positive solutions for three point boundary value problems with dependence on the first order derivative abstract a new fixed point theorem in a cone is applied to obtain the existence of at least one positive solution for the second order three point boundary value problem x f t x x 0 0 x 0 0 x 1 x where f is a nonnegative continuous function 0 0 1

local łojasiewicz exponents milnor numbers and mixed multiplicities of ideals let g mathbb c n 0 to mathbb c n 0 be a finite analytic map we give an expression for the local ojasiewicz exponent and for the multiplicity of g when the component functions of g satisfy certain condition with respect to a set of n monomial ideals i1 in we give an effective method to compute ojasiewicz exponents based on the computation of mixed multiplicities as a consequence of our study we give a numerical characterization of a class of functions that includes semi weighted homogenous functions and newton non degenerate functions

integral closure and bounds for quotients of multiplicities of monomial ideals abstract given a pair of monomial ideals i and j of finite colength of the ring of analytic function germs c n 0 c we prove that some power of i admits a reduction formed by homogeneous polynomials with respect to the newton filtration induced by j if and only if the quotient of multiplicities e i e j attains a suitable upper bound expressed in terms of the newton polyhedra of i and j we also explore other connections between mixed multiplicities newton filtrations and the integral closure of ideals

a douglas wang finite element approach for transient advection diffusion problems abstract the paper presents an effective finite element method for approximating the two dimensional unsteady advection diffusion transport the new scheme is a direct generalization of the douglas wang finite element method applied to steady advection diffusion and stokes problems higher order spatial derivatives in the new formulation necessitate higher degree polynomial shape function quadratic finite element approximation quadrilateral q9 and triangular t6 are used the finite difference weighting formulation is used for a time discretization a stability analysis using the von neumann method shows that the formulation based on the implicit crank nicholson scheme reduces dissipation and dispersion errors when both advective and diffusive problems are considered also numerical results demonstrate that the accuracy achieved with the present model is excellent even with irregular element grids the results of this work strongly suggest further use and testing of this robust model in engineering practice especially for environmental problems related to pollution transport

the sequence of mixed łojasiewicz exponents associated to pairs of monomial ideals abstract we analyze the sequence l j i of mixed ojasiewicz exponents attached to any pair i j of monomial ideals of finite colength of the ring of analytic function germs c n 0 c in particular we obtain a combinatorial expression for this sequence when j is diagonal we also show several relations of l j i with other numerical invariants associated to i and j

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

an analysis of time discretization in the finite element solution of hyperbolic problems abstract the problem of the time discretization of hyperbolic equations when finite elements are used to represent the spatial dependence is critically examined a modified equation analysis reveals that the classical second order accurate time stepping algorithms i e the lax wendroff leap frog and crank nicolson methods properly combine with piecewise linear finite elements in advection problems only for small values of the time step on the contrary as the courant number increases the numerical phase error does not decrease uniformly at all wavelengths so that the optimal stability limit and the unit cfl property are not achieved these fundamental numerical properties can however be recovered while still remaining in the standard galerkin finite element setting by increasing the order of accuracy of the time discretization this is accomplished by exploiting the taylor series expansion in the time increment up to the third order before performing the galerkin spatial discretization using piecewise linear interpolations as a result it appears that the proper finite element equivalents of second order finite difference schemes are implicit methods of incremental type having third and fourth order global accuracy on uniform meshes taylor galerkin methods numerical results for several linear examples are presented to illustrate the properties of the taylor galerkin schemes in one and two dimensional calculations

analysis of time varying errors in quadratic finite element approximation of hyperbolic problems a methodology for analysing the numerical errors generated by schemes using high order approximation is presented based on fourier analysis this methodology is illustrated through the study of the weighting taylor galerkin finite element model applied to an unsteady one dimension advection problem with quadratic elements results show that the dissipation and dispersion errors may be computed by considering simultaneously the so called physical and computational modes and then contrarily to what is shown when linear approximation is considered these errors present a transient behaviour moreover it appears that the errors computed at the end node and at the middle node present in general a different behaviour which in some cases may be opposed to one another numerical tests are presented to support the validity of the proposed strategy we recommend strongly the use of this method for studying the behaviour of numerical schemes based on high order approximations

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

positive solutions of fourth order singular three point eigenvalue problems abstract in this paper by establishing a new comparison theorem and constructing upper and lower solutions some sufficient conditions of existence of positive solutions for the following singular fourth order three point eigenvalue problem u 4 t f t u t 0 1 u 0 u u 1 0 u 0 u u 1 0 are established due to schauder s fixed point theorem for large enough where 0 1 are constants f can be singular at t 0 and or 1 u 0 moreover some peculiar cases are discussed and some further results are obtained

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

multiplicity of positive solutions for second order three point boundary value problems we study the multiplicity of positive solutions for the second order three point boundary value problem u h t f u 0 t 0 1 u 0 0 u u 1 where 0 1 0 1 the methods employed are fixed point index theorems and leray schauder degree and upper and lower solutions

a petrov galerkin finite element method for convection dominated flows an accurate upwinding technique for satisfying the maximum principle abstract in this paper we present a new petrov galerkin method for convection dominated flow problems which is conservative and satisfies the discrete maximum principle this method also possesses no spurious crosswind diffusion and gives very accurate solutions the method is representative of a class of methods which may be described as fixed mesh adaptive

on open boundaries in the finite element approximation of two dimensional advection diffusion flows summary a steady state and transient finite element model has been developed to approximate with simple triangular elements the two dimensional advection di usion equation for practical river surface flow simulations essentially the space time crank nicolson galerkin formulation scheme was used to solve for a given conservative flow field several kinds of point sources and boundary conditions namely cauchy and open were theoretically and numerically analysed steady state and transient numerical tests investigated the accuracy of boundary conditions on inflow noflow and outflow boundaries where di usion is important di usive boundaries with the proper choice of boundary conditions the steady state galerkin and the transient crank nicolson galerkin finite element schemes gave stable and precise results for advectiondominated transport problems comparisons indicated that the present approach can give equivalent or more precise results than other streamline upwind and high order time stepping schemes di usive boundaries can be treated with cauchy conditions when the flow enters the domain inflow and with open conditions when the flow leaves the domain outflow or when it is parallel to the boundary noflow although systems with mainly di usive noflow boundaries may still be solved precisely with open conditions they are more susceptible to be influenced by other numerical sources of error moreover the treatment of open boundaries greatly increases the possibilities of correctly modelling restricted domains of actual and numerical interest 1997 by john wiley sons ltd

the method of lower and upper solutions for fourth order singular m point boundary value problems abstract this paper investigates the existence of positive solutions for fourth order singular m point boundary value problems firstly we establish a comparison theorem then we define a partial ordering in c 2 0 1 c 4 0 1 and construct lower and upper solutions to give a necessary and sufficient condition for the existence of c 2 0 1 as well as c 3 0 1 positive solutions our nonlinearity f t x y may be singular at x y t 0 and or t 1

three positive fixed points of nonlinear operators on ordered banach spaces we generalize the fixed point theorem of leggett williams which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a banach space we then show how to apply our theorem to prove the existence of three positive solutions to a second order discrete boundary value problem 2001 elsevier science ltd all rights reserved

least squares finite elements for first order hyperbolic systems application de la methode des moindres carres a elements finis a l approximation des systemes hyperboliques du premier ordre analyse de la stabilite exemples

a sharper condition for the solvability of a three point second order boundary value problem letf 0 1 r2 rbe a function satisfying caratheodory s conditions ande t l1 0 1 let 0 1 r 1 1 be given this paper is concerned with the problem of existence of a solution for the three point boundary value problem formula omitted this problem was studied earlier by gupta ntouyas and tsamatos when 1 and when 1 with 1 in the general case this problem was studied by gupta as a multi point boundary value problem in this paper sharper existence conditions are obtained for the solvability of the above boundary value problem in the general case

time accurate solution of advection diffusion problems by finite elements abstract the taylor galerkin method recently proposed for the spatial and temporal discretization of hyperbolic equations is employed to derive accurate and efficient numerical schemes for the solution of time dependent advection diffusion problems two distinct numerical strategies are discussed the first is suitable for evolutionary problems while the second is appropriate for situations in which a steady state is eventually reached for purely evolutionary problems the taylor galerkin method is applied to the complete advection diffusion equation and through modifications of the standard mass matrix is shown to generate an incremental form of the crank nicolson time stepping method such an incremental form also lends itself to the derivation of computationally simple but accurate explicit algorithms to deal with transient situations which evolve towards a highly convective steady state the global taylor galerkin method is found to be ineffective since it reduces to the standard galerkin formulation as the temporal term vanishes for such cases we suggest the use of a splitting up method in which advection and diffusion are treated separately by appropriate taylor galerkin methods the proposed methods are illustrated first for linear constant coefficient equations they are successively extended to deal with nonlinear and multi dimensional problems numerical applications indicate their effectiveness

a three point boundary value problem for nonlinear fourth order differential equations abstract in this paper the authors consider the nonlinear fourth order ordinary differential equation e u t g t f u 0 with the boundary conditions b u 0 u 1 u 0 u p u 1 0 some results on the existence and nonexistence of positive solutions to problem e b are obtained results on the existence of infinitely many positive solutions are also presented examples are included to demonstrate that the results are sharp

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