on error estimates of the penalty method for unsteady navier stokes equations the penalty method has been widely used for numerical computations of the unsteady navier stokes equations however the best error estimates available to the author s knowledge were not optimal an

classifying thick subcategories of the stable category of cohen macaulay modules abstract various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics in this paper as a higher dimensional version of the classification theorem of thick subcategories of the stable category of finitely generated representations of a finite p group due to benson carlson and rickard we consider classifying thick subcategories of the stable category of cohen macaulay modules over a gorenstein local ring the main result of this paper yields a complete classification of the thick subcategories of the stable category of cohen macaulay modules over a local hypersurface in terms of specialization closed subsets of the prime ideal spectrum of the ring which are contained in its singular locus

on error estimates of some higher order projection and penalty projection methods for navier stokes equations this paper is a continuation of our previous work 10 on projection methods we study first existing higher order projection schemes in the semidiscretized form for the navier stokes equations one error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent neumann boundary condition satisfied by the pressure approximations we then propose a penalty projection scheme for which we obtain improved error estimates

optimal error estimates for semidiscrete galerkin approximations to equations of motion described by kelvin voigt viscoelastic fluid flow model in this paper a finite element galerkin method is applied to equations of motion arising in the kelvin voigt viscoelastic fluid flow model when the forcing function is in l l 2 some a priori estimates for the exact solution which are valid uniformly in time as t and even uniformly in the retardation time an 0 are derived it is shown that the semidiscrete method admits a global attractor further with the help of a priori bounds and sobolev stokes projection optimal error estimates for the velocity in l l 2 and l h 1 norms and for the pressure in l l 2 norm are established since the constants involved in error estimates have an exponential growth in time therefore in the last part of the article under certain uniqueness condition the error bounds are established which are valid uniformly in time finally some numerical experiments are conducted which confirm our theoretical findings

a new shape representation scheme and its application to shape discrimination using a neural network abstract a new method of shape representation and feature extraction is suggested a shape is approximated by a constant point polygon in which between any two adjacent vertices of the polygon the number of points on the contour of the shape is constant this representation is applicable for both concave and convex shapes and there is no chance of missing any spikes on the boundary the sequence of the angle of variation between two consecutive line segments is taken as the primary feature representation of the shape this sequence is then modelled by an autoregressive ar process and the least square error estimate of the ar coefficient vector is used as input to a multilayer perceptron mlp network for learning and classification robustness of the shape representation scheme and the mlp classifier is also investigated empirically adaptive ar modelling is used for estimating the numerically stable and robust coefficient vector

an incremental pressure correction finite element method for the time dependent oldroyd flows abstract in this paper we present an incremental pressure correction finite element method for the time dependent oldroyd flows this method is a fully discrete projection method as we all know most projection methods have been studied without space discretization then the ensuing analysis may not extend to this case we also give the stability analysis and the optimal error analysis the analysis is based on a time discrete error and a spatial discrete error in order to show the effectiveness of the method we also present some numerical results the numerical results confirm our analysis and show clearly the stability and optimal convergence of the incremental pressure correction finite element method for the time dependent oldroyd flows

stochastic models for closed boundary analysis representation and reconstruction the analysis of closed boundaries of arbitrary shapes on a plane is discussed specifically the problems of representation and reconstruction are considered a one to one correspondence between the given closed boundary and a univariate or multivariate sequence of real numbers is set up univariate or multivariate circular autoregressive models are suggested for the representation of the sequence of numbers derived from the closed boundary the stochastic model representing the closed boundary is invariant to transformations like sealing translation choice of starting point and rotation over angles that are multiples of 2 pi n where n is the number of observations methods for estimating the unknown parameters of the model are given and a decision rule for choosing the appropriate number of coefficients is included constraints on the estimates are derived so that the estimates are invariant to the transformations of the boundaries the stochastic model enables the reconstruction of a dosed boundary using fft algorithms results of simulations are included and the application to contour coding is discussed

stabilized finite element methods for the velocity pressure stress formulation of incompressible flows abstract formulated in terms of velocity pressure and the extra stress tensor the incompressible navier stokes equations are discretized by stabilized finite element methods the stabilized methods proposed are analyzed for a linear model and extended to the navier stokes equations the numerical tests performed confirm the good stability characteristics of the methods these methods are applicable to various combinations of interpolation functions including the simplest equal order linear and bilinear elements

a taxonomy of consistently stabilized finite element methods for the stokes problem stabilized mixed methods can circumvent the restrictive inf sup condition without introducing penalty errors for properly chosen stabilization parameters these methods are well posed for all conforming velocity pressure pairs however their variational forms have widely varying properties first stabilization offers a choice between weakly or strongly coercive bilinear forms that give rise to linear systems with identical solutions but very different matrix properties second coercivity may be conditional upon a proper choice of a stabilizing parameter here we focus on how these two aspects of stabilized methods affect their accuracy and efficient iterative solution we present results that indicate a preference of krylov subspace solvers for strongly coercive formulations stability criteria obtained by finite element and algebraic analyses are compared with numerical experiments while for two popular classes of stabilized methods sufficient stability bounds correlate well with numerical stability our experiments indicate the intriguing possibility that the pressure stabilized galerkin method is unconditionally stable

shape matching of two dimensional objects in this paper we present results in the areas of shape matching of nonoccluded and occluded two dimensional objects shape matching is viewed as a segment matching problem unlike the previous work the technique is based on a stochastic labeling procedure which explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification to reduce the computation time the technique is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels this basic technique has been extended to the situation where various objects partially occlude each other to form an apparent object and our interest is to find all the objects participating in the occlusion in such a case several hierarchical processes are executed in parallel for every object participating in the occlusion and are coordinated in such a way that the same segment of the apparent object is not matched to the segments of different actual objects these techniques have been applied to two dimensional simple closed curves represented by polygons and the power of the techniques is demonstrated by the examples taken from synthetic aerial industrial and biological images where the matching is done after using the actual segmentation methods

a new stabilized finite element method for the transient navier stokes equations abstract this paper is concerned with the development and analysis of a new stabilized finite element method based on two local gauss integrations for the two dimensional transient navier stokes equations by using the lowest equal order pair of finite elements this new stabilized finite element method has some prominent features parameter free avoiding higher order derivatives or edge based data structures and stabilization being completely local at the element level an optimal error estimate for approximate velocity and pressure is obtained by applying the technique of the galerkin finite element method under certain regularity assumptions on the solution compared with other stabilized methods using the same pair of mixed finite elements for the two dimensional transient navier stokes equations through a series of numerical experiments it is shown that this new stabilized method has better stability and accuracy results

a priori error estimates of fully discrete finite element galerkin method for kelvin voigt viscoelastic fluid flow model abstract in this article a finite element galerkin method is applied to the kelvin voigt viscoelastic fluid model when its forcing function is in l l 2 some new a priori bounds for the velocity as well as for the pressure are derived which are independent of inverse powers of the retardation time the second order error estimate in l l 2 norm the first order error estimate in l h 0 1 norm for the velocity and the first order error estimate in l l 2 norm for the pressure for the semidiscrete method are derived which hold uniformly with respect to as 0 with the initial condition only in h 2 h 0 1 further under the smallness assumption on the data these error estimates are shown to be uniform in time as t for the complete discretization of the semidiscrete system a first order accurate backward euler method is applied and fully discrete error estimates are established finally numerical experiments are conducted to verify the theoretical results the results derived in this article are sharper than those derived earlier for finite element analysis of the kelvin voigt fluid model in the sense that the error estimates in this article hold true uniformly even as 0

stabilized mixed methods for the stokes problem the solution of the stokes problem is approximated by three stabilized mixed methods one due to hughes balestra and franca and the other two being variants of this procedure in each case the bilinear form associated with the saddle point problem of the standard mixed formulation is modified to become coercive over the finite element space error estimates are derived for each procedure

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

on the convergence of a time discretization scheme for the navier stokes equations version linearisee du schema d euler implicite utilisee pour l approximation des solutions des equations de navier stokes dans un domaine bidimensionnel

finite element approximation for the viscoelastic fluid motion problem in this article the variational formulation of the two dimensional viscoelastic fluid motion problem and its finite element approximation are considered an local error estimate for the velocity with h1 norm and the pressure with l2 norm is obtained and a uniform error estimate for the velocity and pressure with the above norms is provided if the given data satisfies the uniqueness condition

a better consistency for low order stabilized finite element methods abstract the standard implementation of stabilized finite element methods with a piece wise function space of order lower than the highest derivative present in the partial differential equation often suffers from a weak consistency that can lead to reduced accuracy the popularity of these low order elements motivates the development of a new stabilization operator which globally reconstructs the derivatives not present in the local element function space this new method is seen to engender a stronger consistency leading to better convergence and improved accuracy applications to the navier stokes equations are given which illustrate the improvement at a negligible additional cost

stability and convergence of the higher projection method for the time dependent viscoelastic flow problem abstract in this paper the time discrete higher order projection method is proposed and analyzed for the time dependent viscoelastic flow problem our numerical method is based on the time iterative discrete schemes by the projection method the considered problem is decoupled into two linear subproblems one is for the velocity and the other is for the pressure unconditional stability of the numerical schemes is established convergence results for the velocity and pressure are also derived our main results of this paper are that the convergence analysis for the velocity is weakly second order and for the pressure is weakly first order finally some numerical examples are provided to confirm the performances of the developed numerical algorithms

asymptotic behavior of ext functors for modules of finite complete intersection dimension let r be a local ring and let m and n be finitely generated r modules such that m has finite complete intersection dimension in this paper we define and study under certain conditions a pairing using the modules rm ext r i m n which generalizes buchweitz s notion of the herbrand difference we exploit this pairing to examine the number of consecutive vanishing of rm ext r i m n needed to ensure that rm ext r i m n 0 for all i gg 0 our results recover and improve on most of the known bounds in the literature especially when r has dimension at most two

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

long time numerical solution of a parabolic equation with memory long time stability and convergence properties of two time discreti zation methods for an integro differential equation of parabolic type are studied the methods are based on the standard backward euler and second order back ward differencing methods the memory term is approximated by a quadrature rule with emphasis on such rules with reduced computational memory require ments discretization of the spatial partial differential operators by the finite element method is also considered

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

decent intersection and tor rigidity for modules over local hypersurfaces first published in transactions of the american mathematical society in 2013 published by the american mathematical society also available electronically from http www ams org journals tran 2013 365 06 s0002 9947 2012 05574 7 home html

a multigrid version of a simple finite element method for the stokes problem we consider a finite element method for the stokes problem on a rectangular domain based on piecewise bilinear velocities and piecewise constant pressures on a uniform rectangular grid it is shown that by a simple stabilization strategy the method can be implemented in a convergent multigrid procedure introduction one of the most natural ways of discretizing the stokes equations on a two dimensional rectangular domain is to apply the finite element techniques with continuous piecewise bilinear velocities and piecewise constant pressures on a rectangular grid this method is easily extended to more general quadrilateral meshes and it has proved to be quite effective in practice the convergence analysis of the method was first carried out in 10 on a rectangular domain in 12 the estimates of 10 are improved and extended to more general quadrilateral meshes so far the above method has been used mainly in connection with direct band solvers usually combined with penalty perturbation techniques to eliminate the pressure 9 in this paper we consider an iterative variant of the method based on multigrid techniques such an algorithm seems attractive especially since the un derlying finite difference equations are relatively simple multigrid methods for the stokes problem and for more general elliptic systems were considered previously by hackbusch 8 and verfurth 14 in 14 it is shown that a convergent multigrid algorithm for the stokes problem can be constructed by appropriately scaling the variables provided that the underlying finite element scheme satisfies the babu ka brezzi stability condition 2 5 in our case however the finite element method is not stable in this sense and we have not been able to show that the straightforward application of the algorithm proposed in 14 yields a convergent process therefore we suggest first modifying the finite element method in such a way that it becomes stable in the ordinary sense the usual way of stabilizing an unstable mixed method is to add more velocity or primary variables a classical example of this is the quadratic linear velocity pres sure element of crouzeix and raviart 6 where added bubble functions act as stabilizers in the velocity space increasing the dimension of the velocity space would be an alternative in our case however we propose another method which seems to yield a simpler algorithm it is based on adding an extra stabilizing term into the

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

a new absolutely stable simplified galerkin least squares finite element method using nonconforming element for the stokes problem we propose a new absolutely stable simplified galerkin least squares sgls finite element method using equal order linear nonconforming element for the stokes problem we prove that our method is absolutely stable and has optimal error estimates numerical tests confirm and illustrate the theoretical analysis compare with the conforming galerkin least squares method and conforming sgls method our nonconforming method is more accuracy

penalty finite element method for stokes problem with nonlinear slip boundary conditions abstract the penalty finite element method for stokes problem with nonlinear slip boundary conditions based on the finite element subspace v h m h which satisfies the discrete inf sup condition is investigated in this paper since this class of nonlinear slip boundary conditions include the subdifferential property the weak variational formulation associated with stokes problem is variational inequality under some regularity assumptions we obtain the optimal h 1 and l 2 error estimates between u and u h and between u and u h e where the error orders are e h for h 1 error and e h 2 for l 2 error

tensor products of modules and the rigidity of tor let r be a hypersurface domain that is a ring of the form s f where s is a regular local ring and f is a prime element suppose m and n are finitely generated r modules we prove two rigidity theorems on the vanishing of tor in the first theorem we assume that the regular local ring s is unramified that m r n has finite length and that dim m dim n dim r with these assumptions if tor r m n 0 for some j 0 then tor r m n 0 for all i j the second rigidity theorem states that if m r n is reflexive then tor r m n 0 for all i 1 we use these theorems to prove the following theorem valid even if s is ramified if m r n is a maximal cohen macaulay r module then both m and n are maximal cohen macaulay modules and at least one of them is free

on a linearized backward euler method for the equations of motion of oldroyd fluids of order one in this paper a linearized backward euler method is discussed for the equations of motion arising in the oldroyd model of viscoelastic fluids some new a priori bounds are obtained for the solution under realistically assumed conditions on the data further the exponential decay properties for the exact as well as the discrete solutions are established finally a priori error estimates in bh 1 and bl 2 norms are derived for the the discrete problem which are valid uniformly for all time t 0

error analysis of some galerkin least squares methods for the elasticity equations the recent technique of stabilizing mixed finite element methods by augmenting the galerkin formulation with least squares terms calculated separately on each element is considered the error analysis is performed in a unified manner yielding improved results for some methods introduced earlier in addition a new formulation is introduced and analyzed method is used within two different contexts the first is in connection with the plain strain or three dimensional problems near the incompressible limit for which the poisson ratio equals one half it is well known that for these problems a standard lower order displacement finite element method will break down by now it is also well known how a working method can be obtained a new unknown the pressure is introduced and discretized with a finite element space different from that used for the displacements the finite element method obtained falls into the class of saddlepoint problems for which there is a general theory developed by brezzi and babuska 5 7 the application of this theory shows that the method converges optimally if the discrete spaces for the displacement and pressure satisfy a stability condition for a particular choice of displacement and pressure approximations it can be a difficult task to verify this babuska brezzi or inf sup condition during the last decade this problem has been intensively studied and the performances of many combinations are now known cf 18 and 23 26 for some recent extensions in addition there exists a general technique utilizing bubble functions by which a stable method can

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

error estimates with smooth and nonsmooth data for a finite element method for the cahn hilliard equation a finite element method for the cahn hilliard equation a semilinear parabolic equation of fourth order is analyzed both in a spatially semidiscrete case and in a completely discrete case based on the backward euler method error bounds of optimal order over a finite time interval are obtained for solutions with smooth and nonsmooth initial data a detailed study of the regularity of the exact solution is included the analysis is based on local lipschitz conditions for the nonlinearity with respect to sobolev norms and the existence of a ljapunov functional for the exact and the discretized equations is essential a result concerning the convergence of the attractor of the corresponding approximate nonlinear semigroup upper semicontinuity with respect to the discretization parameters is obtained as a simple application of the nonsmooth data error estimate

on error estimates of projection methods for navier stokes equations first order schemes in this paper projection methods or fractional step methods are studied in the semi discretized form for the navier stokes equations in a two or three dimensional bounded domain error estimates for the velocity and the pressure of the classical projection scheme are established via the energy method a modified projection scheme which leads to improved error estimates is also proposed

a gauge uzawa finite element method for the time dependent viscoelastic oldroyd flows abstract in this paper we present the gauge uzawa finite element method for the time dependent viscoelastic oldroyd flow this method is a fully discrete projection method whereas most projection methods have been studied without space discretization and the ensuing analysis may not extend to this case we also give the stability analysis and the optimal error analysis the analysis is based on an iterated time discrete system with which the error function is split into a temporal error and a spatial error in order to show the effect of the method we present some numerical results the numerical results confirm our analysis and show clearly the stability and optimal convergence of the gauge uzawa finite element method for the viscoelastic oldroyd flow

analysis of locally stabilized mixed finite element methods for the stokes problem in this paper a locally stabilized finite element formulation of the stokes problem is analyzed a macroelement condition which is sufficient for the stability of locally stabilized mixed methods based on a piecewise constant pressure approximation is introduced by satisfying this condition the stability of the qi po quadrilateral and the pi po triangular element can be established

a bivariate autoregressive technique for analysis and classification of planar shapes a bivariate autoregressive model is introduced for the analysis and classification of closed planar shapes the boundary coordinate sequence of a digitized binary image is sampled to produce a polygonal approximation to an object s shape this circular sample sequence is then represented by a vector autoregressive difference equation which models the individual cartesian coordinate sequences as well as coordinate interdependencies several classification features which are functions or transformations of the estimated coefficient matrices and the associated residual error covariance matrices are developed these features are shown to be invariant to object transformations such as translation rotation and scaling laboratory experiments involving object sets representative of industrial shapes are presented superior classification results are demonstrated

contour sequence moments for the classification of closed planar shapes abstract a technique for classifying closed planar shapes is described in which a shape is characterized by a one dimensional sequence that represents the euclidean distance between the centroid and all contour pixels of the shape contour sequences obtained from shapes belonging to the same class are similar and are considered to be different realizations of a stochastic process statistical moment functions derived from contour sequences are used to characterize the process and hence the shapes it is shown that these moment functions are invariant to shape translation rotation and scale transformations examples are presented to illustrate the performance of these moment functions in the classification of noisy shapes

a two level method with backtracking for the navier stokes equations we consider a two level method for resolving the nonlinearity in finite element approximations of the equilibrium navier stokes equations the method yields l2 and h1 optimal velocity approximations and an l2 optimal pressure approximation the two level method involves solving one small nonlinear coarse mesh system one oseen problem hence linear with positive definite symmetric part on the fine mesh and one linear correction problem on the coarse mesh the algorithm we study produces an approximate solution with the optimal asymptotic in h accuracy for any fixed reynolds number we do not consider the behavior of the error for fixed h as re rightarrow infty i e for flows in transition to turbulence

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

iterative methods in penalty finite element discretization for the steady mhd equations this paper characterizes one penalty finite element method for the incompressible mhd equations the method is an interesting combination of the classic iterative schemes stokes newton and oseen iterations with two different finite element pairs p1b p1 p1b and p1 p0 p1 moreover the rigorous analysis of stability and error estimate for the proposed methods are given finally the applicability and effectiveness of the presented schemes are illustrated in several numerical experiments

a penalty finite element method based on the euler implicit explicit scheme 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 where the time discretization is based on the euler implicit explicit scheme with some implicit linear terms and an explicit nonlinear term and the finite element spatial discretization is based on the p 1b p 1 element pair which satisfies the discrete inf sup condition this method allows us to separate the computation of the velocity from the computation of the pressure with a larger time step size dt so that the numerical velocity u e h n and the pressure p e h n are easily computed an optimal error estimate of the numerical velocity and the pressure is provided for the fully discrete penalty finite element method when the penalty parameter e the time step size dt and the mesh size h satisfy the following stability conditions ec 1 1 dt k 1 1 and h 2 b 1 dt respectively for some positive constants c 1 k 1 and b 1 finally some numerical tests to confirm the theoretical results of the penalty finite element method are provided

support varieties and cohomology over complete intersections quillen s geometric approach to the cohomology of finite groups 30 has revolutionized modular representation theory the ideology and techniques involved have been generalized and extended to representations of various hopf algebras culminating in the recent work of friedlander and suslin 17 on finite group schemes in this paper we develop geometric methods for the study of finite modules over a local complete intersection r if r is such a ring and m is its maximal ideal then the m adic completion r has the form q f where f is a regular sequence and q is a regular local ring that can be taken to be a ring of formal power series over a field or a discrete valuation ring the least number of equations needed to cut out r from a regular local ring equals the codimension of r where codim r r m dim r and r m denotes the minimal number of generators of an r module m in 5 a cone that is a homogeneous algebraic set vr m is attached to each finite r module m and used to study its minimal free resolution here we prove

two level penalty finite element methods for the stationary incompressible magnetohydrodynamics problem in the paper we consider the penalty finite element method for the stationary incompressible magnetohydrodynamics mhd problem with a factor of penalty parameter stability and convergence of numerical solutions are established furthermore two level penalty methods are also developed for the mhd problem our methods consist of solving a nonlinear mhd problem by the usual penalty method on a coarse mesh with mesh size h and then a linearized mhd problem based on the stokes newton and oseen iterations on a fine mesh is solved by the penalty method with mesh size h h h respectively stability and error estimates of numerical solutions in two level penalty methods are presented finally some numerical tests are provided to demonstrate the effectiveness of the developed algorithms

a pressure poisson stabilized finite element method for the non stationary stokes equations to circumvent the inf sup condition in this article stabilized finite element methods are considered for the non stationary stokes equations based on some lowest equal order finite elements space pair x h m h which do not satisfy the discrete inf sup condition the stability of two kinds of methods is derived under some regularity assumptions then the convergence of the penalty method and the pressure poisson stabilized method is compared the result shows that the former error limits the order of approximation to o e h e and the latter yields the optimal error estimate o h

stability and convergence of second order time discrete projection method for the linearized oldroyd model abstract in this paper we consider the second order time discrete projection method for the linearized oldroyd model based on the time iterative discrete scheme by the projection method the original problem is decoupled into two linear subproblems and each subproblem can be solved easily unconditional stability and the corresponding convergence results of the numerical solutions are derived our main results are that the convergence orders in time for the velocity in l 2 norm is second order and for the pressure in h 1 norm is first order finally some numerical examples are provided to verify the performances of the developed numerical method

a finite element penalty method for the linearized viscoelastic oldroyd fluid motion equations abstract in this paper a fully discrete finite element penalty method is considered for the two dimensional linearized viscoelastic fluid motion equations arising from the oldroyd model for the non newton fluid flows with the finite element method for the spatial discretization and the backward euler scheme for the temporal discretization the velocity and pressure are decoupled in this method which leads to a large reduction of the computational scale under some realistic assumptions the unconditional stability of the fully discrete scheme is proved moreover the optimal error estimates are obtained which are better than the existing results finally some numerical results are given to verify the theoretical analysis the difference between the motion of the newton and non newton fluid is also observed

a neural network approach to robust shape classification abstract a neural network approach for the classification of closed planar shapes is described the primary foci are the development of an effective representation for planar shapes which may be used in conjunction with neural nets the selection of a suitable neural network structure and determining training methods to increase the degree of robustness in classification a three layer perception using backpropagation is initially trained with contour sequences of noisefree reference shapes and its generalization capability is demonstrated the network is then gradually retrained with increasingly noisy data to improve the robustness of the classifier the advantages and improvement in robustness using this extended training scheme are shown and typical classification results are presented

an absolutely stable pressure poisson stabilized finite element method for the stokes equations the pressure poisson stabilized galerkin method for the stokes equation requires the choice of a positive parameter existing theoretical predictions for the range of parameter values that yield stable discretizations seem to be very pessimistic when compared to the computational evidence motivated by this wide gap we first examine a continuous prototype for this class of schemes we show that the prototype is absolutely stable i e it is stable for all parameter values and is optimally accurate we then define a new practical variant of the well known pressure poisson stabilized scheme we prove that the new method is absolutely stable just like its continuous prototype and that it achieves optimal convergence rates with respect to the same mesh independent norms the new method differs from the standard pressure poisson stabilized method in several important aspects first its definition does not degrade to a penalty formulation for the lowest order nodal spaces second the method is absolutely stable with respect to the natural norm for the problem while the standard pressure poisson stabilized method is stable with respect to a mesh dependent norm

tor and torsion on a complete intersection abstract let r m be a complete intersection that is a ring whose m adic completion is the quotient of a regular local ring by a regular sequence supposemandnare finitely generatedr modules we give a necessary condition for the vanishing of torri m n for alli 0 in terms of the intersection of certain affine algebraic sets associated tomandn we apply this condition to the study of torsion in tensor products for example we show that ifris a domain andmis anr module of infinite projective dimension then there exist infinitely manynfor which the tensor product ofmwith one of itsnth syzygy modules has torsion we also give a sufficient condition for the vanishing torri m n for alli 0 in terms of the ability to leftmandnto disjoint complete intersections of smaller codimension we use this condition to construct tensor products of non free modules which are maximal cohen macaulay

the boundary penalty method for the diffusion equation subject to the specification of mass in this paper we concern with a new boundary penalty finite element method for the one dimensional time dependent diffusion equation subject to the specification of mass instead of solving the diffusion equation directly we will use the finite element method to solve a boundary penalty problem which is derived from the diffusion equation and analyse the error estimate of the semi discrete and fully discrete approximations when the penalty parameter e is sufficiently small the numerical experiments show that our method is very effective and supports our analysis