fixed point theory for self maps between frechet spaces abstract using krasnoselskii s fixed point theorem in a cone we present a new fixed point theory for multivalued self maps between frechet spaces our analysis relies on a diagonal process and a result on hemicompact maps due to k k tan and x z yuan 1994 j math anal appl 185 378 390 an application is given to illustrate the theory

runge kutta methods applied to fully implicit differential algebraic equations of index 1 in this paper we study the order of runge kutta methods applied to differential algebraic equations of index one we derive general order conditions for the local order kl and give a convergence result which shows that the order kg of the global error satisfies kg kl 1 we also describe some numerical experiments which are in agreement with our results

asymptotic boundary value problems in banach spaces abstract a continuation principle is given for solving boundary value problems on arbitrary possibly infinite intervals to caratheodory differential inclusions in banach spaces for this aim the appropriate fixed point index is defined to condensing decomposable multivalued operators in frechet spaces this index extends and unifies the one for compact maps in andres et al trans amer math soc 351 1999 4861 4903 as well as the one for operators in banach spaces in bader ph d thesis university of munich 1995 as an application we prove the existence of an entirely bounded solution of a semilinear evolution inclusion

a comparison of preconditioned iterative techniques using rapid operator application against direct solution methods the p version of the finite element method which uses high order hierarchic basis functions within an element allows for ease of adaptive computation and high accuracy with relatively few degrees of freedom however the solution time and storage requirements for large 3 d problems can be very high when direct methods are used to factor global matrices iterative techniques with rapid operator application have minimal storage requirements because neither element nor global matrices are formed but may not converge rapidly enough we study an approach that attempts to combine the two methods by using direct factorization of the matrix corresponding to low level polynomials as a preconditioner to an iterative method at a higher polynomial level this resulting solution scheme converges more rapidly than an unpreconditioned scheme but has much lower storage requirements than direct methods we illustrate the effectiveness of this scheme on some large three dimensional problems in structural analysis

multiple positive solutions for a class of integral inclusions this paper deals with sufficient conditions for the existence of at least two positive solutions for a class of integral inclusions arising in the traffic theory to show our main results we apply a norm type expansion and compression fixed point theorem for multivalued map due to agarwal and o regan a note on the existence of multiple fixed points for multivalued maps with applications j differential equation 160 2000 389 403

fifteen node tetrahedral elements for explicit methods in nonlinear solid dynamics abstract despite the ease in meshing and benefits for modeling flexure curved shapes etc second order tetrahedral elements are not contained in typical explicit solid dynamic programs this is primarily due to the lack of both a satisfactory consistent nodal loading distribution and mass lumping technique row summation lumping for instance produces negative vertex node masses for the popular ten node serendipity tetrahedron which also has zero vertex node loads resulting from a constant pressure on an element face this has led to piecewise composites of four node tetrahedrons to represent a ten node one in explicit codes in this paper truly second order fifteen node formulations for compressible and for nearly incompressible materials are presented and evaluated in addition to producing all positive nodal loads from a uniform traction row summation mass lumping for the fifteen node element is shown to produce all positive nodal masses performance is assessed in standard benchmark problems and practical applications using various elastic and elastic plastic material models and involving very large strains deformations severe distortions and contact impact comparisons are also made with several first order elements and second order hexahedral formulations the offered elements performed satisfactorily in all examples as recently found for second order hexahedral elements it is shown that the inclusion of face and centroidal nodes is vital for robust performance with row summation lumping and high order quadrature rules are crucial with explicit methods these second order elements are shown to be viable for practical applications especially using today s parallel computers whereas the reliable performance is generally attained at significant computational expense compared with first order and brick types these elements can be more computationally competitive in flexure and have the desirable trait that they are amenable to automatic tetrahedral meshing software

some random approximation theorems with applications fan 8 proved a very interesting theorem which provides a tool to study xed point theory in connection with best approximation various aspects of that theorem have been studied by fan 9 ha 10 singh and watson 22 lin 14 lin and yen 16 and many others fan s theorem has been of great importance in nonlinear analysis approximation theory game theory and minimax theorems the study of random approximations and random xed points have been a very active area of research in probabilistic functional analysis in the last decade see sehgal and waters 21 sehgal and singh 20 papageorgiou 18 lin 15 xu 25 tan and yuan 23 24 and beg and shahzad 1 4 most random xed point theorems in banach spaces deal with condensing or nonexpansive random operators what about the random operators which are neither of the above cases the interesting case would be a 1 set contractive random operator the class of 1 set contractive random operators includes condensing and nonexpansive random operators besides it also includes other important random operators such as semicontractive random operators and lane locally almost nonexpansive random operators recently beg and shahzad 3 studied these random operators in details and gave many results regarding random approximations and random

multiplicity of positive radial solutions for an elliptic inclusion system on an annulus in this paper we present the sufficient conditions for existence and multiplicity of positive radial solutions for elliptic inclusion systems our results are obtained by utilizing the generalization of leggett and williams s fixed point theorem established in this paper for the norm type cone expansion and compression of multivalued operators

random fixed point equations and inverse problems using collage method for contraction mappings abstract in this paper we are interested in the direct and inverse problems for the following class of random fixed point equations t w x w x w where t x x is a given operator is a probability space and x is a polish metric space the inverse problem is solved by recourse to the collage theorem for contractive maps we then consider two applications i random integral equations and ii random iterated function systems with greyscale maps rifsm for which noise is added to the classical ifsm

coincidence points generalized i nonexpansive multimaps and applications we establish coincidence point results for multimaps satisfying generalized i nonexpansive type conditions several invariant approximation results are obtained as applications a random coincidence point result is also proved and as applications random invariant approximation results are obtained our results unify extend and complement several well known results

p refinement and p threads abstract p type refinement leads to exponential decay of numerical errors for sufficiently smooth solutions and has been used effectively in turbulence and structural mechanics simulations in the context of spectral and hp finite element discretizations however it induces a computational cost of o p d 1 in d dimensions which is higher than lower order methods in this paper we demonstrate that by employing multi threading within mpi processes we manage to counter balance the cost increase associated with p refinement this approach reduces effectively the wall clock time and keeps it essentially constant as the polynomial order is increased while achieving exponential convergence rate since the number of threads within mpi processes can be dynamically adjusted through thread library functions the algorithm can be readily adapted for dynamic p refinement the resulting hybrid mpi threads dual level parallelism is particularly suitable for modern supercomputers consisting of symmetric multiprocessor nodes we demonstrate this approach in simulations of two three dimensional fluid dynamics problems

a note on the existence of multiple fixed points for multivalued maps with applications abstract in this paper we discuss the existence of multiple fixed points for multivalued maps our fixed point results automatically lead to new existence principles for integral inclusions

cone compression and expansion fixed point theorems in frechet spaces with applications abstract new fixed point theory for multivalued maps between frechet spaces is presented applications are given to illustrate how the theory can be applied in practice

axisymmetric indentation of a thin incompressible elastic layer axisymmetric indentation of an incompressible elastic layer by a frictionless rigid sphere is considered estimates of the contact radius and the force required to produce a given indentation are given when the thickness of the layer is small compared to the contact radius the elastic layer is either bonded to or slips along a rigid substrate the estimates are obtained by asymptotically matching a lubrication type expansion valid in the contact region to an edge layer expansion studied using the wiener hopf technique a substantially larger force is required to equally indent a bonded layer compared to a slipping layer in the former case the force is inversely proportional to the cube of the layer thickness rather than to the layer thickness itself if the layer is free to slip

fixed point theory for admissible multimaps defined on closed subsets of frechet spaces abstract this paper presents new fixed point results for a general class of maps defined on frechet spaces our results in particular apply to kakutani acyclic o neill approximable admissible with respect to gorniewicz and u c maps

on order reduction for runge kutta methods applies to differential algebraic systems and to stiff systems of odes in this short note the order reduction results of petzold siam j numer anal 23 1986 pp 837 852 for implicit runge kutta methods applied to index 1 differential algebraic systems are extended to include a larger class of methods the relationship between the order reduction results for differential algebraic systems and recent results for stiff systems of ordinary differential equations is explained

integral φ type contractions and existence of continuous solutions for nonlinear integral inclusions abstract in this paper we discuss a general common fixed point theorem of integral type for two pairs of weakly compatible mappings satisfying certain integral type implicit relations in symmetric spaces by using the notion of a pair of mappings satisfying property e a our main result improves and extends the recent results of aliouche a aliouche a common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type j math anal appl 322 2006 796 802 pathak tiwari and khan h k pathak rakesh tiwari m s khan a common fixed point theorem satisfying implicit relation appl math e notes 7 2007 222 228 and several other known results subsequently a multi valued version of krasnoselski fixed point theorem in a cone is used to discuss the existence of c 0 t and l p 0 t solutions to nonlinear integral inclusion y t 0 t k t s a s g s y s f s y s y s ds which improves the recent result of agarwal meehan and o regan r p agarwal m meehan d o regan positive l p and continuous solutions for fredholm integral inclusions in set valued mappings with applications in nonlinear analysis gordon breach amsterdam simaa 4 2002 1 9

the numerical solution of higher index differential algebraic equations by implicit methods this paper studies the order stability and convergence properties of implicit runge kutta irk methods applied to differential algebraic systems with index greater than one these methods do not in general attain the same order of accuracy for higher index differential algebraic systems as they do for index 1 systems or for purely differential systems necessary and sufficient conditions on the method coefficients are derived to ensure that the local and global errors of the method attain a given order of accuracy for higher index linear constant coefficient systems irk methods applied to nonlinear semi explicit index 2 systems are studied and a sufficient set of conditions is derived which ensures that a method is accurate to a given order for these systems finally some numerical experiments are presented that illustrate the theoretical results and demonstrate the effects of roundoff errors on the solution

fixed points of discontinuous multivalued increasing operators in banach spaces with applications by using relatively weakly compactness conditions we obtain existence theorems of fixed points for discontinuous multivalued increasing operators in banach spaces as an application we utilize the results obtained in section 2 to lead to the existence principles for integral inclusions of hammerstein type multivalued maps

boundary value problems on infinite intervals and semiconductor devices the nonlinear differential equation y f x y y 0 x f satisfying bernstein type growth conditions we also examine an important application which occurs in the theory of semiconductor devices

p 2 continuous finite elements on tetrahedra with local mass matrix inversion abstract when using continuous finite element methods for unsteady simulations one must invert a global mass matrix even for an explicit time advancement scheme in this paper we develop a local mass matrix inversion procedure for p 2 c 0 tetrahedral elements and also show that unlike on triangles b t helenbrook siam j numer anal 47 2009 1304 1318 this procedure does not generalize to higher order for the p 2 basis it is demonstrated that the accuracy of the local inversion is better than any previous mass lumping scheme this allows the development of fast and low memory iterative algorithms as well as accurate explicit computations to be performed the efficiency of using the approach as an iterative relaxation scheme for solving the helmholtz equation is shown by comparing to more standard approaches such as p multigrid with jacobi relaxation lastly the local mass matrix inversion is used to march the unsteady heat equation explicitly with third order spatial accuracy

on continuity and compactness of some nonlinear operators associated with differential equations in noncompact intervals soit x t f t x t t j x s ou jcr est un intervalle donne f j r n r n est une fonction continue et s un sous ensemble de c j r n l espace des fonctions continues de j dans r n on considere l equation operateur associee x t x ou t est un operateur non lineaire discontinu dans son domaine

optimization of high order diagonally implicit runge kutta methods abstract this article presents constrained numerical optimization of high order linearly and algebraically stable diagonally implicit runge kutta methods after satisfying the desired order conditions undetermined coefficients are optimized with respect to objective functions which consider accuracy stability and computational cost constraints are applied during the optimization to enforce stability properties to ensure a well conditioned method and to limit the domain of the abscissa two promising third order methods are derived using this approach labelled sdirk 3 1 2 2 3 l 14 and sdirk 3 1 4 l sa 5 both optimized schemes have a good balance of properties the relative error norm of the latter the l 2 norm scaled by a function of the number of implicit stages is a factor of two smaller than comparable methods found in the literature variations on these methods are discussed relative to trade offs in their accuracy and stability properties a novel fifth order scheme sdirk 5 1 5 l 02 is derived with a significantly lower relative error norm than the comparable fifth order a stable reference method in addition the optimized scheme is l stable the accuracy and relative efficiency of the runge kutta methods are verified through numerical simulation of van der pol s equation as well as numerical simulation of vortex shedding in the laminar wake of a circular cylinder and in the turbulent wake of a naca 0012 airfoil these results demonstrate the value of numerical optimization for selecting undetermined coefficients in the construction of high order runge kutta methods with a balance between competing objectives

robustness of isogeometric structural discretizations under severe mesh distortion abstract this paper investigates higher order and higher continuity functions in isogeometric structural analysis under distortion of the control and physical meshes first the concepts behind isogeometric analysis are briefly reviewed the effect of perturbing control points upon the geometrical mapping is observed in the one dimensional setting the concept is extended to multiple dimensions with a series of cases where the interior of a cube is distorted in different ways and patch tests are performed to assess accuracy a circular fillet patch is introduced through the appropriate degeneration of a control mesh in order to address the problem of modeling small features in finite element models the fillet patch is tested with two problems of linear elasticity and is shown to be accurate the investigation is further extended to the setting of large deformation nearly incompressible nonlinear elasticity with two examples which make use of the recently proposed f projection method

nonlinear urysohn discrete equations on the infinite interval a fixed point approach abstract this paper presents a variety of existence results for nonlinear urysohn discrete equations on the infinite interval in particular we consider for i 0 1 2 existence is established using fixed point arguments

a matrix d alembert formula for coupled wave initial value problems if c is an invertible matrix in cr r the coupled wave equation initial value problem utt c2uxx 0 u x 0 f x and ut x 0 g x for x is studied a matrix d alembert formula for the closed form solution of the coupled wave equation is given the approach is based on the fourier transform the holomorphic matrix functional calculus and some elements of complex variable functions for the scalar case the proposed d alembert formula coincides with the classical one

multiparametric shell eigenvalue problems abstract the eigenproblem for thin shells of revolution under uncertainty in material parameters is discussed here the focus is on the smallest eigenpairs shells of revolution have natural eigenclusters due to symmetries moreover the eigenpairs depend on a deterministic parameter the dimensionless thickness the stochastic subspace iteration algorithms presented here are capable of resolving the smallest eigenclusters in the case of random material parameters it is possible that the eigenmodes cross in the stochastic parameter space this interesting phenomenon is demonstrated via numerical experiments finally the effect of the chosen material model on the asymptotics in relation to the deterministic parameter is shown to be negligible

hybrid fixed points of multivalued operators in metric spaces with applications abstract this paper deals with the existence of hybrid fixed points involving two multivalued operators in a complete metric space our claim is also illustrated with applications to a class of integral inclusions for proving the existence results

goal oriented adaptive finite element methods for elliptic problems revisited a goal oriented a posteriori error estimation of an output functional for elliptic problems is presented continuous finite element approximations are used in quadrilateral and triangular meshes the algorithm is similar to the classical dual weighted error estimation however the dual weight contains solutions of the proposed patch problems the patch problems are introduced to apply clement and scott zhang type interpolation operators to estimate point values with the finite element polynomials the algorithm is shown to be reliable efficient and convergent

multiple positive solutions of some boundary value problems abstract we study the existence of multiple positive solutions of the equations u t u subject to linear boundary conditions we show that there are at least two positive solutions if t u is superlinear at one end point zero or infinity and sublinear at the other applications of these results are provided to yield multiple positive solutions of some elliptic boundary value problems on an annulus

on capacity computation for symmetric polygonal condensers abstract making use of two different analytical numerical methods for capacity computation we obtain matching to a very high precision numerical values for capacities of a wide family of planar condensers these two methods are based respectively on the use of the lauricella function bezrodnykh and vlasov 2002 bezrodnykh 2016 64 65 and riemann theta functions bogatyrev 2012 grigoriev 2013 bogatyrev and grigor ev 2017 bogatyrev and grigor ev 2018 we apply these results to benchmark the performance of numerical algorithms which are based on adaptive h p finite element method hakula et al 2011 2013 2018 and boundary integral method tsuji 1959 jaswon and symm 1977 albrecht and collatz 1980

a new method for theoretical analysis of static indentation test a new mathematical method was developed to study the indentation problem of an infinite elastic layer overlaid on a rigid foundation rigid flat ended cylindrical or spherical indenters are pressed onto the upper surface of the elastic layer causing a small deformation mode shear stresses between the indenter and the layer are assumed negligible and the layer is assumed to be either bonded or unbonded to the rigid foundation the problem is equivalent to a mixed boundary value problem of the theory of elasticity instead of using the fredholm integral equation reported in the literature the new approach obtained closed form solutions through an infinite series convergence can be achieved using less than 10 terms of the series

high order finite elements applied to the discrete boltzmann equation a discontinuous galerkin approach for solving the discrete boltzmann equation is presented allowing to compute approximate solutions for fluid flow problems based on a two dimensional high order finite element and an explicit euler time stepping scheme the d2q9 model is discretized and the results are compared to the exact solution of the navier stokes equation four numerical examples are considered including stationary and instationary problems with curved boundaries it is demonstrated that the proposed method allows to obtain the desired highly efficient exponential convergence copyright 2006 john wiley sons ltd

one step and extrapolation methods for differential algebraic systems the paper analyzes one step methods for differential algebraic equations dae in terms of convergence order in view of extrapolation methods certain perturbed asymptotic expansions are shown to hold for the special dae extrapolation solver based on the semi implicit euler discretization the perturbed order pattern of the extrapolation tableau is derived in detail the theoretical results lead to modifications of the known code the efficiency of the modifications is illustrated by numerical comparisons over critical examples mainly from chemical combustion

leggett williams norm type fixed point theorems for multivalued mappings this paper presents several norm type versions of the leggett williams fixed point theorem for multivalued maps with nonempty convex compact values

runge kutta methods and differential algebraic systems for the solution of differential algebraic systems only those runge kutta formulae with nonsingular coefficient matrix a have been considered up to now to retain the algorithmic simplicity of dirk formulae while overcoming order reduction a is allowed here to be singular algebraic conditions on the formula are given that are necessary and sufficient for it to solve unambiguously constant coefficient linear differential algebraic systems of arbitrary index for a special class the regular formulae an expression is derived for the local discretization error this expression reduces to the one known when the runge kutta matrix a is nonsingular the paper concludes with some computational illustrations

random fixed points for several classes of 1 ball contractive and 1 set contractive random maps a general random fixed point theorem for continuous random operators is proved as applications a number of random fixed points theorems for various classes of 1 set and 1 ball contractive random operators e g operators of contractive type with compact or completely continuous perturbations operators of semicontractive type etc are derived our results unify and extend most of the known random fixed points theorems 1991 ams subject classification 47h10 60h25

random fixed points of set valued maps some random fixed point theorems for set valued random operators under very mild conditions are established some recent results of o regan proc amer math soc 126 1998 3045 3053 and computers math applic 35 1998 27 34 are improved significantly the discussion in this paper underlines in addition to generality the unifying aspects of our result

spectral element method in time for rapidly actuated systems in this paper the spectral element se method is applied in time to find the entire time periodic or transient solution of time dependent differential equations the time periodic solution is computed by enforcing periodicity of the element set of particular interest are periodic forcing functions possessing high frequency content to maintain the spectral accuracy for such forcing functions an h refinement scheme is employed near the semi discontinuity without increasing the number of degrees of freedom time discretization by spectral elements is applied initially to a standard form of a set of linear first order differential equations subject to harmonic excitation and an excitation admitting rapid variation other case studies include the application of the se approach to parabolic and hyperbolic partial differential equations the first order form of these equations is obtained through semi discretization using conventional finite element spectral element and finite difference schemes element clustering h refinement is applied to maintain the high accuracy and efficiency in the region of the forcing function admitting rapid variation the convergence in time of the method is demonstrated in some cases machine precision is obtained with 25 degrees of freedom per cycle finally the method is applied to a weakly nonlinear problem with time periodic solution to demonstrate its future applicability to the analysis of limit cycle oscillations in aeroelastic systems

hypersingular residuals a new approach for error estimation in the boundary element method summary this paper presents a new approach for a posteriori pointwise error estimation in the boundary element method the estimator relies upon evaluation of the residual of hypersingular integral equations and is therefore intrinsic to the boundary integral equation approach a methodology is developed for approximating the error on the boundary as well as in the interior of the domain extensive computational experiments have been performed for the two dimensional laplace equation and the numerical results indicate that the error estimates successfully track the form of the exact error curve moreover a reasonable estimate of the magnitude of the actual error is also predicted

automatic integration of euler lagrange equations with constraints abstract numerical difficulties in the integration of euler lagrange and similar equations are discussed a technique for reducing their index from three to two is introduced and it is shown that variable order variable step bdf methods converge for these index two problems the practical application of this reduction in a numerical setting is examined

fixed point theorems for countably condensing maps on frechet spaces abstract new fixed point results for countably condensing operators defined on frechet spaces are presented applications to integral inclusions are also discussed

on weak residual error estimation a general framework for weak residual error estimators applying to various types of boundary value problems in connection with finite element and finite volume approximations is developed basic ideas commonly shared by various applications in error estimation and adaptive computation are presented and illustrated some numerical results are given to show the effectiveness and efficiency of the estimators

order results for implicit runge kutta methods applied to differential algebraic systems in this paper we study the order stability and convergence properties of implicit runge kutta methods applied to a relatively simple class of nonlinear differential algebraic systems these methods often do not attain the same order of accuracy for differential algebraic systems as they do for purely differential systems we derive a set of order conditions which the method coefficients should satisfy in addition to the usual order conditions to ensure a given order of accuracy and we present results on the stability and convergence properties of these methods

existence of ground states with exponential decay for semi linear elliptic equations in ofrn abstract in this paper we prove the existence of a positive solution tending exponentially to zero at infinity for a class of semi linear elliptic equations with nonconstant coefficients in ofr n

mid node admissible spaces for quadratic triangular 2d finite elements with one edge curved a robust element distortion metric based on the new concept of mid node admissible spaces for two dimensional quadratic triangular finite elements is developed the metric is based on the jacobian determinant over the entire element without requiring that it actually be computed everywhere on the element the metric is relatively inexpensive to compute especially for mildly distoted elements the metric is able to detect elementsof poor quality that other distortion metrics fall to detect it also has the ability to approve elements of good quality regardless of the extent to which they may appear geometrically distorted copyright 2001 john wiley sons ltd

dynamics in coupled oscillators with recurrent random forcing a pde approach the current paper is devoted to the study of coupled oscillators with recurrent random forcing special attention is given to the solutions having the same recurrence randomness as that of the forcing recurrent random solutions for short by embedding coupled oscillators into coupled parabolic equations it establishes a general theorem on the existence of recurrent random solutions it also finds conditions under which such solutions are unique when the recurrent forcing is actually quasi periodic or almost periodic recurrent solutions are refereed to as quasi periodic or almost periodic solutions in a weak sense and they are quasi periodic or almost periodic in the classical sense under the uniqueness conditions in addition applications of the general theory to coupled duffing type oscillators and josephson junctions are considered and the results obtained extend several existing ones for quasi periodic duffing oscillators

numerical analysis of singularities in two dimensions part 1 computation of eigenpairs a numerical method is described for the computation of eigenpairs which characterize the exact solution of linear second order elliptic partial differential equations in two dimensions in the vicinity of singular points the singularities may be caused by re entrant corners and abrupt changes in boundary conditions or material properties such singularities are of great interest from the point of view of failure initiation the eigenpairs characterize the straining modes and their amplitudes quantify the amount of energy residing in particular straining modes for this reason failure theories directly or indirectly involve the eigenpairs and their amplitudes this paper addresses the problem of determining the eigenpairs numerically on the basis of the steklov formulation numerical results are presented for several cases importantly the method is applicable to three dimensional cases

spectral element feti dp and bddc preconditioners with multi element subdomains abstract the discrete systems generated by spectral or hp version finite elements are much more ill conditioned than the ones generated by standard low order finite elements or finite differences this paper focuses on spectral elements based on gauss lobatto legendre gll quadrature and the construction of primal and dual non overlapping domain decomposition methods belonging to the family of balancing domain decomposition methods by constraints bddc and dual primal finite element tearing and interconnecting feti dp algorithms new results are presented for the spectral multi element case and also for inexact feti dp methods for spectral elements in the plane theoretical convergence estimates show that these methods have a convergence rate independent of the number of subdomains and coefficient jumps of the elliptic operator while there is only a polylogarithmic dependence on the spectral degree p and the ratio h h of subdomain and element sizes parallel numerical experiments on a linux cluster confirm these results for tests with spectral degree up to p 32 thousands of subdomains and coefficient jumps up to 8 orders of magnitude

three dimensional mixed explicit implicit generalized galerkin spectral element methods for high speed turbulent compressible flows abstract in high speed flows the interactions of shock waves with turbulent boundary layers are important design considerations because of the complex flowfields resulting in increased adverse pressure gradients skin friction and temperatures unsteadiness and three dimensional flowfield structure are also characteristic of shock wave turbulent boundary layer interactions such physical phenomena require sophisticated numerical schemes in the solution of governing equations the purpose of this paper therefore is to introduce an accurate and efficient approach the mixed explicit implicit generalized galerkin spectral element method mei gg sem with legendre polynomial spectral elements in which flowfield dependent implicitness parameters provide automatically adequate computational requirements for compressible and incompressible flows or high speed and low speed flows this is in contrast to the traditional approach in which all speed regime analysis requires a separate hyperbolic elliptic pressure equation for pressure correction if the flow becomes incompressible in the mei gg sem scheme mesh refinements are carried out adaptively until shock waves are resolved followed then by the adaptive increase of legendre polynomial degrees until turbulence microscales are resolved in which the traditional turbulence modeling is no longer required aimed toward direct numerical simulation in order to demonstrate the validity of the theory and numerical procedure two dimensional flat plate and compression corner high speed flows are investigated followed by a three dimensional sharp leading edged fin for swept shock wave turbulent boundary layer interactions comparisons of the present study with experimental measurements and other numerical studies show favorable agreement

bounds for positive solutions for a focal boundary value problem we will be concerned with the focal boundary value problem 1 n n p t ny t n f h t y t n 1y t iy 0 n iy b 1 0 0 i n 1 using cone theory in a banach space we show that under certain assumptions on f this focal boundary value problem has two positive solutions in the special case 2y t 1 h2 y t y t y 0 b 1 0 where 0 1 we are able to exhibit upper and lower bounds for these two positive solutions

random fixed points of 1 set contractive random maps in frechet spaces a random fixed point theorem for more general 1 set contractive random operators in frechet spaces is proved as applications some random fixed point theorems for nonexpansive semicontractive and lane random operators are also derived thus the results of itoh j math anal appl 67 1979 261 273 lin proc amer math soc 123 1995 1167 1176 proc amer math soc 103 1988 1129 1135 shahzad j math anal appl 203 1996 712 718 tan and yuan stochastic anal appl 15 1997 103 123 and xu proc amer math soc 110 1990 495 500 are extended

generalized multivalued quasi variational inequalities in this paper we introduce and study a new class of variational inequalities known as generalized multivalued quasi variational inequalities this class is the most general and unifying one using essentially the projection technique we establish the equivalence between this class and the implicit wiener hopf equations this equivalence is used to suggest a number of iterative algorithms for solving the generalized multivalued quasi variational inequalities the convergence analysis of these algorithms is also studied the results proved in this paper represent a significant improvement and refinement of the previously known results in this area

analytical parametric analysis of the contact problem of human buttocks and negative poisson s ratio foam cushions abstract analytical investigations on the contact problems between two homogeneous and isotropic soft bodies were performed to simulate the contact of human buttocks and seat cushions the cushion materials poisson s ratio were allowed to be negative the human buttocks were modeled as an ideal sphere with radius 15 cm and assumed to have a low young s modulus and a poisson s ratio close to 0 5 these parameters were held constant during our analysis peak contact pressure was reduced by adjusting the contour curvature of cushions according to hertz theory as expected moreover analysis by both the hertz model and a finite thickness 3d elasticity model showed that using negative poisson s ratio cushions could further reduce the pressure negative poisson s ratio cushions may be beneficial in the prevention of pressure sores or ulcers in the sick and in reduction of pressure induced discomfort in seated people

stability of runge kutta methods for stiff ordinary differential equations this work analyzes the integration of initial value problems for stiff systems of ordinary differential equations by runge kutta methods the author uses the characterization of stiff initial value problems due to kreiss the jacobian matrix is essentially negative dominant and satisfies a relative lipschitz condition the existence and regularity of the numerical solution are established and conditions under which the runge kutta formula is stable are given

implicit runge kutta methods for differential algebraic equations this paper deals with the numerical solution of semi explicit differential algebraic equations dae of index 1 a complete characterization of the order and convergence of implicit runge kutta irk methods for such equations is given the order results appear in a very simple and natural way that relies on the theory of rooted trees and butcher series developed by roche numer math 52 1988 pp 45 63

new fixed points results for 1 set contractive set valued maps abstract new fixed point theorems and random fixed point theorems are presented for multivalued maps

matching experimental and three dimensional numerical models for structural vibration problems with uncertainties abstract the simulation model which examines the dynamic behavior of real structures needs to address the impact of uncertainty in both geometry and material parameters this article investigates three dimensional finite element models for structural dynamics problems with respect to both model and parameter uncertainties the parameter uncertainties are determined via laboratory measurements on several beam like samples the parameters are then considered as random variables to the finite element model for exploring the uncertainty effects on the quality of the model outputs i e natural frequencies the accuracy of the output predictions from the model is compared with the experimental results to this end the non contact experimental modal analysis is conducted to identify the natural frequency of the samples the results show a good agreement compared with experimental data furthermore it is demonstrated that geometrical uncertainties have more influence on the natural frequencies compared to material parameters and material uncertainties are about two times higher than geometrical uncertainties this gives valuable insights for improving the finite element model due to various parameter ranges required in a modeling process involving uncertainty

g1 interpolation and geometry reconstruction for higher order finite elements abstract the paper proposes a new g1 interpolation and geometry reconstruction scheme for regular surfaces approximated with unstructured quadrilateral grids the parametrization is based on c1 transfinite interpolation and sixth order polynomials the g1 conforming approximation of surfaces guarantees continuity of surface normals and it is critical for higher order finite and boundary element discretizations on curvilinear domains the proposed interpolation reconstruction scheme is illustrated with a number of numerical examples including the geometry of human head

random fixed point theorems and approximation in cones a very general random fixed point theorem is first proved as applications some random approximation theorems and random fixed point theorems are obtained recent results due to itoh j math anal appl 67 1979 261 273 lin proc amer math soc 103 1988 502 506 and xu proc amer math soc 110 1990 495 500 either are improved or are direct consequences of our results the stochastic versions of the recent results of lin 1988 and li proc amer math soc 97 1986 277 280 are also given

existence of bounded solutions for multivalued differential systems on demontre l existence de solutions bornees pour le systeme x t a t x t f t x t x s sur un intervalle i reel non borne ou f est une application a valeur convexe semi continue superieurement a est une matrice n n avec conditions de caratheodory s est un sous ensemble d un espace de banach

reproducing kernel hierarchical partition of unity part i formulation and theory this work is concerned with developing the hierarchical basis for meshless methods a reproducing kernel hierarchical partition of unity is proposed in the framework of continuous representation as well as its discretized counterpart to form such hierarchical partition a class of basic wavelet functions are introduced based upon the built in consistency conditions the differential consistency conditions for the hierarchical kernel functions are derived it serves as an indispensable instrument in establishing the interpolation error estimate which is theoretically proven and numerically validated for a special interpolant with different combinations of the hierarchical kernels a synchronized convergence effect may be observed being different from the conventional legendre function based p type hierarchical basis the new hierarchical basis is an intrinsic pseudo spectral basis which can remain as a partition of unity in a local region because the discrete wavelet kernels form a partition of nullity these newly developed kernels can be used as the multi scale basis to solve partial differential equations in numerical computation as a p type refinement copyright 1999 john wiley sons ltd

the stress analysis of thin contact layers a singular perturbation method for integral equations in this paper a contact problem is considered with a circular indenter pressed normally against a semi infinite elastic composite that consists of a contact layer with uniform thickness welded tog

coincidences for admissible and φ maps and minimax inequalities abstract a coincidence theory for and admissible maps is presented in this paper one can also deduce from this theory new minimax inequalities of von neumann sion type

locking free mixed hp finite element methods for curvilinear domains mixed hp finite element methods fems are robust with respect to poisson ratio locking when straight sided quadrilateral elements are used for the p version which uses fixed and generally large elements curved elements are necessary to represent curved domains accurately we show that mixed hp curved quadrilateral elements retain the robustness of their straight sided counterparts provided degenerate elements are avoided we also show that hp version triangles are robust we use these concepts to develop a locking free fem for geometrically nonlinear elasticity

a mathematical approximation for the solution of a static indentation test abstract the classical contact problem of the indentation of a thin compressible linear elastic layer bonded to a rigid substrate is considered closed form mathematical approximations of the deformation are presented for the cases of plane indentation by a rectangular block and three dimensional indentation by a plane ended axisymmetric cyclinder the approximations are analyzed in the context of a static indentation test by comparison of applied load values to those obtained using a classical integral transform solution in the case of plane indentation the mathematical and classical predictions agree to within 2 relative error for aspect ratios between 0 1 and 1 0 and apparent poisson ratio between 0 0 and 0 3 comparisons for the axisymmetric case indicate a similar pattern the main advantage of the new approach is that it yields closed form approximations of the static indentation solution which can also capture the essential singular behavior

nonzero solutions of nonlinear systems of differential equations via fixed point theorems for multivalued maps in the present paper we consider a nonlinear system of differential equations x a t x x f t x and a condition x e b x t 0 where a t x is a n x n real matrix defined and continuous on a x r a denotes a compact interval of r f a x r r is continuous and b is a banach space of continuous functions to solve this problem we use a comparison technique and we reduce the existence of solutions for this problem to that of a fixed point of a suitably defined multivalued map s see also anichini l kartsatos 3 and schmitt 4 in these papers the eilenberg montgomery futed point theorem is applied first we consider the problem x a x x and the condition using the eilenberg montgomery theorem 3 1 of 3 fixed point theorem we improve