark null tsi distribution created from added low noise inputs examples show that compared with other procedures the proposed method provides more consistent and accurate results for high dimensional screening additional details and computer code are provided in supplementary materials available online

computation of inner outer factorization of rational matrices we propose a new numerically reliable computational approach to determine the inner outer factorization of a rational transfer matrix g of a linear descriptor system in contrast to existing computationally involved one shot methods which require the solution of riccati or generalized riccati equations the new approach relies on an efficient recursive zeros dislocation technique the resulting inner and outer factors always have minimal order descriptor representations the approach proposed is completely general being applicable whenever g is proper strictly proper or not or of full column row rank or not

generalized lqr control and kalman filtering with relations to computations of inner outer and spectral factorizations we investigate the generalized linear quadratic regulator lqr control where the dimension of the control input is strictly greater than the dimension of the controlled output and the weighting matrix on the control signal is singular the dual problem is the generalized kalman filtering where the dimension of the input noise process is strictly smaller than the dimension of the output measurement and the covariance of the observation noise is singular these two problems are intimately related to inner outer factorizations for nonsquare stable transfer matrices with square inners of the smaller size such inner outer factorizations are in turn related to spectral factorizations for power spectral density psd matrices whose normal ranks are not full we propose iterative algorithms and establish their convergence for inner outer and spectral factorizations which in turn solve the generalized lqr control and kalman filtering

stability of finite elements under divergence constraints a finite dimensional stability test for checking velocity pressure finite element trial spaces is presented applications are made to a new class of element pairs proposed in this paper as well as to existing spaces

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

inner outer factorization for non square proper functions with infinite and finite jω axis zeros the inner outer factorization of a non square proper function which has infinite and finite jomega axis zeros and has no poles in the open right half plane is studied in this paper via the concept of an infinite zero compensator for a stabilizable and detectable realization of the above function with full normal column rank the eigenstructures of the system matrix pencils of the function and its spectral density matrix are discussed based on kronecker s theory and a simple state space solution to the inner outer factorization is given via the solutions of the generalized eigenvalue problems in terms of the original realization of the function

h control problem with jω axis zeros abstract in this paper we discuss the so called one block h control problem in the case where the plant has j axis including infinity poles and zeros first we derive a necessary and sufficient condition for the h model matching problem to have a solution in the transfer function setting second we give a solvability condition which enables us to check the solvability by i examining matrix norm conditions related to j axis zeros and ii solving two generalized riccati equations finally we extend our result to the standard h problem

a generalized mac scheme on curvilinear domains we propose a simple finite difference scheme for navier stokes equations in primitive formulation on curvilinear domains with proper boundary treatment and interplay between covariant and contravariant components the spatial discretization admits exact hodge decomposition and energy identity as a result the pressure can be decoupled from the momentum equation with explicit time stepping no artificial pressure boundary condition is needed in addition it can be shown that this spatially compatible discretization leads to uniform inf sup condition which plays a crucial role in the pressure approximation of both dynamic and steady state calculations numerical experiments demonstrate the robustness and efficiency of our scheme

a rectangular mixed element method with continuous flux approximation for coupling stokes and darcy flows we construct and analyze herein a mixed element method with continuous flux approximation based on staggered rectangular meshes for solving the model of stokes equation coupled with darcy equation with beavers joseph saffman interface condition we prove the inf sup condition and the approximate solution existence uniquely the l 2 error estimates are established for both the velocity and pressure numerical experiments are given to verify the convergence rate for the problem

searching for important factors in simulation models with many factors sequential bifurcation abstract this paper deals with the problem of screening that is how to find the important factors in simulation models that have many for example 300 factors also called simulation parameters or input variables screening assumes that only a few factors are really important parsimony principle this paper solves the screening problem by a novel technique called sequential bifurcation this technique is both effective and efficient that is it does find all important factors yet it requires relatively few simulation runs the technique is demonstrated through a realistic case study concerning a complicated simulation model called image this simulation models the greenhouse phenomenon the worldwide increase of temperatures this case study gives surprising results the technique identifies some factors as being important that the ecological experts initially thought to be unimportant sequential bifurcation assumes that the input output behavior of the simulation model may be approximated by a first order polynomial main effects possibly augmented with interactions between factors the technique is sequential that is it specifies and analyzes simulation runs one after the other

computation of general inner outer and spectral factorizations in this paper we solve two problems in linear systems theory the computation of the inner outer and spectral factorizations of a continuous time system considered in the most general setting we show that these factorization problems rely essentially on solving for the stabilizing solution a standard algebraic riccati equation of order usually much smaller than the mcmillan degree of the transfer function matrix of the system the proposed procedures are completely general being applicable for a polynomial proper improper system whose transfer function matrix could be rank deficient and could have poles zeros on the imaginary axis or at infinity as an application we discuss the extension to the case of rational matrices of the complete orthogonal decomposition of a constant matrix numerical refinements and examples illustrating the proposed approach are discussed in detail

fast orthogonalization to the kernel of the discrete gradient operator with application to stokes problem abstract we obtain a simple tensor representation of the kernel of the discrete d dimensional gradient operator defined on tensor semi staggered grids we show that the dimension of the nullspace grows as o n d 2 where d is the dimension of the problem and n is one dimensional grid size the tensor structure allows fast orthogonalization to the kernel the usefulness of such procedure is demonstrated on three dimensional stokes problem discretized by finite differences on semi staggered grids and it is shown by numerical experiments that the new method outperforms usually used stabilization approach

analysis of some mixed elements for the stokes problem abstract in this paper we discuss some mixed finite element methods related to the reduced integration penalty method for solving the stokes problem we prove optimal order error estimates for bilinear constant and biquadratic bilinear velocity pressure finite element solutions the result for the biquadratic bilinear element is new while that for the bilinear constant element improves the convergence analysis of johnson and pitkaranta 1982 in the degenerate case when the penalty parameter is set to be zero our results reduce to some related known results proved in by brezzi and fortin 1991 for the bilinear constant element and bercovier and pironneau 1979 for the biquadratic bilinear element our theoretical results are consistent with the numerical results reported by carey and krishnan 1982 and oden et al 1982

stable cheapest nonconforming finite elements for the stokes equations we introduce two pairs of stable cheapest nonconforming finite element space pairs to approximate the stokes equations one pair has each component of its velocity field to be approximated by the p 1 nonconforming quadrilateral element while the pressure field is approximated by the piecewise constant function with globally two dimensional subspaces removed one removed space is due to the integral mean zero property and the other space consists of global checker board patterns the other pair consists of the velocity space as the p 1 nonconforming quadrilateral element enriched by a globally one dimensional macro bubble function space based on d s s y douglas santos sheen ye nonconforming finite element space the pressure field is approximated by the piecewise constant function with mean zero space eliminated we show that two element pairs satisfy the discrete inf sup condition uniformly and we investigate the relationship between them several numerical examples are shown to confirm the efficiency and reliability of the proposed methods

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