existence results for the flow of viscoelastic fluids with a differential constitutive law where 2 is the symmetric extra stress tensor the total stress is given by g pl i where p is the hydrodynamic pressure 4 is the rate of deformation tensor g u vu vu u being the velocity field a is the relaxation time a2 the retardation time 0 i a a1 and q is the fluid viscosity the symbol a d t denotes an objective frame indifferent derivative i 181 more precisely

a fractional step θ method approximation of time dependent viscoelastic fluid flow a fractional step q method for the approximation of time dependent viscoelastic fluid flow equations is described and analyzed in this article the algorithm uses substeps within a time step to sequentially update velocity pressure and stress this lagged approach to temporal integration requires a resolution of smaller systems than a fully implicit approach while achieving a second order temporal accuracy we establish a priori error estimates for our scheme and provide numerical computations to support the theoretical results and demonstrate the capability of this method

high order finite difference techniques for linear singular perturbation boundary value problems abstract three high order finite difference techniques are developed for the second order singularity perturbed linear boundary value problem in one dimension taylor series expansions and error conversions are used for the development of the techniques convergence and stability conditions of these techniques are proved and some numerical results are given

subgrid stabilized defect correction method for a steady state natural convection problem in this paper we consider a subgrid stabilized defect correction method for the steady state natural convection problem we state the stabilities and error results for the defect step and the first correction step of the defect correction method the derived theoretical results are supported by several numerical examples

mathematical and numerical analysis of a simplified time dependent viscoelastic flow a time dependent model corresponding to an oldroyd b viscoelastic fluid is considered the convective terms being disregarded global existence in time is proved in banach spaces provided the data are small enough using the implicit function theorem and a maximum regularity property for a three fields stokes problem a finite element discretization in space is then proposed existence of the numerical solution is proved for small data so as a priori error estimates using again an implicit function theorem

solving singularly perturbed problems by a weak form integral equation with exponential trial functions abstract the second order singularly perturbed problem is transformed to a singularly perturbed parabolic type partial differential equation by using a fictitious time technique then we use green s second identity to derive a boundary integral equation in terms of the adjoint trefftz test functions namely a weak form integral equation method wfiem it accompanying with the exponential trial functions which are designed to satisfy the boundary conditions automatically can provide very accurate numerical solutions of linear and nonlinear singularly perturbed problems for the latter problem the iterative procedure is convergent very fast

analysis of a defect correction method for viscoelastic fluid flow we study a defect correction method for a viscoelastic fluid flow obeying an oldroyd btype constitutive law in the defect step the constitutive equation is computed with the artificially reduced weissenberg parameter for stability and the residual is taken care of in the correction step we show the convergence of the defect correction method and derive an error estimate

a finite element approximation for the steady solution of a second grade fluid model abstract the aim of this work is to present a finite element method for the approximation of the steady solution of an incompressible second grade fluid model in two dimensions the equations for second grade fluids form a system of nonlinear partial differential equations of mixed elliptic hyperbolic type in the steady state using a fixed point argument associated with the decomposition of the system into a transport equation and a stokes system existence and uniqueness of the approximate solution are proved and error estimates are obtained this technique allows the construction of a decoupled fixed point algorithm converging to the discrete solution of the original problem

existence of approximate solutions and error bounds for viscoelastic fluid flow characteristics method abstract in this paper we study a finite element approximation of a steady viscoelastic fluid flow obeying an oldroyd b type constitutive law the approximate stress velocity and pressure are respectively p 1 discontinuous p 2 continuous p 1 continuous we use the method of characteristics for the convection of the extra stress tensor we suppose that the continuous problem admits a sufficiently smooth and sufficiently small solution we show by a fixed point method that the approximate problem has a solution and an error bound is given

defect deferred correction method for the two domain convection dominated convection diffusion problem abstract we present a method for solving a fluid fluid interaction problem two convection dominated convection diffusion problems adjoined by an interface which is a simplified version of the atmosphere ocean coupling problem the method resolves some of the issues that can be crucial to the fluid fluid interaction problems it is a partitioned time stepping method yet it is of high order accuracy in both space and time the two step algorithm considered in this report provides second order accuracy it allows for the usage of the legacy codes which is a common requirement when resolving flows in complex geometries yet it can be applied to the problems with very small viscosity diffusion coefficients this is achieved by combining the defect correction technique for increased spatial accuracy and for resolving the issue of high convection to diffusion ratio with the deferred correction in time which allows for the usage of the computationally attractive partitioned scheme yet the time accuracy is increased beyond the usual result of partitioned methods being only first order accurate into the defect deferred correction method ddc the results are readily extendable to the higher order accuracy cases by adding more correction steps both the theoretical results and the numerical tests provided demonstrate that the computed solution is unconditionally stable and the accuracy in both space and time is improved after the correction step

defect correction finite element method for the stationary incompressible magnetohydrodynamics equation in this study we give the defect correction finite element method for the stationary incompressible mhd equation firstly the nonlinear mhd equation is solved with an artificial viscosity term then the numerical solution is improved on the same grid by a linearized defect correction technique then we give the numerical analysis including stability analysis and error analysis the numerical analysis proves that our method is stable and has an optimal convergence rate then we give some numerical results from the numerical results we can see that our method is efficient for solving the mhd equations

analysis and finite element approximation of an optimal control problem for the oseen viscoelastic fluid flow in this article we study a boundary control problem for an oseen type model of viscoelastic fluid flow the existence of a unique optimal solution is proved and an optimality system is derived by the first order necessary condition we investigate finite element approximations to a solution of the optimality system and a solution algorithm for the system based on the gradient method

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

the universal regular quotient of the chow group of points on projective varieties let x be a projective variety of dimension n de ned over an algebraically closed eld k for x irreducible and non singular matsusaka ma constructed an abelian variety alb x and a morphism a x alb x called the albanese variety and mapping respectively depending on the choice of a base point on x which is universal among the morphisms to abelian varieties see lang la serre se for other constructions over the eld of complex numbers the existence of alb x and a was known before and has a purely hodge theoretic description see igusa i for the hodge theoretic construction incidentally the terminology albanese variety was introduced by a weil for reasons explained in his commentary on the article 1950a of volume i of his collected works see w one of which is that the paper alb of albanese de nes it for a surface as a quotient of the group of 0 cycles of degree 0 modulo an equivalence relation let chn x deg 0 denote the chow group of 0 cycles of degree 0 on x modulo rational equivalence when x is irreducible and non singular a remarkable feature of the albanese morphism a is that it factors through a regular homomorphism u chn x deg 0 alb x that is a homomorphism which when composed with the cycle map c x chn x deg 0 gives an algebraic morphism this follows immediately from the fact that an abelian variety does not contain any rational curve thus one can reformulate matsusaka s theorem as the invent math 135 595 664 1999 doi 10 1007 s002229900890

numerical solution of the stationary navier stokes equations using a multilevel finite element method the numerical implementation of a multilevel finite element method for the steady state navier stokes equations is considered the multilevel method proposed here for the navier stokes equations is a multiscale method in which the full nonlinear navier stokes equations are only solved on a single coarse grid subsequent approximations are generated on a succession of refined grids by solving a linearized navier stokes problem two numerical examples are considered the first is an example for which an exact solution is known and the second is the driven cavity problem we demonstrate numerically that for an appropriate choice of grids a two or three level finite element method is significantly more efficient than the standard one level finite element method

subgrid stabilized defect correction methods for the navier stokes equations we consider the synthesis of a recent subgrid stabilization method with defect correction methods the combination is particularly efficient and combines the best algorithmic features of each we prove convergence of the method for a fixed number of corrections as the mesh size goes to zero and derive parameter scalings from the analysis we also present some numerical tests which both verify the theoretical predictions and illustrate the method s promise

approximation of time dependent viscoelastic fluid flow supg approximation in this article we consider the numerical approximation to the time dependent viscoelasticity equations with an oldroyd b constitutive equation the approximation is stabilized by using a streamline upwind petrov galerkin supg approximation for the constitutive equation we analyze both the semidiscrete and fully discrete numerical approximations for both discretizations we prove the existence of and derive a priori error estimates for the numerical approximations

finite element approximation of viscoelastic fluid flow existence of approximate solutions and error bounds we study a finite element approximation of viscoelastic fluid flow obeying an oldroyd b type constitutive law the approximate stress velocity and pressure are respectivelyp 1 discontinuous p 2 continuous p 1 continuous we use the method of lesaint raviart for the convection of the extra stress tensor we suppose that the continuous problem admits a sufficiently smooth and sufficiently small solution we show by a fixed point method that the approximate problem has a solution and we give an error bound

computing the eigenvalues of the generalized sturm liouville problems based on the lie group sl 2 r for the generalized sturm liouville problems we can construct an sl 2 r lie group shooting method to find eigenvalues by using the closure property of the lie group a one step lie group transformation between the boundary values at two ends of the considered interval is established hence we can theoretically derive an analytical characteristic equation to determine the eigenvalues for the generalized sturm liouville problems because the closed form formulas are derived to calculate the unknown left boundary values in terms of l the present method provides an easy numerical implementation and has a cheap computational cost numerical examples are examined to show that the present sl 2 r lie group shooting method is effective

iterative schemes for the non homogeneous navier stokes equations based on the finite element approximation in this paper we consider the stability and convergence of three iterative schemes for the non homogeneous steady navier stokes equations as a nonlinear problem we will get a nonlinear discrete system if approximating the non homogeneous navier stokes equations after proving the stability and error estimates of the finite element method for the non homogeneous navier stokes equations three iterative schemes are investigated for solving the resulted nonlinear discrete system the stability and convergence conditions for these iterative methods are also analyzed respectively furthermore new results for the stop criterion are proved finally we show some numerical experiments to illustrate the theoretical prediction

a computational method for solving third order singularly perturbed boundary value problems in this paper a new computational method is presented for solving a class of third order singularly perturbed boundary value problems with a boundary layer at the left of the underlying interval in this method first the given third order singularly perturbed boundary value problem is transformed into a system of two odes subject to suitable initial and boundary conditions and a zeroth order asymptotic expansion for the solution of the given problem is constructed then the reduced terminal value problem is solved analytically in the reproducing kernel space this method is effective and easy to implement a numerical examples is studied to demonstrate the accuracy of the present method results obtained by the method are found to be in good agreement with the exact solution not only in the boundary layer but also away from the layer

stabilization of explicit coupling in fluid structure interaction involving fluid incompressibility abstract in this work we propose a stabilized explicit coupling scheme for fluid structure interaction problems involving a viscous incompressible fluid the coupled discrete formulation is based on nitsche s method with a time penalty term giving l 2 control on the fluid pressure variations at the interface for a linear model problem we prove that the scheme is stable in the energy norm irrespectively of the so called added mass effect namely the fluid structure density ratio and the geometry of the domain numerical experiments in the linear and non linear case show that optimal time accuracy can be obtained by performing one defect correction iteration

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

on generalizations of the albanese variety in this note the relation between two generalizations of the classical albanese variety namely the one for smooth non complete varieties by faltings and wustholz and the one for singular varieties by esnault srinivas and viehweg is investigated over the field of complex numbers

using reproducing kernel for solving a class of singularly perturbed problems this paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of partial differential equations with a singularly perturbed term in a reproducing kernel space two numerical examples are studied to demonstrate the accuracy of the present method results obtained by the method indicate the method is simple and effective

murthy s conjecture on 0 cycles we show that the levine weibel chow group of 0 cycles mathrm ch d a of a reduced affine algebra a of dimension d ge 2 over an algebraically closed field is torsion free among several applications it implies an affirmative solution to an old conjecture of murthy in classical k theory

approximation of time dependent multi component viscoelastic fluid flow abstract in this article we analyse a fully discrete approximation to the time dependent viscoelasticity equations allowing for multicomponent fluid flow the oldroyd b constitutive equation is used to model the viscoelastic stress for the discretization time derivatives are replaced by backward difference quotients and the non linear terms are linearized by lagging appropriate factors the modeling equations for the individual fluids are combined into a single system of equations using a continuum surface model the numerical approximation is stabilized by using an supg approximation for the constitutive equation under a small data assumption on the true solution existence of the approximate solution is proven a priori error estimates for the approximation in terms of the mesh parameter h the time discretization parameter t and the supg coefficient are also derived numerical simulations of viscoelastic fluid flow involving two immiscible fluids are also presented

decoupled approach for the problem of viscoelastic fluid flow of ptt model i continuous stresses we present in this work a numerical analysis of a decoupled approach with continuous stresses for the viscoelastic fluid flows obeying the ptt model the streamline upwind petrov galerkin is used to treat the transport part of the equations this model introduces supplementary difficulties linked to the non linearities of the exponential type present in the constitutive equation in exchange it seems to be more realistic and gives best numerical results the method is tested on the classical benchmark problem stick slip flow numerical results show that our method is remarkably stable and no upper weissenberg limit number was encountered for reasonable values of a material depending parameter

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

finite element approximation of viscoelastic fluid flow existence of approximate solutions and error bounds continuous approximation of the stress the author studies a finite element approximation of viscoelastic fluid flow obeying an oldroyd b type constitutive law the approximate stress velocity and pressure are respectively p 1 continuous p 2 continuous and p 1 continuous the streamline upwinding petrov galerkin method for the convection of the extra stress tensor is used suppose that the continuous problem admits a sufficiently smooth and sufficiently small solution it is shown by a fixed point method that the approximate problem has a solution and an error bound is given

an algorithm for solving nonlinear singular perturbation problems with mechanization in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of pade approximation method for solving nonlinear singular perturbation problems was established a new maple procedure spp was established too the procedure spp give not only the approximate analytic solutions but also the numerical solutions of spp six examples are presented to illustrate the implementation of the program the method is very simple and effective for most of singular perturbation problems this would be useful for solving differential equations

an extra stress vorticity formulation of stokes problem for the oldroyd viscoelastic model we present a three fields formulation of the stokes problem with the following unknowns extra stress tensor stream function and vorticity this formulation is motivated by the oldroyd model for viscoelastic flows in fact it appears that problems in and are uncoupled and moreover that the problem reduces to the solution of two laplacians and one u p stokes problem an another important feature is that the symmetry of the stresses is dualized the purpose of this paper is to describe this new formulation to show that it satisfies an inf sup condition and that classical finite element spaces can be used for its approximation

torsion and divisibility for reciprocity sheaves and 0 cycles with modulus the notion of modulus is a striking feature of rosenlicht serre s theory of generalized jacobian varieties of curves it was carried over to algebraic cycles on general varieties by bloch esnault park rulling krishna levine recently kerz saito introduced a notion of chow group of 0 cycles with modulus in connection with geometric class field theory with wild ramification for varieties over finite fields we study the non homotopy invariant part of the chow group of 0 cycles with modulus and show their torsion and divisibility properties modulus is being brought to sheaf theory by kahn saito yamazaki in their attempt to construct a generalization of voevodsky suslin friedlander s theory of homotopy invariant presheaves with transfers we prove parallel results about torsion and divisibility properties for them

an analysis of the discontinuous galerkin method for a scalar hyperbolic equation we prove lp stability and error estimates for the discontinuous galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain using finite element analysis techniques we obtain l2 estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials lp estimates for p 2 are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree the latter estimates are proved by combining finite difference and finite element analysis techniques

error estimates for a stabilized finite element method for the oldroyd b model abstract in this paper we study a new approximation scheme of transient viscoelastic fluid flow obeying an oldroyd b type constitutive equation the new stabilized formulation bases on the choice of a modified euler method connected to the streamline upwinding petrov galerkin supg method m bensaada d esselaoui d sandri stabilization method for continuous approximation of transient convection problem numer methods partial differential equations 21 2004 170 189 in order to stabilize the tensorial transport term of the oldroyd derivative suppose that the continuous problem admits a sufficiently smooth and sufficiently small solution a priori error estimates for the approximation in terms of the mesh parameter h and the time discretization parameter t are derived

decoupled algorithm for solving phan thien tanner viscoelastic fluid by finite element method in this paper we present a decoupled algorithm for the viscoelastic fluid flow obeying the phan thien tanner ptt differential model the method consists to solve alternatively a stokes like problem by weighted least squares wls finite element method and the constitutive equation by streamline upwind petrov galerkin supg method a priori error estimate for the wls supg finite element method is derived the existence and uniqueness of the approximate solution are obtained using fixed point techniques we show that the mapping of the decoupled algorithm is locally contracting the planar channel flow problem is used to illustrate our theoretical results we encounter no limit of the weissenberg number for reasonable values of e a dimensionless material parameter in our calculations

tangent space correction method for the galerkin approximation based on two grid finite element abstract a novel fully discrete two grid finite element method for certain semi linear parabolic equations is presented in this paper the new scheme is based on two different finite element subspaces defined respectively on one coarse grid with grid size h and one fine grid with grid size h h nonlinearity is treated in the coarse grid subspace by solving the standard galerkin equation while in the fine grid subspace only a linear equation has to be solved differing from the usual two grid method the splitting of the coarse grid subspace and its related fine grid incremental subspace is based on a new projection in which sense the incremental subspace is closely identified with the tangent space of certain operator on each time step with linear finite element discretization the stability and error estimate results for such new scheme are derived the results show that the difference between this new approximation and the fine grid standard galerkin approximation in h 1 norm is of the order h 4 d 2 where d 1 2 3 is the space dimension

a new discrete evss method for the viscoelastic flows in this paper we propose a new discrete elastic viscous split stress evss method for the viscoelastic flows obeying an oldroyd b type constitutive equation supposing that the velocity and pressure are approximated by the taylor hood elements and applying the orthogonal projection technique we introduce two gauss integrations as a stabilizing term in the discrete evss method compared with the popular one the new method does not need to introduce any extra variable and reduces the degrees of freedom of the discrete system a lot but gets the same stabilized result additionally some numerical experiments are shown to verify its efficiency

a defect correction method for unsteady conduction convection problems ii time discretization in this paper a fully discrete defect correction mixed finite element method mfem for solving the non stationary conduction convection problems in two dimension which is leaded by combining the back euler time discretization with the two step defect correction in space is presented in this method we solve the nonlinear equations with an added artificial viscosity term on a finite element grid and correct these solutions on the same grid using a linearized defect correction technique the stability and the error analysis are derived the theory analysis shows that our method is stable and has a good convergence property some numerical results are also given which show that this method is highly efficient for the unsteady conduction convection problems

two level finite element discretization of viscoelastic fluid flow abstract we propose and analyze a two level method of discretizing the equations of steady state flow of a viscoelastic fluid obeying an oldroyd type constitutive equation with no slip boundary condition the two level algorithm consists of solving a small non linear system of equations on the coarse mesh and then using that solution to solve a larger linear system on the fine mesh specifically following najib and sandri numer math 72 1995 223 we linearize the oldroyd type constitutive equation about the coarse mesh solution thus nullifying the difficulties brought by the advection term our theoretical error estimates show that it has optimal order accuracy provided the true solution is smooth and its norm is sufficiently small in addition our computational error estimates exhibit the validity of our analysis

computation of viscoelastic fluid flows using continuation methods the numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter the weissenberg number increases specifically at a weissenberg number larger than a critical value the iterative nonlinear solver fails to converge a phenomenon known as the high weissenberg number problem in this work we describe the application and implementation of continuation methods to the nonlinear johnson segalman model for steady state viscoelastic flows simple natural and pseudo arclength continuation approaches in weissenberg number are investigated for a discontinuous galerkin finite element discretization of the equations computations are performed for a benchmark contraction flow and several aspects of the performance of the continuation methods including high weissenberg number limits are discussed

numerical methods for singular perturbation problems consider the two point boundary value problem for a stiff system of ordinary differential equations an adaptive method to solve these problems even when turning points are present is discussed

error analysis of a fully discrete finite element variational multiscale method for the natural convection problem abstract for the natural convection problem we propose a new projection based finite element variational multiscale method by defining the stabilization terms via two local gauss integrations at the element level based on the implicit backward euler and implicit crank nicolson schemes for temporal discretization and stabilized mixed finite element spatial discretization we establish two numerical schemes for the natural convection problem unconditional stabilities of the two numerical schemes are proved we derive error bounds of the fully discrete solution which are first and second order in time respectively the optimal error estimates in space could be achieved for velocity and temperature in the h 1 semi norm and for pressure in the l 2 norm with the proper choosing of stabilized parameters however the error estimates in space are suboptimal for velocity and temperature in the l 2 norm the derived theoretical results are supported by two numerical examples

a domain decomposition method for the oseen viscoelastic flow equations we study a non overlapping domain decomposition method for the oseen viscoelastic flow problem the data on the interface are transported through newmann and dirichlet boundary conditions for the momentum and constitutive equations respectively the discrete variational formulations of subproblems are presented and investigated for the existence of solutions we show convergence of the domain decomposition solution to a solution of the one domain problem convergence of an iterative algorithm and some numerical results are also presented

numerical solutions of linear and nonlinear singular perturbation problems a new method is developed by detecting the boundary layer of the solution of a singular perturbation problem on the non boundary layer domain the singular perturbation problem is dominated by the reduced equation which is solved with standard techniques for initial value problems while on the boundary layer domain it is controlled by the singular perturbation its numerical solution is provided with finite difference methods of which up to sixth order methods are developed the numerical error is maintained at the same level with a constant number of mesh points for a family of singular perturbation problems numerical experiments support the analytical results

a defect correction method for the incompressible navier stokes equations a defect correction method for the incompressible navier stokes equation with a high reynolds number is considered in the defect step the artificial viscosity parameter s is added to the reynolds number as a stability factor and the residual is taken care of in the correction step h 1 and l 2 error estimations are derived for the one step defect correction method and the results of some numerical experiments are presented these results show that for the driven cavity two defect correction steps antidiffuse the artificial viscosity approximation nearly optimally this combination gives on a very coarse mesh results indistinguishable from a benchmark very fine mesh calculation

a multigrid method for viscoelastic fluid flow we study a multigrid finite element method for a viscoelastic fluid flow obeying an oldroyd b type constitutive law the multigrid method is a time saving method in which the full nonlinear system is solved on a coarse grid and subsequent approximations are generated on a succession of refined grids by solving a linearized problem we show that the linearized problem has an approximate solution and present an error bound for a two grid method we also numerically demonstrate that the multigrid method is significantly more efficient than the standard one grid finite element method

zero cycles and k theory on normal surfaces in this paper we prove a formula conjectured by bloch and srinivas s2 which describes the chow group of zero cycles of a normal quasi projective surface x over a field as an inverse limit of relative chow groups of a desingularisation x relative to multiples of the exceptional divisor we then give several applications of this result a relative version of the famous bloch conjecture on 0 cycles the triviality of the chow group of 0 cycles for any 2 dimensional normal graded q algebra analogue of the bloch beilinson conjecture and the analogue of the roitman theorem for torsion 0 cycles in characteristic p 0 for normal varieties including the case of p torsion

a new defect correction method for the navier stokes equations at high reynolds numbers abstract in this paper a new defect correction method for the navier stokes equations is presented with solving an artificial viscosity stabilized nonlinear problem in the defect step and correcting the residual by linearized equations in the correction step for a few steps this combination is particularly efficient for the navier stokes equations at high reynolds numbers in both the defect and correction steps we use the oseen iterative scheme to solve the discrete nonlinear equations furthermore the stability and convergence of this new method are deduced which are better than that of the classical ones finally some numerical experiments are performed to verify the theoretical predictions and show the efficiency of the new combination

non standard difference schemes for singular perturbation problems revisited non standard finite difference techniques for solving various linear two point singularly perturbed boundary value problems are considered they consist of replacing the original differential equation by a related differential equation with a small deviating argument this related problem is then discretized using finite differences this discretized problem is solved using standard matrix methods the accuracy and robustness of these numerical schemes are then carefully investigated and compared to standard centered finite differences in particular earlier claims for the superiority of such schemes over standard finite differences are shown to be invalid

on conforming finite element methods for the inhomogeneous stationary navier stokes equations we consider the stationary navier stokes equations written in terms of the primitive variables in the case where both the partial differential equations and boundary conditions are inhomogeneous under certain conditions on the data the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed a conforming finite element method is presented and optimal estimates for the error of the approximate solution are proved in addition the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are given numerical examples using an efficient choice of finite element spaces are also provided

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

a two parameter defect correction method for computation of steady state viscoelastic fluid flow the numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter the weissenberg number increases specifically at a weissenberg number larger than a critical value the iterative nonlinear solver fails to converge in this paper a two parameter defect correction method for viscoelastic fluid flow is presented and analyzed in the defect step the weissenberg number is artificially reduced to solve a stable nonlinear problem the approximation is then improved in the correction step using a linearized correction iteration numerical experiments support the theoretical results and demonstrate the effectiveness of the method

an operator compact implicit method of exponential type a fourth order accurate tridiagonal operator compact implicit finite difference method for diffusion convection equations is developed the coefficients of the difference operator contain exponentials of the coefficients of the differential operator in this way the method avoids spurious oscillations when the cell reynolds number is large numerical results and comparisons to other methods are presented

mechanization for solving spp by reducing order method in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of reduction of order approximation method for solving singular perturbation problems was established a new maple procedure redordproc was established too the procedure redordproc give not only the approximate analytic solutions but also the numerical solutions of the kinetics problems some examples are presented to illustrate the implementation of the program

gls and evss methods for a three field stokes problem arising from viscoelastic flows in this paper order one finite elements together with galerkin least squares gls methods are used for solving a three held stokes problem arising from the numerical study of viscoelastic hows stability and convergence results are established even when the solvent viscosity is small compared to the viscosity due to the polymer chains an iterative algorithm decoupling velocity pressure and stress calculations is proposed the link with the modified elastic viscous split stress evss method studied in m fortin r guenette r pierre comput methods appl mech engrg 143 1997 79 95 r guenette m fortin j non newtonian fluid mech 60 1995 27 52 is presented numerical results are in agreement with theoretical predictions and with those presented in m fortin r guenette r pierre comput methods appl mech engrg 143 1997 79 95 c 2001 elsevier science b v all rights reserved

stable high order methods for differential equations with small coefficients for the second order terms abstract stable high order methods are developed for solving differential equations with small coefficients for the second order terms in particular second fourth and sixth order methods are developed the methods are developed for general linear two point boundary value problems and proved to be stable and accurate results are presented for the one dimensional convection diffusion equation involving problems with and without boundary layers the methods converged for all values of parameters attempted and the results compared favorably with other methods the methods developed in this paper are accurate stable easy to use and applicable to other problems

on a decoupled algorithm for solving a finite element problem for the approximation of viscoelastic fluid flow the aim of this work is to study a decoupled algorithm of a fixed point for solving a finite element fe problem for the approximation of viscoelastic fluid flow obeying an oldroyd b differential model the interest for this algorithm lies in its applications to numerical simulation and in the cost of computing furthermore it is easy to bring this algorithm into play the unknowns are sigma the viscoelastic part of the extra stress tensor u the velocity and p the pressure we suppose that the solution sigma u p is sufficiently smooth and small the approximation of stress velocity and pressure are resp p 1 discontinuous p 2 continuous p 1 continuous fe upwinding needed for convection of sigma is made by discontinuous fe the method consists to solve alternatively a transport equation for the stress and a stokes like problem for velocity and pressure previously results of existence of the solution for the approximate problem and error bounds have been obtained using fixed point techniques with coupled algorithm in this paper we show that the mapping of the decoupled fixed point algorithm is locally in a neighbourhood of sigma u p contracting and we obtain existence unicity locally of the solution of the approximate problem and error bounds

analyse numerique des ecoulements quasi newtoniens dont la viscosite obeit a la loi puissance ou la loi de carreau we prove abstract error estimates for the approximation of the velocity and the pressure by a mixed fem of quasi newtonian flows whose viscosity obeys the power law or the carreau law these estimates are optimal in some cases they can be applied to most finite elements used for the solution of stokes s problem on prouve des estimations d erreur abstraites pour l approximation de la vitesse et la pression par une mef mixtes d ecoulements quasi newtoniens dont la viscosite obeit a la loi puissance ou la loi de carreau ces estimations sont optimales dans certains cas elles peuvent etre appliquees a la plupart des elements finis utilises pour la resolution du probleme de stokes

finite element approximation of viscoelastic fluid flow using characteristics method abstract it is known that for the numerical approximation of oldroyd s b model for viscoelastic fluid flows some upwinding is needed for the convection of the extra stress tensor in this paper we make the numerical analysis of such an approximation with upwinding by the method of characteristics in a finite element context the approximate stress velocity and pressure are respectively p 1 discontinuous p 2 continuous and p 1 continuous we suppose that the continuous problem admits a sufficiently smooth and sufficiently small solution we show by a fixed point method that the approximate problem has a solution and an error bound is given

numerical analysis of a fem for a transient viscoelastic flow abstract we present the numerical analysis of a coupled method for the numerical simulation of transient viscoelastic flows obeying a differential constitutive equation with a newtonian viscosity the scheme used is based on euler implicit method in time and maintain at each time step a coupling between the velocity u and the viscoelastic part of the stress approximation in space is made by finite element method fe the approximate stress velocity and pressure are respectively p 1 discontinuous p 2 continuous and p 1 continuous upwinding needed for convection of is made by a discontinuous galerkin fe method

hyperbolicity and change of type in the flow of viscoelastic fluids the equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators propagation of singularities is discussed and conditions for a change of type are investigated the vorticity equation for steady flow can change type when a critical condition involving speed and stresses is satisfied this leads to a partitioning of the field of flow into subcritical and supercritical regions as in the problem of transonic flow

adaptive defect correction methods for convection dominated convection diffusion problems abstract we present a posteriori error estimates for a defect correction method for approximating solutions of convection diffusion problems the algorithms and estimators include the possibility of using in the discretization a nonlinear selection mechanism which we find improves solution quality in and near layers energy norm and l2 a posteriori error estimates are proven for the full algorithm two examples of fully adaptive finite element defect correction calculations are presented these examples illustrate the scheme and demonstrate the effectiveness of the method

numerical analysis of a three fields model for a quasi newtonian flow abstract we study a finite element approximation of a non linear three fields version of stokes system for incompressible fluids such a problem arises when one considers a white metzner type model for a viscoelastic fluid flow and sets the relaxation time to zero the non linear aspect comes from the fact that a fraction of the viscosity of the fluid depends on the second invariant of the rate of deformation tensor we give existence and unicity results for the continuous problem and its approximation and we prove the error bound

chow group of 0 cycles with modulus and higher dimensional class field theory one of the main results of this article is a proof of the rank one case of an existence conjecture on lisse q over bar l sheaves on a smooth variety u over a finite field due to deligne and drinfeld the problem is translated into the language of higher dimensional class field theory over finite fields which describes the abelian fundamental group of u by chow groups of 0 cycles with moduli a key ingredient is the construction of a cycle theoretic avatar of a refined artin conductor in ramification theory originally studied by kazuya kato

two level picard and modified picard methods for the navier stokes equations abstract iterative methods of picard type for the navier stokes equations are known to converge only for quite small reynolds numbers however we study methods involving just one such iteration at general reynolds numbers for the initial approximation a coarse mesh of width h0 is used the corrected approximation is computed by just one picard or modified picard step on a fine mesh of width h1 for example h1 may be of order o h 0 2 when linear velocity elements are used the resulting method requires the solution of a small system of nonlinear equations on the coarse mesh and only one larger linear system on the fine mesh this two level picard method is proven to converge for fixed reynolds number as h 0 further the fine mesh solution satisfies a quasi optimal error bound the error constants grow as re as for the usual finite element method one very heuristic explanation why one step of the divergent picard method might work when beginning with a coarse mesh approximation is that the terms neglected involve lower order derivatives thus they are approximated with higher accuracy on the coarse mesh this is linked with a smoothing property of the fine mesh step

finite element approximation of viscoelastic fluid flow with slip boundary condition we present a theoretical study of a creeping steady state isothermal flow of a viscoelastic fluid obeying an oldroyd type constitutive law with slip boundary condition the slip boundary condition is appropriate for problems that involve free boundaries and other examples where the usual no slip condition u 0 is not valid such as fiber spinning and microfluidics first we study the newtonian problem with slip boundary condition where the viscoelastic stress is added into the list of unknowns in addition the normal viscoelastic stress component associated with the slip boundary condition is introduced in order to balance its effects a second inf sup condition is proven to treat the discrete case we assume that the continuous solution of the non newtonian problem exists and is small and smooth approximating the extra stress velocity pressure and normal viscoelastic stress component via p 1 discontinuous p 2 continuous p 1 continuous and p 0 discontinuous elements respectively yields a stable finite element scheme finally via a fixed point argument we establish the existence of an approximate solution and derive error estimates

an analysis of a defect correction method for a model convection diffusion equation the error in a defect correction method for a model one dimensional convection diffusion problem without turning points is analyzed although the analysis is limited to the one dimensional problem the scheme is a computationally attractive way to increase the accuracy in smooth regions of first order schemes for general multidimensional problems it is shown that in one dimension the kth approximation converges uniformly in varepsilon in regions bounded away from the layer with rate o varepsilon 0 varepsilon k h 2 varepsilon 0 o h the estimates degrade to o 1 near layers numerical experiments confirm that this is precisely the behavior of the method