on a multiplier conjecture for univalent functions let y be the set of normalized univalent functions and let 0 be the subset of 5 containing functions with the property if z l o jzl 1 in particular we prove that the conjecture holds with 5 replaced by f the class of close to convex functions and show its truth for a number of special members of r these latter results are extensions of old ones of szego and kobori about sections of univalent functions

existence of positive solutions for 2nth order singular sublinear boundary value problems abstract this paper investigates the existence of positive solutions for 2nth order n 1 singular sub linear boundary value problems a necessary and sufficient condition for the existence of c 2 n 2 0 1 as well as c 2 n 1 0 1 positive solutions is given by constructing lower and upper solutions and with the maximal theorem our nonlinearity f t x 1 x 2 x n may be singular at x i 0 i 1 2 n t 0 and or t 1

a parameter free dynamic diffusion method for advection diffusion reaction problems abstract in this paper we present a two scale finite element formulation named dynamic diffusion dd for advection diffusion reaction problems by decomposing the velocity field in coarse and subgrid scales the latter is used to determine the smallest amount of artificial diffusion to minimize the coarse scale kinetic energy this is done locally and dynamically by imposing some constraints on the resolved scale solution yielding a parameter free consistent method the subgrid scale space is defined by using bubble functions whose degrees of freedom are locally eliminated in favor of the degrees of freedom that live on the resolved scales convergence tests on a two dimensional example are reported yielding optimal rates in addition numerical experiments show that dd method is robust for a wide scope of application problems

on partial sums of the libera integral operator abstract letsbe the class of functionsf z which are analytic and univalent in the open unit diskuwithf 0 0 andf 0 1 thenth partial sums of the libera integral operatorf z forf z sare denoted bysn z f in the present paper the starlikeness property ofsn z f is proved

convergence analysis of the residual free bubble method for bilinear elements we present an a priori error analysis for the residual free bubble rfb method applied to diffusion convection equations with a dominating and antisymmetric convection operator special attention is paid to the case of piecewise bilinears in mathbb r 2 and the theoretical comparison with the streamline diffusion finite element sdfe equivalently streamline upwind petrov galerkin supg method

a multiscale stabilized finite element method for the advection diffusion equation this paper presents a multiscale method that yields a stabilized finite element formulation for the advection diffusion equation the multiscale method arises from a decomposition of the scalar field into coarse resolved scale and fine unresolved scale the resulting stabilized formulation possesses superior properties like that of the supg and the gls methods a significant feature of the present method is that the definition of the stabilization term appears naturally and therefore the formulation is free of any user designed or user defined parameters another important ingredient is that since the method is residual based it satisfies consistency ab initio based on the proposed formulation a family of 2 d elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed numerical results show the good performance of the method on uniform skewed as well as composite meshes and confirm convergence at optimal rates 2004 elsevier b v all rights reserved

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

the method of lower and upper solutions for fourth order two point boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u iv f x u x u x u 0 u 1 u 0 u 1 0 where f 0 1 r r r is continuous

a finite element technique for solving first order pdes in lp an approximation technique for solving first order pdes in l p omega 1 le p infty is proposed the method is a generalization of the least squares method to non hilbertian settings a priori and a posteriori error estimates are proven numerical tests in l 1 omega show that this type of technique can handle discontinuities without resorting to limiting procedures

a bubble stabilized finite element method for dirichlet constraints on embedded interfaces we examine a bubble stabilized finite element method for enforcing dirichlet constraints on embedded interfaces by embedded we refer to problems of general interest wherein the geometry of the interface is assumed independent of some underlying bulk mesh as such the robust imposition of dirichlet constraints using a lagrange multiplier field is not trivial to focus issues we consider a simple one sided problem that is representative of a wide class of evolving interface problems the bulk field is decomposed into coarse and fine scales giving rise to coarse scale and fine scale one sided sub problems the fine scale solution is approximated with bubble functions permitting static condensation and giving rise to a stabilized form bearing strong analogy with a classical method importantly the method is simple to implement readily extends to multiple dimensions obviates the need to specify any free stabilization parameters and can lead to a symmetric positive definite system of equations the performance of the method is then examined through several numerical examples the accuracy of the lagrange multiplier is compared to results obtained using a local version of the domain integral method the variational multiscale approach proposed herein is shown to both stabilize the lagrange multiplier and improve the accuracy of the post processed fluxes copyright 2006 john wiley sons ltd

solving singular boundary value problems of higher even order in this paper we present a new algorithm to solve a kind of singular boundary value problems of higher even order based on the theory of numerical analysis in the reproducing kernel space w 2 2 m 3 0 1 singular boundary value problem of sixth order has been discussed for the problem u 6 x a x u 4 x b x u x c x u x f x 0

applications of the pseudo residual free bubbles to the stabilization of convection diffusion reaction problems it is known that the enrichment of the polynomial finite element space of degree 1 by bubble functions results in a stabilized scheme of the supg type for the convection diffusion reaction problems in particular the residual free bubbles rfb can assure stabilized methods but they are usually difficult to compute unless the configuration is simple therefore it is important to devise numerical algorithms that provide cheap approximations to the rfb functions contributing a good stabilizing effect to the numerical method overall here we propose a stabilization technique based on the rfb method and particularly designed to treat the most interesting case of small diffusion we replace the rfb functions by their cheap yet efficient approximations which retain the same qualitative behavior the approximate bubbles are computed on a suitable sub grid the choice of whose nodes are critical and determined by minimizing the residual of a local problem with respect to l 1 norm the resulting numerical method has similar stability features with the rfb method for the whole range of problem parameters this fact is also confirmed by numerical experiments we also note that the location of the sub grid nodes suggested by the strategy herein coincides with the one in brezzi et al math models methods appl sci 13 445 461 2003

applications of the pseudo residual free bubbles to the stabilization of convection diffusion problems abstract residual free bubbles have been recently introduced in order to compute optimal values for the stabilization methods a la hughes franca however unless in very special situations one dimensional problems limit cases etc they require the actual solution of pde problems the bubble problems in each element thus they are very difficult to be used in practice in this paper we present for the special case of convection dominated elliptic problems a cheap way to compute approximately the solution of the bubble problem in each element this provides as a consequence a cheap way to compute good approximations for the optimal values of the stabilization parameters

multiple positive solutions of a m point boundary value problem for 2nth order singular integro differential equations in banach spaces abstract in this paper we obtain the existence of multiple positive solutions of a m point boundary value problem for 2 n th order singular nonlinear integro differential equations in a banach space by means of fixed point index theory of completely continuous operators

an arbitrary lagrangian eulerian finite element method for solving three dimensional free surface flows abstract this paper discusses numerical solution of unsteady three dimensional free surface flows the governing equilibrium equations are written in the framework of the arbitrary lagrangian eulerian kinematic description the corresponding variational formulation is established afterwards since the variational problems are nonlinear with respect to the moving coordinates a second order approximate variational problem is derived after a consistent linearization of the referential motion stability of the discrete formulations is ensured with the help of a new stabilization method a robust preconditioned gmres algorithm is then used to solve the resulting set of nonlinear equations finally the computational algorithms are assessed through numerical studies of various problems a large sloshing flow in a three dimensional reservoir a discharge flow from a reservoir simulation of a liquid vortex produced inside a cylindrical container with a disk rotating at the bottom and a three dimensional practical hydraulic problem

an anisotropic gls stabilized finite element method for incompressible flow problems abstract we consider a stabilized finite element approximation of incompressible flow problems in primitive velocity pressure variables which is based on a gls formulation equal order interpolation for the velocity and the pressure can be employed with this formulation the method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios rather than using a single stabilization parameter within each element the jacobian matrix of the affine transformation from the reference element is employed for stabilization purposes stability and anisotropic error estimates in a suitable mesh dependent norm are proved for the linear stokes problem numerical results confirm the accuracy and robustness of the proposed method compared to similar previous stabilized schemes

on a two level finite element method for the incompressible navier stokes equations we consider the galerkin finite element method for the incompressible navier stokes equations in two dimensions where the finite dimensional space s employed consist of piecewise polynomials enriched with residual free bubble rfb functions to find the bubble part of the solution a two level finite element method tlfem is described and its application to the navier stokes equation is displayed numerical solutions employing the tlfem are presented for three benchmark problems we compare the numerical solutions using the tlfem with the numerical solutions using a stabilized method

multiple positive solutions of a boundary value problem for a class of 2 nth order m point singular integro differential equations in banach spaces in this paper we obtain the existence of multiple positive solutions of a boundary value problem for 2nth order singular nonlinear integro differential equations in a banach space by means of fixed point index theory of completely continuous operators

positive solutions of 2nth order ordinary differential equations with multi point boundary conditions in this paper we study the existence of positive solutions for 2nth order n 1 boundary value problems 1 nu 2n t f t u 0 t 1 subject to the 2 n m point boundary value conditions u 2j 0 u 2j 1 0 j 0 1 2 m m n 2 u 2j 0 bju 2j j 1 0 u 2j 1 dju 2j j 2 0 j m 1 n 1 where bj 0 dj 0 0 j 1 j 2 1 j m 1 n 1 by means of the fixed point theorems and the lower and upper solution method some results on the existence of positive solutions to the above 2 n m point boundary value problems are obtained

a necessary and sufficient condition for 2nth order singular super linear m point boundary value problems abstract in this paper we study the existence of positive solutions for singular super linear m point boundary value problems of 2nth order ordinary differential equations a necessary and sufficient condition for the existence of c 2 n 2 0 1 positive solutions as well as c 2 n 1 0 1 positive solutions is given by means of the fixed point theorems on cones

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

a finite difference scheme for multidimensional convection diffusion reaction equations abstract in this paper a finite difference scheme is proposed for multidimensional convection diffusion reaction equations particularly designed to treat the most interesting case of small diffusion it is based closely on the work endur and nesliturk 2011 application of the method to multidimensional convection diffusion reaction equation is based on a simple splitting of the convection diffusion reaction equation and then joining their approximations obtained with endur and nesliturk 2011 the method adapts very well to all regimes with continuous transitions from one regime to another numerical tests show good performance of the method and superiority with respect to well known stabilized finite element methods

notes on ruscheweyh s multiplier conjecture abstract in this note we show that ruscheweyh s multiplier conjecture is true in several special cases the results obtained here are closely related to the partial sums of certain analytic functions defined by means of univalent functions we also answer a question of ponnusamy concerning the n th partial sums of certain univalent functions

finite difference approximations of multidimensional convection diffusion reaction problems with small diffusion on a special grid a numerical scheme for the convection diffusion reaction cdr problems is studied herein we propose a finite difference method on a special grid for solving cdr problems particularly designed to treat the most interesting case of small diffusion we use the subgrid nodes in the link cutting bubble lcb strategy 5 to construct a numerical algorithm that can easily be extended to the higher dimensions the method adapts very well to all regimes with continuous transitions from one regime to another we also compare the performance of the present method with the streamline upwind petrov galerkin supg and the residual free bubbles rfb methods on several benchmark problems the numerical experiments confirm the good performance of the proposed method

a priori error analysis of residual free bubbles for advection diffusion problems we develop an a priori error analysis of a finite element approximation to the elliptic advection diffusion equation eps delta u conv cdot nabla u f subject to a homogeneous dirichlet boundary condition based on the use of residual free bubble functions an optimal order error bound is derived in the so called stability norm biggl eps nabla v 2 l 2 omega sum t h t conv cdot nabla v 2 l 2 t biggr 1 2 where ht denotes the diameter of element t in the subdivision of the computational domain

positive solutions for a class of 2nth order singular boundary value problems abstract we establish sufficient and necessary conditions for guaranteeing the existence of c 2 n 2 0 1 as well as c 2 n 1 0 1 positive solutions for 2 n th order singular boundary value problems the arguments are based upon the fixed point theorem an the maximal principle as well as constructing lower and upper solutions our nonlinearity f t x 1 x 2 x n may be singular at x i 0 i 1 2 n t 0 and or t 1 meanwhile an example is worked out to demonstrate the main results

bubble and multiscale stabilization of bilinear finite element methods for transient advection diffusion equations on rectangular grids in this paper a petrov galerkin type stabilization for a time dependent advection diffusion equation is considered we first enrich the bilinear test space with bubble functions and the bilinear trial space with a special combination of bubble and multiscale functions for the steady state advection diffusion equation it is known that solving the residual equation obtained by the bubble elimination procedure is as difficult as solving the steady case of the original problem which makes the enriched methods quite costly for two dimensional problems in this study we instead utilize their cheap and efficient approximations in each rectangular element then we suggest a recipe for a proper adaptation of these functions combined with the generalized euler time integration to the unsteady problem some numerical experiments for typical model problems are presented to illustrate the accuracy of our method

integrated partial sums of convolutions of univalent functions abstract let s be the set of normalized univalent functions we show that for f z k 1akzk g z k 1bkzk s formula if n 6 for n 4 we obtain the corresponding result if g is restricted to the class of close to convex functions the results that we obtain are special cases of a multiplier conjecture for univalent functions as well as an extension of an old result about sections of univalent functions

positive solutions for 2nth order singular sub linear m point boundary value problems abstract this paper investigates the existence of positive solutions for 2nth order singular sub linear m point boundary value problems firstly we establish a comparison theorem then we define a partial ordering in c2n 2 a b c2n a b and construct lower and upper solutions to give a necessary and sufficient condition for the existence of c2n 2 0 1 as well as c2n 1 0 1 positive solutions our nonlinearity f t x1 x2 xn may be singular at xi 0 i 1 2 n t 0 and or t 1

on the choice of stabilizing sub grid for convection diffusion problem on rectangular grids a stabilizing sub grid which consists of a single additional node in each rectangular element is analyzed for solving the convection diffusion problem especially in the case of small diffusion we provide a simple recipe for spotting the location of the additional node that contributes a very good stabilizing effect to the overall numerical method we further study convergence properties of the method under consideration and prove that the standard galerkin finite element solution on augmented grid produces a discrete solution that satisfies the same type of a priori error estimates that are typically obtained with the supg method some numerical experiments that confirm the theoretical findings are also presented

global and local error analysis for the residual free bubbles method applied to advection dominated problems we prove the stability and a priori global and local error analysis for the residual free bubbles rfb finite element method applied to advection dominated advection diffusion problems

on the stability of residual free bubbles for convection diffusion problemsand their approximation by a two level finite element method we consider the galerkin finite element method for partial diffferential equations in two dimensions where the finite dimensional space used consists of piecewise isoparametric polynomials enriched with bubble functions writing l for the differential operator we show that for elliptic convection diffusion problems the component of the bubble enrichment that stabilizes the method is essentially equivalent to a petrov galerkin method with an l spline exponentially fitted trial space and piecewise polynomial test space the remaining component of the bubble influences the accuracy of the method a stability inequality recently obtained by brezzi franca and russo for a limiting case of bubbles applied to convection diffusion problems is shown to be slightly weaker than the standard stability inequality that is obtained for the sdfem supg method thereby demonstrating that the bubble approach is in general slightly less stable than the streamline diffusion method when the trial functions are piecewise linear we show that residual free bubbles are as stable as sdfem supg and we extend this stability inequality to include positive mesh peclet numbers in the convection dominated regime approximate computations of the residual free bubbles are performed using a two level finite element method

on the choice of a stabilizing subgrid for convection diffusion problems abstract supg and residual free bubbles are closely related methods that have been used with success to stabilize a certain number of problems including advection dominated flows in recent times a slightly different idea has been proposed to choose a suitable subgrid in each element and then solving standard galerkin on the augmented grid for this however the correct location of the subgrid node s plays a crucial role here for the model problem of linear advection diffusion equations we propose a simple criterion to choose a single internal node such that the corresponding plain galerkin scheme on the augmented grid provides the same a priori error estimates that are typically obtained with supg or rfb methods

the method of lower and upper solutions for a bending of an elastic beam equation abstract in this paper by combining a new maximum principle and the theory of the two parameter linear eigenvalue problem we develop the monotone method in the presence of lower and upper solutions for the problem u 4 x f x u x u x 0 x 1 u 0 u 1 u 0 u 1 0 where f 0 1 r r r is continuous

existence of solutions for 2n order boundary value problem in this paper we discuss the existence of solutions for the 2n order boundary value problem 1 nu 2 n t f t u t u t u 2 n 2 t 0r is continuous

on a theorem of kobori let s and s denote the well known classes of normalized analytic functions which are respectively univalent and starlike in z 1 a theorem of kobori states that for a function g z email protected k 2 a kz email protected l the sequence of the nth sections g n z email protected k 21ka kz kmust be starlike in z 12 recently silverman 1 gruenberg et al 2 and ronning 3 extended the above result in this note we first improve the results of ilieff 4 ruscheweyh 5 and silverman 1 we then give a remarkable simple proof of a result of gruenberg et al 2 and ronning 3 that s 4 z is starlike in z 12 for email protected

a class of 2nth order singular boundary value problems abstract this paper investigates the existence of positive solutions for 2 n th order n 1 singular sub linear boundary value problems first of all we establish the maximal principle and some important lemmas then we define a partial ordering in c 2 n 2 0 1 c 2 n 0 1 and construct lower and upper solutions to give a necessary and sufficient condition for the existence of c 2 n 2 0 1 as well as c 2 n 1 0 1 positive solutions our nonlinearity f t x 1 x 2 x n may be singular at x i 0 i 1 2 n t 0 and or t 1

a stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation abstract a stabilized finite element formulation for incompressible viscous flows is derived the starting point are the modified navier stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus fic procedure application of the standard finite element galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields the fic method also provides a natural explanation for the stabilization terms appearing in all equations for both the navier stokes and the simpler stokes equations transient solution schemes with enhanced stabilization properties are also proposed finally a procedure for computing the stabilization parameters is presented

the method of lower and upper solutions for second third fourth and higher order boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u n t t u t u i a u i b i r i 0 n 1 where is a caratheodory function we obtain necessary and sufficient conditions in to guarantee the existence of solutions between a lower solution and an upper solution for n 2 if n 3 either or and n 4 if furthermore we obtain sufficient conditions in for n 2 k 6 when

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