nonconventional large deviations theorems we obtain large deviations theorems for both discrete time expressions of the form sum n 1 nf big x q 1 n ldots x q ell n big and similar expressions of the form int 0 tf big x q 1 t ldots x q ell t big dt in continuous time here x n n ge 0 or x t t ge 0 is a markov process satisfying doeblin s condition f is a bounded continuous function and q i n in for i le k while for i k they are positive functions taking on integer values on integers with some growth conditions which are satisfied for instance when q i s are polynomials of increasing degrees applications to some types of dynamical systems such as mixing subshifts of finite type and hyperbolic and expanding transformations will be obtained as well

a modified streamline diffusion method for solving the stationary navier stokes equation recently hughes et al 11 12 proposed new finite element schemes of petrov galerkin type for solving the stokes problem which do not require the discrete version of the ladyshenskaya babuska brezzi condition lbb condition in this paper we derive a conforming finite element method for solving the stationary navier stokes equations which combines the advantages of arbitrary finite element spaces for velocity pressure with the favourable properties of the streamline diffusion method in the case of moderate and high reynolds number

a stabilized finite element method for the incompressible magnetohydrodynamic equations we propose and analyze a stabilized finite element method for the incompressible magnetohydrodynamic equations the numerical results that we present show a good behavior of our approximation in experiments which are relevant from an industrial viewpoint we explain in particular in the proof of our convergence theorem why it may be interesting to stabilize the magnetic equation as soon as the hydrodynamic diffusion is small and even if the magnetic diffusion is large this observation is confirmed by our numerical tests

a velocity pressure streamline diffusion finite element method for navier stokes equations a streamline diffusion finite element method is introduced for the time dependent incompressible navier stokes equations in a bounded domain in r squared and r cubed in the case of a flow with a high reynolds number an error estimate is proved and numerical results are given the method is based on a mixed velocity pressure formulation using the same finite element discretization of space time for the velocity and the pressure spaces which consist of piecewise linear functions together with certain least squares modifications of the galerkin variational formulation giving added stability without sacrificing accuracy

eigenvalue bounds for the schur complement with a pressure convection diffusion preconditioner in incompressible flow computations if the stationary navier stokes system or an implicit time discretization of the evolutionary navier stokes system is linearized by a picard iteration and discretized in space by a mixed finite element method there arises a saddle point system which may be solved by a krylov subspace method or an uzawa type approach for each of these resolution methods it is necessary to precondition the schur complement associated to the saddle point problem in question in the work at hand we give upper and lower bounds of the eigenvalues of this schur complement under the assumption that it is preconditioned by a pressure convection diffusion matrix

a least squares petrov galerkin finite element method for the stationary navier stokes equations in this paper a galerkin least squares type finite element method is proposed and analyzed for the stationary navier stokes equations the method is consistent and stable for any combination of discrete velocity and pressure spaces without requiring a babuska brezzi stability condition the existence uniqueness and convergence at optimal rate of the discrete solution is proved in the case of sufficient viscosity or small data

singular boundary value problems for superlinear second order ordinary and delay differential equations abstract existence criteria are established for singular boundary value problems for nonlinear second order ordinary and delay differential equations the theorems obtained are very general and complement previous known results

a least squares galerkin petrov nonconforming mixed finite element method for the stationary conduction convection problem abstract in this paper a least squares galerkin petrov nonconforming mixed finite element method lsgpnmfm is proposed and analyzed for the stationary conduction convection problem we use p 2 nonconforming as approximation space for the velocity the linear element for the pressure space and the quadratic element for the temperature space the mixed finite element spaces x h and m h need not satisfy inf sup condition the existence uniqueness and convergence of the discrete solution are presented and error estimates of optimal order are derived in the case of sufficient viscosity

analysis of a discontinuous galerkin method for the biot s consolidation problem in this paper a fully discrete stabilized discontinuous galerkin method is proposed to solve the biot s consolidation problem the existence and uniqueness of the finite element solution are obtained the stability of the fully discrete solution is discussed the corresponding error estimates for the approximation of displacement and pressure in a mesh dependent norm are obtained the error estimate for the approximation of pressure in l 2 norm is also obtained

existence of positive solutions for higher order functional differential equations abstract under suitable conditions on f t y t the boundary value problem of higher order functional differential equation fde of the form bvp fde y n t f t y t 0 t 0 1 a bc y i 0 0 0 i n 3 y n 2 t y n 1 t t t 0 y n 2 t y n 1 t t t 1 1 a has at least one positive solution where a is a fixed constant moreover we also apply this main result to establish several existence theorems which guarantee bvp has multiple positive solutions

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

stabilized reduced basis methods for parametrized steady stokes and navier stokes equations abstract it is well known in the reduced basis approximation of saddle point problems that the galerkin projection on the reduced space does not guarantee the inf sup approximation stability even if a stable high fidelity method was used to generate snapshots for problems in computational fluid dynamics the lack of inf sup stability is reflected by the inability to accurately approximate the pressure field in this context inf sup stability is usually recovered through the enrichment of the velocity space with suitable supremizer functions the main goal of this work is to propose an alternative approach which relies on the residual based stabilization techniques customarily employed in the finite element literature such as brezzi pitkaranta franca hughes streamline upwind petrov galerkin galerkin least square in the spirit of offline online reduced basis computational splitting two such options are proposed namely offline only stabilization and offline online stabilization these approaches are then compared to and combined with the state of the art supremizer enrichment approach numerical results are discussed highlighting that the proposed methodology allows to obtain smaller reduced basis spaces i e neglecting supremizer enrichment for which a modified inf sup stability is still preserved at the reduced order level

a new projection based stabilized method for steady convection dominated convection diffusion equations abstract we propose a new projection based stabilized method for the steady convection dominated convection diffusion equations this method directly increases the l 2 stability instead of the h 1 stability which the variational multiscale vms methods do numerical analysis and numerical experiments illustrate and confirm that our new method has effective numerical performances on convection dominated convection diffusion problems

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

existence results for differential delay equations i abstract existence principles for systems of differential difference equations of delay type are established also applications are given to first order delay equations throughout our topological arguments are based on a nonlinear alternative

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

triple positive solutions for a class of boundary value problems for second order neutral functional differential equations abstract we obtain sufficient conditions for the existence of at least three positive solutions for the second order neutral functional differential equation x t q t f t x t x t x t x t 0 0 t 1 0 subject to one of the following two pairs of boundary conditions x t t t 0 x 1 0 x t t t 0 x 1 0 and generalize and correct some conditions of theorem 3 2 in x b shu y t xu triple positive solutions for a class of boundary value problems of second order functional differential equations nonlinear anal 61 8 2005 1401 1411 this is an application of a new fixed point theorem introduced by avery and peeterson r i avery a c peeterson three positive fixed points of nonlinear operators on ordered banach spaces comput math appl 42 2001 313 322

existence of positive solutions for functional differential equations under suitable conditions on f t yt the boundary value problem of second order functional differential equation fde with the form fde y t f t yt 0 for t 0 1 a bc y t y t t for t 0 bvp y t y e t for t 1 1 a has at least one positive solution moreover we also apply this main result to establish several existence theorems which guarantee bvp has the multiple positive solutions

averaging in dynamical systems and large deviations the paper treats ordinary differential equations of the form frac dz varepsilon left t right dt varepsilon b z varepsilon t f t y wheref t is a hyperbolic flow large deviations bounds for the averaging principle are obtained here in the form appeared previously in f1 f2 for the case when the flowf t is replaced by a markov process

local projection stabilized method on unsteady navier stokes equations with high reynolds number using equal order interpolation in this paper we propose and analyze a stabilized method for unsteady navier stokes equations with high reynolds number using local projection stabilized method to control spurious oscillations in the velocities due to dominant convection or in the pressure due to the velocity pressure coupling using equal order conforming elements in space and crank nicolson difference in time we derive a fully discrete formulation we prove stability and convergence of the approximate solution the error estimates hold irrespective of the reynolds number provided the exact solution is smooth this result is comparable with the streamline diffusion and continuous interior penalty methods

triple positive solutions for a class of boundary value problem of second order functional differential equations abstract we obtain sufficient conditions for the existence of at least three positive solutions for the functional differential equation x t q t f t x t x t 1 0 subject to some boundary conditions this is an application of a new fixed point theorem introduced by avery and peterson ann differential equations 8 1992 261 268

limit theorems for partially hyperbolic systems we consider a large class of partially hyperbolic systems containing among others affine maps frame flows on negatively curved manifolds and mostly contracting diffeomorphisms if the rate of mixing is sufficiently high the system satisfies many classical limit theorems of probability theory

a stabilized nonconfirming finite element method based on multiscale enrichment for the stationary navier stokes equations abstract in the paper we proposed a stabilized nonconforming finite element method for the stationary incompressible navier stokes equations which is a petrov galerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions and we studied the stability of the method for p 1 p 0 triangular element q 1 p 0 quadrilateral element and obtained the optimal error estimates of the stabilized nonconforming finite element method for the stationary navier stokes equations

finite element methods for first order hyperbolic systems with particular emphasis on the compressible euler equations a petrov galerkin finite element formulation is presented for first order hyperbolic systems of conservation laws with particular emphasis on the compressible euler equations applications of the methodology are made to one and two dimensional steady and unsteady flows with shocks results obtained suggest the potential of the type of methods developed

existence of positive solutions for boundary value problem of second order fde abstract we use a fixed point theorem in cones to investigate the existence of positive solutions for boundary value problem of a second order functional differential equation fde with the form y t r t y t 0 0 y t y t t r t 0 y t y t n t 1 t 1 a where y t y t for a we allow that r t has the singularity at the endpoints t 0 and t 1 of 0 1 our results include the situations that f is either superlinear or sublinear

numerical method for a singularly perturbed convection diffusion problem with delay this paper deals with the singularly perturbed boundary value problem for a linear second order delay differential equation for the numerical solution of this problem we use an exponentially fitted difference scheme on a uniform mesh which is accomplished by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form it is shown that one gets first order convergence in the discrete maximum norm independently of the perturbation parameter numerical results are presented which illustrate the theoretical results

the existence of multiple positive solutions for singular functional differential equations with sign changing nonlinearity in this paper we study the existence of multiple positive solutions for boundary value problems based on second order functional differential equations with the form y t f t y t t 0 t 0 1 t y t h t t t 0 y 1 0 where 0 is continuous may be singular at t 0 1 y 0 and takes negative values by applying the fixed point index theorem we obtain the conditions for the existence of at least two and of three positive solutions an example to illustrate our results is given

eigenvalue criteria for existence of multiple positive solutions to boundary value problems of second order delay differential equations abstract criteria are established for existence of multiple positive solutions to the boundary value problems expressed by second order delay differential equations of the form p t y t q t y t f t y t y t a t 0 1 y t y t t t 0 y t y t t t 1 1 a where 0 a 1 4 are suitably small p c 1 0 1 p 0 q c 0 1 and q 0