pseudo divergence free element free galerkin method for incompressible fluid flow abstract incompressible modeling in finite elements has been a major concern since its early developments and has been extensively studied however incompressibility in mesh free methods is still an open topic thus instabilities or locking can preclude the use of mesh free approximations in such problems here a novel mesh free formulation is proposed for incompressible flow it is based on defining a pseudo divergence free interpolation space that is the finite dimensional interpolation space approaches a divergence free space when the discretization is refined note that such an interpolation does not include any overhead in the computations the numerical evaluations are performed using the inf sup numerical test and two well known benchmark examples for stokes flow

predictor corrector iterative algorithms for solving generalized mixed variational like inequalities the concept of partially relaxed h strong monotonicity of set valued mappings is introduced by applying the auxiliary variational inequality technique some new predictor corrector iterative algorithms for solving generalized mixed variational like inequalities are suggested and analyzed the convergence of the algorithms only need the continuity and the partially relaxed h strongly monotonicity of set valued mappings the algorithm and convergence result are new and generalize some known results in literatures

new approximation schemes for general variational inequalities in this paper we suggest and consider a class of new three step approximation schemes for general variational inequalities our results include ishikawa and mann iterations as special cases we also study the convergence criteria of these schemes

perturbed proximal point algorithms for general quasi variational like inclusions in this paper we introduce two new concepts of subdifferential and proximal mappings of proper functionals on hilbert spaces the existence and lipschitz continuity of proximal mapping of a proper functional are proved by applying these concepts we introduce and study a class of general quasi variational like inclusions and develop some new perturbed proximal point algorithms of mann and ishikawa type for finding the approximate solutions of the general quasi variational like inclusions the convergence criteria of the sequences of approximate solutions generated by these new algorithms are also discussed our algorithms and results improve and generalize many known results in the literature

mixed quasi variational inequalities in this paper we use the resolvent operator and auxiliary principle techniques to suggest and analyze several iterative algorithms for solving mixed quasi variational inequalities and related problems we study the convergence criteria of these algorithms under mild conditions we also study the global stability and existence of a unique solution of these quasi variational inequalities by using the dynamical systems approach our results represent refinement and improvement of the previously known results for variational inequalities

a variational like inequality for multifunctions with applications abstract we study a variational like inequality problem for a multifunction a certain relevant complementarity problem is defined we establish some existence theorems for the above two problems an application to convex mathematical programming is also shown

auxiliary principle and iterative algorithms for generalized set valued strongly nonlinear mixed variational like inequalities in this paper we extend the auxiliary principle technique to study a class of generalized set valued strongly nonlinear mixed variational like inequalities we prove the existence of a solution of the auxiliary problem for the generalized set valued strongly nonlinear mixed variational like inequalities construct the iterative algorithm for the generalized set valued strongly nonlinear mixed variational like inequalities and show the existence of a solution of the generalized set valued strongly nonlinear mixed variational like inequality by using the auxiliary principle technique we also prove the convergence of iterative sequences generated by the algorithm

an extended pressure finite element space for two phase incompressible flows with surface tension we consider a standard model for incompressible two phase flows in which a localized force at the interface describes the effect of surface tension if a level set or vof method is applied then the interface which is implicitly given by the zero level of the level set function is in general not aligned with the triangulation that is used in the discretization of the flow problem this non alignment causes severe difficulties w r t the discretization of the localized surface tension force and the discretization of the flow variables in cases with large surface tension forces the pressure has a large jump across the interface in standard finite element spaces due to the non alignment the functions are continuous across the interface and thus not appropriate for the approximation of the discontinuous pressure in many simulations these effects cause large oscillations of the velocity close to the interface so called spurious velocities in this paper for a simplified model problem we give an analysis that explains why known standard methods for discretization of the localized force term and for discretization of the pressure variable often yield large spurious velocities in the paper s grosz a reusken finite element discretization error analysis of a surface tension force in two phase incompressible flows preprint 262 igpm rwth aachen siam j numer anal accepted for publication we introduce a new and accurate method for approximation of the surface tension force in the present paper we use the extended finite element space xfem presented in n moes j dolbow t belytschko a finite element method for crack growth without remeshing int j numer meth eng 46 1999 131 150 t belytschko n moes s usui c parimi arbitrary discontinuities in finite elements int j numer meth eng 50 2001 993 1013 for the discretization of the pressure we show that the size of spurious velocities is reduced substantially provided we use both the new treatment of the surface tension force and the extended pressure finite element space

iterative algorithm of solutions for generalized mixed implicit equilibrium like problems in this paper we introduce a new class of generalized mixed implicit equilibrium like equilibrium problems gmielp by using auxiliary principle technique some new predictor corrector iterative algorithms for solving generalized mixed implicit equilibrium like problems are suggested and analyzed the convergence of the suggested methods only requires the continuity and the partially relaxed email protected monotonicity of mappings

a multi objective programming approach to 1 5 dimensional assortment problem in this paper we study a 1 5 dimensional cutting stock and assortment problem which includes determination of the number of different widths of roll stocks to be maintained as inventory and determination of how these roll stocks should be cut by choosing the optimal cutting pattern combinations we propose a new multi objective mixed integer linear programming milp model in the form of simultaneously minimization two contradicting objectives related to the trim loss cost and the combined inventory cost in order to fulfill a given set of cutting orders an equivalent nonlinear version and a particular case related to the situation when a producer is interested in choosing only a few number of types among all possible roll sizes have also been considered a new method called the conic scalarization is proposed for scalarizing non convex multi objective problems and several experimental tests are reported in order to demonstrate the validity of the developed modeling and solving approaches

algorithm for generalized multivalued variational inequalities in hilbert spaces abstract we introduce a new class of generalized multivalued variational inequality problems 1 1 which contain several existing variational inequality problems as special cases an iterative algorithm for finding approximate solutions of problem 1 1 is considered several convergence results for this algorithm are derived and in particular several existence results of problems 1 1 are obtained we also introduce a new class of generalized multivalued complementarity problems 5 1 which also contain several known complementarity problems as special cases it is shown that problem 5 1 is equivalent to problem 1 1 of special type from which several existence results of problem 5 1 are obtained

solvability of multivalued general mixed variational inequalities in this paper we use the auxiliary principle technique to suggest a new class of predictor corrector algorithms for solving multivalued general mixed variational inequalities the convergence of the proposed method only requires the partially relaxed strong monotonicity of the operator which is weaker than co coercivity as special cases we obtain a number of known and new results for solving various classes of variational inequalities

predictor corrector iterative algorithms for solving generalized mixed quasi variational like inclusion by applying the concept of partially relaxed h strong monotonicity of set valued mappings due to author and the auxiliary variational inequality technique some new predictor corrector iterative algorithms for solving generalized mixed quasi variational like inclusions are suggested and analyzed the convergence of the algorithms only need the continuity and the partially relaxed h strongly monotonicity of set valued mappings the algorithm and convergence result are new and generalize some recent known results in literatures

a new class of iterative algorithms for approximation solvability of nonlinear variational inequalities abstract consider the convergence of the projection methods based on a new iterative algorithm for the approximation solvability of the following class of nonlinear variational inequality nvi problems find an element x k such that t x x x 0 for all x k where t k h is a mapping from a nonempty closed convex subset k of a real hilbert space h into h the new iterative procedure is characterized as a nonlinear variational inequality for any arbitrarily chosen initial point x0 k and for constants and 0 pt y k x k 1 y k x x k 1 0 for all x k and for k 0 where t x k y k x k x y k 0 for all x k this nonlinear variational inequality type algorithm has an equivalent projection formula x k 1 p k y k pt y k where y k p k x k t x k for the projection pk onto k

generalized mixed quasi variational like inequalities in this paper we use the auxiliary principle technique to suggest and analyze some iterative methods for solving generalized mixed quasi variational like inequalities we show that the convergence of the proposed method requires either pseudomonotonicity or partially relaxed strongly monotonicity under some mild condition as special cases one can obtain a number of new and known algorithms for solving variational inequalities and complementarity problems our results represent significant and important refinements of the previously known results

gap function and global error bounds for generalized mixed quasi variational inequalities in this paper we obtain some gap functions for generalized mixed quasi variational inequality problems in terms of regularized gap function and d gap function further by using these gap functions we obtain global error bounds for the solution of generalized mixed quasi variational inequality problems in hilbert spaces the results obtained in this paper generalize and improve some corresponding known results in literatures

a modified forward backward splitting method for maximal monotone mappings we consider the forward backward splitting method for finding a zero of the sum of two maximal monotone mappings this method is known to converge when the inverse of the forward mapping is strongly monotone we propose a modification to this method in the spirit of the extragradient method for monotone variational inequalities under which the method converges assuming only the forward mapping is lipschitz continuous on some closed convex subset of its domain the modification entails an additional forward step and a projection step at each iteration applications of the modified method to decomposition in convex programming and monotone variational inequalities are discussed

algorithm of solutions for mixed implicit quasi variational inequalities with fuzzy mappings abstract in this paper by applying the auxiliary variational principle technique some existence theorems of solutions for a class of mixed implicit quasi variational inequalities with fuzzy mappings are proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria is also given as special cases of these results the open problem put forward by noor is answered positively our results are new and generalize a number of known results to mixed implicity quasi variational inequalities with fuzzy mappings

variational formulations for surface tension capillarity and wetting the interest in the simulation of flows with significant surface tension effects has grown significantly in recent years this has been driven by the substantial advances made in the measurement and manufacturing of microscopic systems since at small length scales surface phenomena are dominant in this article surface tension capillarity and wetting effects are discussed in terms of the virtual work principle and shape sensitivity starting from first principles and arriving at variational formulations that are adequate for numerical treatment by finite elements for example to make the exposition self contained some elements of differential geometry are recalled using a formulation that is fully in cartesian coordinates and may thus be more friendly to readers not familiar with covariant derivatives all necessary results are proved in this cartesian formulation several numerical examples computed with a finite element level set formulation are used to illustrate this challenging physical problem

fuzzy nonlinear set valued variational inclusions the purpose of this paper is to study a new class of fuzzy nonlinear set valued variational inclusions in real banach spaces by using the fuzzy resolvent operator techniques for m accretive mappings we establish the equivalence between fuzzy nonlinear set valued variational inclusions and fuzzy resolvent operator equation problem applying this equivalence and nadler s theorem we suggest some iterative algorithms for solving fuzzy nonlinear set valued variational inclusions in real banach spaces by using the inequality of petryshyn the existence of solutions for these kinds of fuzzy nonlinear set valued variational inclusions without compactness is proved and convergence criteria of iterative sequences generated by the algorithm are also discussed

three step iterative algorithms for solving the system of generalized mixed quasi variational like inclusions in this paper we consider the system of generalized mixed quasi variational like inclusions in hilbert spaces we extend the auxiliary principle technique to develop a three step iterative algorithm for solving the system of generalized mixed quasi variational like inclusions under the assumptions of the continuity and partially relaxed h strong monotonicity of set valued mappings we establish the convergence for our algorithm our algorithm and its convergence results are new and generalize ding s predictor corrector iterative algorithms moreover our results unify some known results in the literature as well

a two objective mathematical model without cutting patterns for one dimensional assortment problems this paper considers a one dimensional cutting stock and assortment problem one of the main difficulties in formulating and solving these kinds of problems is the use of the set of cutting patterns as a parameter set in the mathematical model since the total number of cutting patterns to be generated may be very huge both the generation and the use of such a set lead to computational difficulties in solution process the purpose of this paper is therefore to develop a mathematical model without the use of cutting patterns as model parameters we propose a new two objective linear integer programming model in the form of simultaneous minimization of two contradicting objectives related to the total trim loss amount and the total number of different lengths of stock rolls to be maintained as inventory in order to fulfill a given set of cutting orders the model does not require pre specification of cutting patterns we suggest a special heuristic algorithm for solving the presented model the superiority of both the mathematical model and the solution approach is demonstrated on test problems

co coercivity and its role in the convergence of iterative schemes for solving variational inequalities this paper stresses the role of co coercivity and related notions in the convergence of iterative schemes for solving monotone but not necessarily strongly or even strictly monotone variational inequalities the analysis will be conducted within the conceptual framework of the auxiliary problem principle

auxiliary principle for generalized mixed variational like inequalities abstract in this paper we use the auxiliary principle technique to prove the existence of a solution of some new classes of variational inequalities which are called the generalized mixed variational like inequalities this technique is used to analyze an iterative algorithm several special cases which can be obtained from our main result are also discussed

strongly nonlinear quasivariational inequalities abstract in this paper we develop the algorithms for finding the approximate solution of a strongly nonlinear quasivariational inequality and a strongly nonlinear quasicomplementarity problem and we include as special cases known results in this area we also observe that these two problems are equivalent if the convex set involved in the formulation of these problem is a convex cone

on spurious velocities in incompressible flow problems with interfaces we show that a non physical velocity may appear in the finite element calculation of incompressible two phase flows subjected to an external local force there are different sources responsible for this phenomenon approximation of the incompressibility constraint the interface and the local external force furthermore we demonstrate that this non physical velocity does not vanish with the expected order of convergence we evaluate different concepts and give recommendations for a proper handling of this phenomenon

finite element discretization of the navier stokes equations with a free capillary surface the instationary navier stokes equations with a free capillary boundary are considered in 2 and 3 space dimensions a stable finite element discretization is presented the key idea is the treatment of the curvature terms by a variational formulation in the context of a discontinuous in time space time element discretization stability in weak energy norms can be proved numerical examples in 2 and 3 space dimensions are given

the auxiliary principle and an algorithm for a system of generalized set valued mixed variational like inequality problems in banach spaces in this paper we introduce and study a new system of generalized set valued mixed variational like inequality problems sgsmvlip and its related auxiliary problems in reflexive banach spaces the auxiliary principle technique is applied to study the existence and an iterative algorithm of solutions for the system of generalized set valued mixed variational like inequality problems at first the existence and uniqueness of solutions of the auxiliary problems for sgsmvlip is shown next an iterative algorithm for solving sgsmvlip is constructed by using the existence and uniqueness result finally we prove the existence of solutions of sgsmvlip and discuss the convergence analysis of the algorithm these results improve unify and generalize many corresponding known results given in the literature

a class of gap functions for variational inequalities recently auchmuty 1989 has introduced a new class of merit functions or optimization formulations for variational inequalities in finite dimensional space we develop and generalize auchmuty s results and relate his class of merit functions to other works done in this field especially we investigate differentiability and convexity properties and present characterizations of the set of solutions to variational inequalities we then present new descent algorithms for variational inequalities within this framework including approximate solutions of the direction finding and line search problems the new class of merit functions include the primal and dual gap functions introduced by zuhovickii et al 1969a 1969b and the differentiable merit function recently presented by fukushima 1992 also the descent algorithm proposed by fukushima is a special case from the class of descent methods developed in this paper through a generalization of auchmuty s class of merit functions we extend those inherent in the works of dafermos 1983 cohen 1988 and wu et al 1991 new algorithmic equivalence results relating these algorithm classes to each other and to auchmuty s framework are also given

existence and iterative approximation of solutions of generalized mixed quasi variational like inequality problem in banach spaces in this paper some existence theorems for the mixed quasi variational like inequalities problem in a reflexive banach space are established the auxiliary principle technique is used to suggest a novel and innovative iterative algorithm for computing the approximate solution for the mixed quasi variational like inequalities problem consequently not only the existence of theorems of the mixed quasi variational like inequalities is shown but also the convergence of iterative sequences generated by the algorithm is also proven the results proved in this paper represent an improvement of previously known results

numerical assessment of stability of interface discontinuous finite element pressure spaces abstract the stability of two recently developed pressure spaces has been assessed numerically the space proposed by ausas et al r f ausas f s sousa g c buscaglia an improved finite element space for discontinuous pressures comput methods appl mech engrg 199 2010 1019 1031 which is capable of representing discontinuous pressures and the space proposed by coppola owen and codina a h coppola owen r codina improving eulerian two phase flow finite element approximation with discontinuous gradient pressure shape functions int j numer methods fluids 49 2005 1287 1304 which can represent discontinuities in pressure gradients we assess the stability of these spaces by numerically computing the inf sup constants of several meshes the inf sup constant results as the solution of a generalized eigenvalue problems both spaces are in this way confirmed to be stable in their original form an application of the same numerical assessment tool to the stabilized equal order p 1 p 1 formulation is then reported an interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation s stability an analogous result is also reported for the mini element p 1 p 1 when the velocity bubbles are removed in an arbitrary band of elements

set valued resolvent equations and mixed variational inequalities in this paper we introduce and study a new class of variational inequalities which is called the generalized set valued mixed variational inequality the resolvent operator technique is used to establish the equivalence among generalized set valued variational inequalities fixed point problems and the generalized set valued resolvent equations this equivalence is used to study the existence of a solution of set valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems the results proved in this paper represent a significant refinement and improvement of the previously known results in this area

an iterative method for generalized nonlinear set valued mixed quasi variational inequalities with h monotone mappings generalized nonlinear set valued mixed quasi variational inequalities with maximal monotone mappings have been studied in the literature since the maximal monotone operators are known as special cases of the h monotone operators we generalize the study for these inequality problems with h monotone mappings in this paper precisely we establish the existence of solutions for the generalized nonlinear set valued mixed quasi variational inequality problem with h monotone mappings an iterative method for finding their approximate solutions are proposed furthermore a new convergence criteria for this iterative method is imposed

generalized quasi variational like inclusions with nonconvex functionals in this paper two new concepts of h subdifferential and h proximal mappings of a proper functional is introduced in hilbert spaces the existence and lipschitz continuity of h proximal mapping of a proper functional are proved by applying these concepts we introduce and study a class of generalized quasi variational like inclusions with a nonconvex functional a new iterative algorithms for finding the approximate solutions and the convergence criteria of the iterative sequences generated by the algorithm are also given these algorithm and existence result generalize many known results in the literature

perturbed ishikawa type iterative algorithm for generalized quasivariational inclusions in this paper a perturbed ishikawa type iterative algorithm of solving a new class of generalized nonlinear implicit quasivariational inclusions are suggested and analysed first an existence theorem of solutions for generalized nonlinear implicit quasivariational inclusion is proved under suitable assumptions then the convergence of the perturbed ishikawa type iterative sequences generated by the new algorithm is proved as special cases some known results are also discussed

set valued variational inclusions in banach spaces the purpose of this paper is to introduce and study a class of set valued variational inclusions without compactness condition in banach spaces by using michael s selection theorem and nadler s theorem an existence theorem and an iterative algorithm for solving this kind of set valued variational inclusions in banach spaces are established and suggested

a population heuristic for constrained two dimensional non guillotine cutting abstract in this paper we present a heuristic algorithm for the constrained two dimensional non guillotine cutting problem this is the problem of cutting a number of rectangular pieces from a single large rectangle so as to maximise the value of the pieces cut in addition the number of pieces of each type that are cut must lie within prescribed limits our heuristic algorithm is a population heuristic where a population of solutions to the problem are progressively evolved this heuristic is based on a new non linear formulation of the problem computational results are presented for a number of standard test problems taken from the literature and for a number of large randomly generated problems

generalized multivalued variational inequalities ii abstract in this paper we prove that the generalized multivalued variational inequalities are equivalent to the generalized multivalued wiener hopf equations this equivalence is used to suggest a number of iterative algorithms for solving generalized multivalued variational inequalities we also discuss the convergence of these algorithms

algorithms for general monotone mixed variational inequalities abstract in this paper we suggest and analyze some new iterative methods for solving general monotone mixed variational inequalities which are being used to study odd order and nonsymmetric boundary value problems arising in pure and applied sciences these new methods can be viewed as generalizations and extensions of the methods of he solodov and tseng and noor for solving monotone mixed variational inequalities

iterative algorithms for solving generalized nonlinear mixed variational inequalities a new concept of g partially relaxed strong monotonicity of mappings is introduced by applying the auxiliary variational inequality technique some new predictor corrector iterative algorithms for solving generalized nonlinear mixed variational inequalities are suggested and analyzed the convergence of the algorithms only need the continuity and the g partially relaxed strongly monotonicity of mappings these algorithms and convergence result are new and generalize some known results in literature

predictor corrector algorithms for solving generalized mixed implicit quasi equilibrium problems a new class of generalized mixed implicit quasi equilibrium problems gmiqep with four functions is introduced and studied the new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi variational inequality problems as many special cases by employing the auxiliary principle technique some predictor corrector iterative algorithms for solving the gmiqep are suggested and analyzed the convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings

generalized set valued variational inclusions and resolvent equations in this paper we establish the equivalence between the generalized set valued variational inclusions the resolvent equations and the fixed point problem using the resolvent operator technique this equivalence is used to suggest and analyze some iterative algorithms for solving the generalized set valued variational inclusions and related optimization problems

existence of solutions for lower semicontinuous quasi equilibrium problems in this paper we deal with the following quasi equilibrium problem given a nonempty subset c of a topological vector space x a nonempty set d two functions t c d f x d r and a multifunction s c 2x find x x such that x c x s x and f x tx f x tx for all x s x such a problem recently introduced in 1 extends and unifies several variational inequality problems generalized complementarity problems and nash equilibrium problems we prove several existence results in which the upper semicontinuity of the multifunction s is not assumed

an improved finite element space for discontinuous pressures abstract we consider incompressible stokes flow with an internal interface at which the pressure is discontinuous as happens for example in problems involving surface tension we assume that the mesh does not follow the interface which makes classical interpolation spaces to yield suboptimal convergence rates typically the interpolation error in the l 2 norm is of order h 1 2 we propose a modification of the p 1 conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system the unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element so that the implementation of the proposed space into existing codes is straightforward with this modification numerical tests show that the interpolation order improves to o h 3 2 the new pressure space is implemented for the stable p 1 p 1 mini element discretization and for the stabilized equal order p 1 p 1 discretization assessment is carried out for poiseuille flow with a forcing surface and for a static bubble in all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard p 1 space in addition two navier stokes simulations with moving interfaces rayleigh taylor instability and merging bubbles are reported to show that the proposed space is robust enough to carry out realistic simulations

general nonlinear variational inequalities abstract the fixed point technique is used to prove the existence of a unique solution of a new unified and general class of nonlinear variational inequalities several special cases which can be obtained from our main result are also discussed

normal maps inducted by linear transformations we study a certain piecewise linear manifold which we call the normal manifold associated with a polyhedral convex set and a family of continuous functions called normal maps that are induced on this manifold by continuous functions from rn to rn these normal maps occur frequently in optimization and equilibrium problems and the subclass of normal maps induced by linear transformations plays a key role our main result is that the normal map induced by a linear transformation is a lipschitzian homeomorphism if and only if the determinant of the map in each n cell of the normal manifold has the same nonzero sign

exchange price equilibria and variational inequalities the aim of this paper is to show the relevance of the concept and the theory of variational inequalities in the study of economic equilibria

generalized quasi variational like inequality problem this paper gives some very general results on the generalized quasi variational like inequality problem since the problem includes all the existing extensions of the classical variational inequality problem as special cases our existence theorems extend the previous results in the literature by relaxing both continuity and concavity of the functional the approach adopted in this paper is based on continuous selection type arguments and thus is quite different from the berge maximum theorem or hahn banach theorem approach used in the literature

the analytic hierarchy process and multiobjective 0 1 faculty course assignment abstract this paper gives a general model for the faculty course assignment problem that is a zero one nonlinear multiobjective programming problem because of the nonconvexity of the problem simple weighting scalarization does not guarantee finding all pareto optimal solutions therefore a newly developed three step process consisting of the analytic hierarchy process scalarization and the subgradient method is provided to deal with the problem this approach is used to solve a nonconvex multiobjective faculty course assignment problem for the first time a real life application is included

generalized complementarity problems for fuzzy mappings in this paper we introduce a new class of generalized complementarity problems for the fuzzy mappings and construct a new iterative algorithm we also discuss the existence of solutions for the generalized complementarity problems and the convergence of iterative sequence

variational inequalities for fuzzy mappings ii in this paper we establish the equivalence between the variational inequalities for fuzzy mappings and the wiener hopf equations for fuzzy mappings we use this equivalence to suggest a number of new iterative algorithms for solving the variational inequalities for fuzzy mappings we also study the convergence criteria of these iterative algorithms the auxiliary principle technique is used to study the existence of a solution of the variational inequality for fuzzy mappings and to suggest a novel and innovative iterative algorithm for computing the approximate solution the results proved in this paper represent an improvement of previously known results

generalized strongly nonlinear quasivariational inequalities abstract in this paper we prove an existence theorem of solutions and develop the algorithms of approximating solutions for a generalized strongly nonlinear variational inequality and a generalized strongly nonlinear complementarity problem an algorithm for finding the approximate solution of generalized strongly nonlinear quasivariational inequalities and generalized strongly nonlinear quasicomplementarity problems is also given as special cases these results include the corresponding results of fang and peterson noor siddiqi and ansari and ding

auxiliary problems and algorithm for a system of generalized variational like inequality problems in this paper we consider a system of generalized variational like inequality problems sgvlip involving nondifferentiable terms and its related auxiliary problems in real hilbert spaces an existence theorem for auxiliary problems is established further by exploiting this theorem an algorithm for the sgvlip is constructed furthermore we prove the existence of a unique solution of sgvlip and discuss the convergence analysis of the algorithm the technique and results presented in this paper generalize and unify the corresponding techniques and results given in m a noor general nonlinear variational inequalities j math anal appl 126 1987 78 84 m a noor general variational inequalities appl math lett 1 1988 119 122 m a noor mixed variational like inequalities commun appl nonlinear anal 1 4 1994 63 75

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

the generalized quasi variational inequality problem with applications a new problem called the generalized quasi variational inequality problem is introduced this new problem extends all the existing variational inequality problems in finite dimensional spaces and enlarges the class of problems that can be approached by the variational inequality theory some existence results without convexity assumptions are presented applications to mathematical and equilibrium programming are given

auxiliary principle and iterative algorithm for a new system of generalized mixed equilibrium problems in banach spaces abstract in this paper we study a new system of generalized mixed equilibrium problems involving skew symmetric bifunctions sgmep in reflexive banach spaces a system of auxiliary mixed equilibrium problems samep for solving the sgmep is introduced and the existence and uniqueness of the solutions of the samep is first proved next by using the auxiliary principle technique a new iterative algorithm to compute the approximate solutions of the sgmep is suggested and analyzed finally the strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild conditions these results improve unify and generalize some known results in recent literature

general algorithm of solutions for nonlinear variational inequalities in banach space abstract in this paper we shall study a class of general nonlinear variational inequalities in reflexive banach spaces by applying a minimax inequality obtained by the author some existence uniqueness theorems of solutions for the general nonlinear variational inequalities are proved next by applying the auxiliary problem technique we suggest an innovative iterative algorithm to compute the approximate solutions of the general nonlinear variational inequality finally the convergence criteria is also discussed

a finite element technique for multifluid incompressible flow using eulerian grids the paper presents a finite element method for 3d incompressible fluid flows with capillary free boundaries it uses a fixed eulerian grid of 10 nodes p2 p1 tetrahedra and tracks the free boundary using a six nodes p2 triangular surface grid in order to improve the mass conservation properties of the method a local enrichment of the finite element basis in the elements intersected by the free boundaries is employed in addition to the surface tracking it also advects a smooth indicator function for an easy identification of the fluid properties in the different parts of the domain the advective part of the navier stokes equations is split and integrated with a characteristic method the remaining generalized stokes problem is resolved by means of an inexact outer inner uzawa iteration with a properly chosen preconditioner the performance of this technique is evaluated on several problems involving droplets in viscous liquids

finite element discretization error analysis of a surface tension force in two phase incompressible flows we consider a standard model for a stationary two phase incompressible flow with surface tension in the variational formulation of the model a linear functional which describes the surface tension force occurs this functional depends on the location and the curvature of the interface in a finite element discretization method the functional has to be approximated for an approximation method based on a laplace beltrami representation of the curvature we derive sharp bounds for the approximation error a new modified approximation method with a significantly smaller error is introduced

existence and algorithm of solutions for generalized mixed implicit quasi variational inequalities1this project was supported by the national science foundation of people s republic china 1 in this paper by applying the auxiliary variational principle technique some existence theorems of solutions for a class of generalized mixed implicit quasi variational inequalities are proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria are also given as special cases of these results the open problem put forward by noor is answered positively and some results of existence and algorithm of solutions for generalized implicit quasi complementarity problems are also obtained our results are new and generalize a number of known results of mixed variational inequalities mixed quasi variational inequalities and quasi complementary problems involving single valued and set valued mappings in recent literatures