a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

optimal control of obstacle for quasi linear elliptic variational bilateral problems this paper is concerned with an optimal control problem for quasi linear elliptic variational inequality in which the bilateral obstacles are the control the cost functional of this optimal control problem is of lagrange type in which the pth power of laplacian of the control appears this feature leads to the fact that it is hard to derive the optimality system for the underlying problem in this paper the optimality system is established by utilizing the special structure of the approximate optimality system including the monotonicity of the leading differential operator

the natural element method in solid mechanics the application of the natural element method nem 1 2 to boundary value problems in two dimensional small displacement elastostatics is presented the discrete model of the domain consists of a set of distinct nodes n and a polygonal description of the boundary in the natural element method the trial and test functions are constructed using natural neighbour interpolants these interpolants are based on the voronoi tessellation of the set of nodes n the interpolants are smooth c 1 everywhere except at the nodes where they are c 0 in one dimension nem is identical to linear nite elements the nem interpolant is strictly linear between adjacent nodes on the boundary of the convex hull which facilitates imposition of essential boundary conditions a methodology to model material discontinuities and non convex bodies cracks using nem is also described a standard displacement based galerkin procedure is used to obtain the discrete system of linear equations application of nem to various problems in solid mechanics which include the patch test gradient problems bimaterial interface and a static crack problem are presented excellent agreement with exact analytical solutions is obtained which exemplies the accuracy and robustness of nem and suggests its potential application in the context of other classes of problems crack growth plates and large deformations to name a few 1998 john wiley sons ltd

existence results for obstacle problems for nonlinear hemivariational inequality at resonance in this paper we are interested in studying the existence of solutions to obstacle problems for nonlinear hemivariational inequality at resonance driven by the p laplacian using a variational approach based on the nonsmooth critical point theory for nondifferentiable functionals we prove two existence theorems

the existence results for obstacle optimal control problems this paper is concerned with the existence of an optimal control problem for a quasi linear elliptic obstacle variational inequality in which the obstacle is taken as the control firstly we get some existence results under the assumption of the leading operator of the variational inequality with a monotone type mapping in section 2 in section 3 as an application without the assumption of the monotone type mapping for the leading operator of the variational inequality we prove that the leading operator of the variational inequality is a monotone type mapping existence of the optimal obstacle is proved the method used here is different from y y zhou x q yang k l teo the existence results for optimal control problems governed by a variational inequality j math anal appl 321 2006 595 608

optimal control of bilateral obstacle problems we consider an optimal control problem where the state satisfies a bilateral elliptic variational inequality and the control functions are the upper and lower obstacles we seek a state that is close to a desired profile and the h2 norms of the obstacles are not too large existence results are given and an optimality system is derived a particular case is studied that needs no compactness assumption via a monotonicity method

volumetric locking in natural neighbour galerkin methods the behaviour of natural neighbour galerkin mixed approximation is described at the incompressible limit traditional natural elements based on the sibson mixed interpolation do not verify the lbb or inf sup condition here a study of the possible benefits of enriching the interpolation is considered using the partition of unity paradigm different enrichments were tested leading to different reproducing properties results concerning the numerical verification of the inf sup tests are addressed also the convenience of using different approximations developed in this work is analysed enrichment with the polynomial field 1 xy seems to verify the lbb condition its behaviour has proven to be very similar to the mini finite element widely used in the literature examples proving these results are provided copyright 2004 john wiley sons ltd

optimal control of the obstacle for a parabolic variational inequality abstract an optimal control problem for a parabolic obstacle variational inequality is considered the obstacle in l2 0 t h2 h10 with t l2 q is taken as the control and the solution to the obstacle problem is taken as the state the goal is to find the optimal control so that the state is close to the desired profile while the norm of the obstacle is not too large existence and necessary conditions for the optimal control are established

optimal obstacle control problem for semilinear evolutionary bilateral variational inequalities this paper is concerned with an optimal control problem for semilinear evolutionary bilateral variational inequalities the pair of the upper and lower obstacles is taken as the control and the corresponding state is chosen close to a desired target profile with the norms of the obstacles not too large existence and optimality conditions for the problem are derived

numerical study of an optimal control problem for a catalytic converter function abstract we introduce a model of a catalytic converter and we study mathematical properties of a control function and a cost function as an optimal control problem we give a finite difference scheme for solving various cost functions and discuss the results

modeling and minimization of extinction in volterra lotka type equations with free boundaries abstract an equation of the distributed volterra lotka type with free boundary of the obstacle type with possible applications in ecology when extinction of the biological species is of particular concern is introduced and solved an optimal control problem for such an equation and in particular the problem of minimization of the area of extinction of the species is introduced and to some extent solved

integral representations for elliptic functions we derive new integral representations for constituents of the classical theory of elliptic functions the eisenstein series and weierstrass and functions the derivations proceed from the laplace mellin representation of multipoles and an elementary lemma on the summation of 2d geometric series in addition we present results concerning the analytic continuation of the eisenstein series to an entire function in the complex plane and the value of the conditionally convergent series denoted by e 2 below as a function of summation over increasingly large rectangles with arbitrary fixed aspect ratio 1

functional determinants for laplacians on annuli and elliptical regions in this article we consider the functional determinant on an annulus and elliptic regions with a variety of boundary conditions known results for the annulus are rederived and extended using contour integration techniques conformal transformations are then used to relate these results to ellipsoidal annuli providing very explicit answers similarly for the ellipse answers are related to those for a disc but explicit results can only be found for small eccentricity

boundary optimal control for nonlinear antiplane problems abstract we consider a nonlinear antiplane problem which models the deformation of an elastic cylindrical body in frictional contact with a rigid foundation the contact is modelled with tresca s law of dry friction in which the friction bound is slip dependent the aim of this article is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target by acting with a control on the boundary of the body the existence of at least one optimal control is proved next we introduce a regularized problem depending on a small parameter and we study the convergence of the optimal controls when tends to zero an optimality condition is delivered for the regularized problem

a higher order method based on local maximum entropy approximation we present here a generalization of local maximum entropy max ent approximation for high orders of consistency i e quadratic cubic the method is based upon the application of the de boor s algorithm to the standard linear local max ent approximation the resulting approximation possesses some interesting properties such as non negativity smoothness exact interpolation on the boundary and variation diminishing no gibbs effect the resulting structure has many similarities with b spline surfaces but without the tensor product structure typical of that approximation examples are provided of its use in the framework of a galerkin method showing the potential of the proposed method in solving boundary value problems copyright 2010 john wiley sons ltd

c stationarity for optimal control of static plasticity with linear kinematic hardening an optimal control problem is considered for the variational inequality representing the stress based dual formulation of static elastoplasticity the linear kinematic hardening model and the von mises yield condition are used existence and uniqueness of the plastic multiplier is rigorously proved which allows for the reformulation of the forward system using a complementarity condition in order to derive necessary optimality conditions a family of regularized optimal control problems is analyzed wherein the static plasticity problems are replaced by their viscoplastic approximations by passing to the limit in the optimality conditions for the regularized problems necessary optimality conditions of c stationarity type are obtained

the existence results for optimal control problems governed by a variational inequality in this paper we establish the existence of the optimal control for an optimal control problem where the state of the system is defined by a variational inequality problem with monotone type mappings moreover as an application we get several existence results of an optimal control for the optimal control problem where the system is defined by a quasilinear elliptic variational inequality problem with an obstacle

optimal control for parabolic variational inequalities consider the problem of maximizing a functional that depends on a control function k x t and on the solution u x t of a parabolic variational inequality with k appearing in the data necessary conditions are obtained for the maximizers k 0 x t and the structure of k 0 is then analyzed an application to the stefan problem is given

numerical integration in natural neighbour galerkin methods in this paper issues regarding numerical integration of the discrete system of equations arising from natural neighbour natural element galerkin methods are addressed the sources of error in the traditional delaunay triangle based numerical integration are investigated two alternative numerical integration schemes are analysed first a local approach in which nodal shape function supports are exactly decomposed into triangles and circle segments is shown not to give accurate enough results second a stabilized nodal quadrature scheme is shown to render high levels of accuracy while resulting specially appropriate in a natural neighbour galerkin approximation method the paper is completed with several examples showing the performance of the proposed techniques copyright 2004 john wiley sons ltd

optimal prestress of cracked unilateral structures finite element analysis of an optimal control problem for variational inequalities abstract the structural analysis problem concerning static stabilization of cracked structures through prestress reinforcement is studied in this paper a linearly elastic structure with given crack interfaces along which frictionless no tension no penetration mechanism hold the so called unilateral contact mechanism is assumed the prestressing control which in most civil engineering applications is realized by externally placed prestressed cables is modelled by means of prestressing control forces the static analysis state problem turns out to be a variational inequality the goal of the stabilization is taken to be the healing of the cracks in the structure with the minimum reinforcement among an available and technologically feasible set and this is expressed by means of a suitably written combined cost function the arising optimal control problem is a nonsmooth and nonconvex one thus appropriate techniques recently developed in the area of nonsmooth analysis are used for its solution numerical examples illustrate the theory and parametric numerical experimentation with various algorithms permit us discuss certain aspects of the computer application appropriate condensation techniques for the reduction of the problem dimensionality and the integration of the studied algorithms in a general purpose finite element software are given

non linear elliptic and parabolic equations involving measure data in this paper we prove the existence of solutions for equations of the type div a du f in a bounded open set u 0 on where a is a possibly non linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure we also consider the equation div a du g u f in u 0 on with f l1 or f m u u 0 and the parabolic equivalent of the first elliptic equation

a study on the performance of natural neighbour based galerkin methods in this paper we address the problem of improving natural element simulations in terms of computational cost several problems are discussed that include an efficient natural neighbour search algorithm and a comparison of different natural neighbour based interpolation algorithms in particular we review the so called pseudo nem a moving least squares like approximation scheme that employs natural neighbours and compare it with traditional sibson and laplace interpolation schemes in terms of both accuracy and computational cost some examples in linear elasticity and visco plasticity are analysed in order to test the proposed schemes in engineering problems

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

pontryagin maximum principle for optimal control of variational inequalities in this paper we investigate optimal control problems governed by variational inequalities we present a method for deriving optimality conditions in the form of pontryagin s principle the main tools used are the ekeland s variational principle combined with penalization and spike variation techniques

the pontry agin maximum principle for minimax problems of optimal control the subject of this paper is the pontryagin maximum principle for the minimax problem of optimal control that is we will derive the necessary conditions which a control must satisfy in order to be optimal for the problem in which the cost is measured pointwise in time by the essential supremum over t of some function of time the state and the control it is desired to use controls to minimize this cost

a new extension of the natural element method for non convex and discontinuous problems the constrained natural element method c nem in this paper a new extension of the mesh free natural element method nem is presented in this approach coined as constrained natural element method c nem a visibility criterion is introduced to select natural neighbours in the computation of the shape functions the computation of these shape functions is based on a modified constrained voronoi diagram with this technique some difficulties inherent to this method in non convex domains are avoided and the analysis of problems involving cracks or discontinuities are now easily performed as the nem satisfies the kronecker delta property the imposition of essential boundary conditions is trivial unlike other mesh free methods the c nem technique provides a description of integration cells that allows the use of the stabilized conforming nodal integration scni scheme instead of gauss integration to enhance computational efficiency and accuracy two numerical examples in elastostatics are reported to evaluate the potential of the proposed technique in highly non convex geometries like a crack through which the solution becomes discontinuous

convergence and optimal control problems of nonlinear evolution equations governed by time dependent operator we study an abstract nonlinear evolution equation governed by a time dependent operator of subdifferential type in a real hilbert space in this paper we discuss the convergence of solutions to our evolution equations also we investigate the optimal control problems of nonlinear evolution equations moreover we apply our abstract results to a quasilinear parabolic pde with a mixed boundary condition

optimal control in some variational inequalities we study a nonconvex nondifferentiable problem of optimal control where the state of the system is defined by an elliptic variational inequality with obstacle and where the cost function is quadr

mathematical programs with complementarity constraints in function space c and strong stationarity and a path following algorithm an optimal control problem governed by an elliptic variational inequality is studied the feasible set of the problem is relaxed and a path following type method is used to regularize the constraint on the state variable first order optimality conditions for the relaxed regularized subproblems are derived and convergence of stationary points with respect to the relaxation and regularization parameters is shown in particular c and strong stationarity as well as variants thereof are studied the subproblems are solved by using semismooth newton methods the overall algorithmic concept is provided and its performance is discussed by means of examples including problems with bilateral constraints and a nonsymmetric operator

first order optimality conditions for elliptic mathematical programs with equilibrium constraints via variational analysis mathematical programs in which the constraint set is partially defined by the solutions of an elliptic variational inequality so called elliptic mpecs are formulated in reflexive banach spaces with the goal of deriving explicit first order optimality conditions amenable to the development of numerical procedures variational analytic concepts are both applied and further developed the paper is split into two main parts the first part concerns the derivation of conditions in which the lower level state constraints are assumed to be polyhedric sets this part is then completed by two examples the latter of which involves pointwise bilateral bounds on the gradient of the state the second part focuses on an important nonpolyhedric example namely when the lower level state constraints are presented by pointwise bounds on the euclidean norm of the gradient of the state a formula for the second order mosco epiderivative of the indicator function for this convex set is derived this result is then used to demonstrate the hadamard directional differentiability of the solution mapping of the variational inequality which then leads to the derivation of explicit strong stationarity conditions for this problem

indirect obstacle control problem for semilinear elliptic variational inequalities an optimal control problem for a coupled system of a semilinear elliptic equation and an obstacle variational inequality is considered existence and optimality conditions of optimal triple are established

on the regularity of an obstacle control problem an optimal control problem of the obstacle for an elliptic variational inequality is considered in which the obstacle is regarded as the control to get the regularity of the optimal pair a new related control problem is introduced by proving the existence of an optimal pair to such a new control problem the regularity of the optimal pair to the original problem is obtained it turns out that the regularity obtained is sharp in general some other interesting properties of the optimal pair are also established

boundary optimal control for quasistatic bilateral frictional contact problems abstract we consider a mathematical model describing the quasistatic process of bilateral contact with friction between an elastic body and a rigid foundation our goal is to study a related optimal control problem which allows us to obtain a desired field of displacements on the contact boundary by acting with a control on another part of the boundary of the body using penalization and regularization techniques we derive the necessary conditions of optimality

bilateral obstacle optimal control for a quasilinear elliptic variational inequality with a source term abstract in this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality with a source term and the control functions are the upper and the lower obstacles we assume that the obstacles and are in w 2 2 but this causes difficulty for deriving the optimality condition by applying the weak convergence method we establish existence and incomplete necessary conditions for the optimal control

a bundle free implicit programming approach for a class of elliptic mpecs in function space using a standard first order optimality condition for nonsmooth optimization problems a general framework for a descent method is developed this setting is applied to a class of mathematical programs with equilibrium constraints in function space from which a new algorithm is derived global convergence of the algorithm is demonstrated in function space and the results are then illustrated by numerical experiments

optimal control of parabolic differential equations with two point boundary state constraints this paper deals with the necessary conditions of optimality for some optimal control problems governed by some parabolic differential equations involving monotone graphs the two point boundary time variable state constraints are discussed some analyses on the state equations are given

a posteriori error estimates for optimal control problems governed by parabolic equations in this paper we derive a posteriori error estimates for the finite element approximation of quadratic optimal control problem governed by linear parabolic equation we obtain a posteriori error estimates for both the state and the control approximation such estimates which are apparently not available in the literature are an important step towards developing reliable adaptive finite element approximation schemes for the control problem

a natural element updated lagrangian strategy for free surface fluid dynamics we present a novel algorithm to simulate free surface fluid dynamics phenomena at low reynolds numbers in an updated lagrangian framework it is based on the use of one of the most recent meshless methods the so called natural element method free surface tracking is performed by employing a particular instance of shape constructors called a shapes this means that at each time step the geometry of the domain is extracted by employing a particular member of the finite set of shapes described by the nodal cloud the lagrangian framework allows us to integrate the inertial terms of the navier stokes equations by employing the method of characteristics which are precisely the nodal pathlines a theoretical description of the method is included together with some examples showing its performance

several approaches for the derivation of stationarity conditions for elliptic mpecs with upper level control constraints the derivation of multiplier based optimality conditions for elliptic mathematical programs with equilibrium constraints mpec is essential for the characterization of solutions and development of numerical methods though much can be said for broad classes of elliptic mpecs in both polyhedric and non polyhedric settings the calculation becomes significantly more complicated when additional constraints are imposed on the control in this paper we develop three derivation methods for constrained mpec problems via concepts from variational analysis via penalization of the control constraints and via penalization of the lower level problem with the subsequent regularization of the resulting nonsmoothness the developed methods and obtained results are then compared and contrasted

pontryagin maximum principle for semilinear and quasilinearparabolic equations with pointwise state constraints this paper studies the first order necessary conditions for the optimal controls of semilinear and quasilinear parabolic partial differential equations with pointwise state constraints a pontryagin type maximum principle is obtained

a priori finite element error analysis for optimal control of the obstacle problem an optimal control problem governed by a unilateral obstacle problem is considered the problem is discretized using linear finite elements for the state and the obstacle and a variational discrete approach for the control based on strong stationarity and a quadratic growth condition we establish a priori error estimates which turn out to be quasi optimal under additional assumptions on the data the theoretical findings are illustrated by two numerical tests

an extension of pontryagin s principle for state constrained optimal control of semilinear elliptic equations and variational inequalities this paper deals with state constrained optimal control problems governed by semilinear elliptic equations or variational inequalities by using ekeland s principle a minimum principle of pontryagin s type under some stability conditions of the optimal cost with respect to the state constraints is derived

minimax control for evolutionary variational bilateral problem this paper deals with a minimax control problem for semilinear evolutionary variational inequalities associated with bilateral constraints the control domain is not necessarily convex the cost functional which is to be minimized is the sup norm of some function of the state and the control the major novelty of such a problem lies in the simultaneous presence of the nonsmooth state equation variational inequality and the nonsmooth cost functional the sup norm in this paper the existence and the pontryagin type necessary condition for optimal controls are established

some analytic continuations of the barnes zeta function in two and higher dimensions abstract formulas for the analytic continuation of the barnes zeta function and some affine extensions thereof in two and more dimensions are constructed the expressions are used to deal with determinants of multidimensional harmonic oscillators an example is therewith obtained of the multiplicative anomaly or defect associated with the most common definition due to ray and singer d b ray reidemeister torsion and the laplacian on lens spaces adv math 4 1970 109 126 d b ray i m singer r torsion and the laplacian on riemannian manifolds adv math 7 1971 145 201 d b ray i m singer analytic torsion for complex manifolds ann math 98 1973 154 177 of determinant of a pseudodifferential operator admitting a zeta function m kontsevich s vishik geometry of determinants of elliptic operators in functional analysis on the eve of the 21st century vol 1 1995 pp 173 197

analytic continuation of the doubly periodic barnes zeta function the aim of this work is to study the analytic continuation of the doubly periodic barnes zeta function by using a suitable complex integral representation as a starting point we find the meromorphic extension of the doubly periodic barnes zeta function to the entire complex plane in terms of a real integral containing the hurwitz zeta function and the first jacobi theta function these allow us to explicitly give expressions for the derivative at all non positive integer points

higher order natural element methods towards an isogeometric meshless method the problem of generalizing the natural element method nem in terms of higher order consistency and continuity is addressed here it is done by means of the de boor algorithm the same employed to obtain b splines by linear combinations of linear interpolants in one dimension by noting that any form of natural neighbour interpolation can be considered as a suitable generalization of linear interpolation to two and higher dimensions the de boor algorithm is extended to two or higher dimensions thus obtaining a new form of interpolation that can be used in a galerkin framework to develop a new class of meshless methods this new class of meshless methods closely resembles the isogeometric analysis developed by hughes et al comput methods appl mech eng 2005 194 4135 4195 however unlike b splines the new class of interpolants does not rely on an underlying tensor product quadrilateral mesh it is based on the delaunay triangulation of the cloud of knots and does not require any regularity on the connectivity in addition the new method conserves many of the attractive features of the nem such as strict interpolation on the boundary and thus directs imposition of essential boundary conditions after a theoretical description of the proposed method some numerical examples are shown to test its performance in the context of linear elastostatics copyright 2007 john wiley sons ltd

on the optimal control of variational hemivariational inequalities abstract the present paper represents a continuation of 26 there a continuous dependence result for the solution of an elliptic variational hemivariational inequality was obtained and then used to prove the existence of optimal pairs for two associated optimal control problems in the current paper we complete this study with more general results indeed we prove the continuous dependence of the solution with respect to a parameter which appears in all the data of the problem including the set of constraints the nonlinear operator and the two functionals which govern the variational hemivariational inequality this allows us to consider a general associated optimal control problem for which we prove the existence of optimal pairs together with a new convergence result the mathematical tools developed in this paper are useful in the analysis and control of a large class of boundary value problems which in a weak formulation lead to elliptic variational hemivariational inequalities to provide an example we illustrate our results in the study of an inequality which describes the equilibrium of an elastic body in frictional contact with a foundation made of a rigid body covered by a layer of soft material

optimality conditions for control problems governed by variational inequalities this paper deals with the theory of first order necessary conditions of optimality for nonsmooth control problems governed by variational inequalities we present a general approach in which necessary conditions of first order are obtained by means of differentiation tools based on epi convergence of second order differential quotients

pontryagin s principle for state constrained boundary control problems of semilinear parabolic equations this paper deals with state constrained optimal control problems governed by semilinear parabolic equations we establish a minimum principle of pontryagin s type to deal with the state constraints we introduce a penalty problem by using ekeland s principle the key tool for the proof is the use of a special kind of spike perturbations distributed in the domain where the controls are defined conditions for normality of optimality conditions are given

natural neighbour galerkin methods summary natural neighbour co ordinates sibson co ordinates is a well known interpolation scheme for multivariate data tting and smoothing the numerical implementation of natural neighbour co ordinates in a galerkin method is known as the natural element method nem in the natural element method natural neighbour co ordinates are used to construct the trial and test functions recent studies on nem have shown that natural neighbour co ordinates which are based on the voronoi tessellation of a set of nodes are an appealing choice to construct meshless interpolants for the solution of partial dierential equations in belikov et al computational mathematics and mathematical physics 1997 37 1 9 15 a new interpolation scheme non sibsonian interpolation based on natural neighbours was proposed in the present paper the nonsibsonian interpolation scheme is reviewed and its performance in a galerkin method for the solution of elliptic partial dierential equations that arise in linear elasticity is studied a methodology to couple nite elements to nem is also described two signicant advantages of the non sibson interpolant over the sibson interpolant are revealed and numerically veried the computational eciency of the non sibson algorithm in 2 dimensions which is expected to carry over to 3 dimensions and the ability to exactly impose essential boundary conditions on the boundaries of convex and non convex domains copyright 2001 john wiley sons ltd

optimal control of the obstacle in a quasilinear elliptic variational inequality abstract in this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality and the control function is the obstacle the state is chosen to be close to the desire profile while the h 2 norms of the obstacle is not too large existence and necessary conditions for the optimal control are established

adaptive optimal control of the obstacle problem this article is concerned with the derivation of a posteriori error estimates for optimization problems subject to an obstacle problem to circumvent the nondifferentiability inherent to this type of problem we introduce a sequence of penalized but differentiable problems we show differentiability of the central path and derive separate a posteriori dual weighted residual estimates for the errors due to penalization discretization and iterative solution of the discrete problems the effectivity of the derived estimates and of the adaptive algorithm is demonstrated on two numerical examples

optimal control for variational inequalities consider the problem of maximizing a functional which depends on a control function k and on the solution of an elliptic variational inequality with k appearing in the data the variational problem for k is nondiflerentiable and nonconvex we obtain necessary conditions on a maximizes k 0 and then use them to determine the structure of k 0 in some cases

strong stationarity for optimal control of the obstacle problem with control constraints we consider the distributed optimal control of the obstacle problem with control constraints since mignot proved in 1976 the necessity of a system which is equivalent to strong stationarity it has been an open problem whether such a system is still necessary in the presence of control constraints using moderate regularity of the optimal control and an assumption on the control bounds which is implied by u a 0 le u b quasi everywhere in omega in the case of an upper obstacle y le psi we can answer this question in the affirmative we also present counterexamples showing that strong stationarity may not hold if u a 0 or 0 le u b are violated an erratum is attached

necessary conditions for optimal control of distributed parameter systems the ekeland variational principle is used to prove a maximum principle for the optimal controls of a general semilinear evolutionary control system in a banach space with strictly convex dual the boundary constraint is of general type which includes the optimal periodic control problem as a special case

feedback stabilization and optimal control for the cahn hilliard equation this paper is concerned with the control problem for the cahn hilliard equation 4 the physical background is as follows suppose there is a binary solution in a container sz c ir n 5 3 and suppose the mole fraction of the a component is u then the mole fraction for the other component b is 1 u it is well known that the function u of x e sz and t 1 0 due to mass conservation satisfies the cahn hilliard equation 4 u ya2u ap u in sz x r 1 1 where y 0 is a small positive constant and typically p u u3 24 1 2 suppose u has spatial distribution uo x initially i e u x 0 u x 1 3 then the evolution of u x t is determined by 1 l 1 3 and the boundary conditions au i i aau o an x 1 4

optimal control of an elastic contact problem involving tresca friction law in this paper we establish existence results and necessary optimality conditions for a class of optimal control problems where the state is described by elliptic variational inequalities modelling the frictional contact between an elastic body and a rigid foundation we use the tresca s law of dry friction in which the friction bound is prescribed for the contact condition we assume that slowly varying time dependent volume forces and surface tractions act on the body so that the acceleration in the system will be neglected existence and uniqueness results for initial and boundary value problems involving tresca friction law were obtained in 2 6 10 in the case of an elastic body in 4 in the case of elasto viscoplastic models and in 3 in the case of perfectly plastic solids the aim of this paper is to study optimal control problems for mechanical models describing the quasistatic process of bilateral frictional contact between an elastic body and a rigid foundation the state of this system is governed by a variational inequality

local a posteriori error estimates for convex boundary control problems in this paper we derive some improved a posteriori error estimates for finite element approximation of neumann boundary control problems we first establish local upper a posteriori error estimates for both the state and the control approximation of the general convex boundary control problems we then derive local upper and lower a posteriori error estimates for a class of control problems that frequently appear in applications

control of free boundary problem with hysteresis we consider the problem of controlling the free boundary of the two phase stefan problem by means of boundary hysteresis control based on the preisach model it is proved that for each control mu there is a corresponding solution of the stefan problem and that there exists an optimal control

imposing essential boundary conditions in the natural element method by means of density scaled shapes a new method is proposed for the exact imposition of essential boundary conditions in the context of the natural element method nem this is a new technique in the field of computational mechanics and can be considered as a meshless method unlike most of these methods the ne shape functions are strictly interpolant and the essential boundary conditions can be imposed by directly substituting the corresponding terms in the system of equations however these shape functions are not strictly linear over non convex boundaries and the approach does not make the test functions vanish over the whole essential boundary region a modification of the initial nem version is considered based on shapes and complexes which are widely used in the field of scientific visualization using shapes in the context of the nem allows the construction of models entirely in terms of nodes and also ensures the linear precision of the interpolant over convex and non convex boundaries results on some benchmark problems are presented after a theoretical description of the method copyright 2000 john wiley sons ltd

some optimality conditions of quasilinear elliptic obstacle optimal control problems this paper is concerned with an obstacle optimal control problem for a quasilinear elliptic variational inequality with a source term the pth power of laplacian of the obstacle appears in the cost functional this feature leads that it is hard to derive the optimality system for the underlying problem the existence for the optimal control is proved and we also show how to obtain optimality system using a passage to the limit in the approximation process

a posteriori error estimates for some model boundary control problems in this paper we derive a posteriori error estimates for the finite element approximation of quadratic optimal boundary control problems we derive a posteriori error estimates for both the state and the control approximation on polygonal domains such estimates which are apparently not available in the literature can be used to construct reliable adaptive finite element approximation schemes for the control problems

meshless methods with application to metal forming in recent years a new family of computational methods has emerged the so called meshless or mesh free methods have been investigated and used by many researchers for treating a large variety of engineering problems involving usually large displacements as encountered for example in forming process simulations the main advantage of meshless methods is the fact that the interpolation accuracy is not significantly affected by the nodal distribution nevertheless a troublesome task in these techniques is the imposition of essential boundary conditions as in general the kronecker delta property is not satisfied despite of several techniques have been proposed to overcome this problem an appealing alternative technique which allows to circumvent this difficulty lies in the use of the natural neighbor interpolation nem this paper focuses on the description and analysis of the natural element method and its application for simulating some forming processes involving large displacements as well as fixed or moving discontinuities

optimal control for semilinear evolutionary variational bilateral problem this paper is concerned with an optimal control problem for some semilinear evolutionary variational inequalities associated with bilateral constraints the control domain is a general separable metric space and has no algebraic structure in particular it is not necessarily convex existence and optimality conditions of optimal pairs are established

distributed control of systems governed by a general class of quasilinear elliptic equations abstract in this paper we are concerned with optimal control problems governed by a general class of quasilinear elliptic equations our aim is to prove existence of solution and derive optimality conditions in order to deal with this last question we begin investigating differentiability of state solution of equation with respect to the control second term of equation obtaining it only in certain cases a perturbation method is used to treat other cases as a consequence of the optimality system regularity of optimal control and state is establised

on the c1 continuous discretization of non linear gradient elasticity a comparison of nem and fem based on bernstein bezier patches in gradient elasticity the appearance of strain gradients in the free energy density leads to the need of c 1 continuous discretization m ethods in the present work the performances of c 1 finite elements and the c 1 natural element method nem are compared the triangular argyris and hsieh clough tocher finite elements are reparametrized in terms of the bernstein polynomials the quadrilateral bogner fox schmidt element is used in an isoparametric framework for which a preprocessing algorithm is presented additionally the c 1 nem is applied to non linear gradient elasticity several numerical examples are analyzed to compare the convergence behavior of the different methods it will be illustrated that the isoparametric elements and the nem show a significantly better performance than the triangular elements

optimal control of problems governed by abstract elliptic variational inequalities with state constraints in this paper we investigate optimal control problems governed by elliptic variational inequalities with additional state constraints we present a relaxed formulation for the problem with penalization methods and approximation techniques we give qualification conditions to get first order optimality conditions

optimal control of static elastoplasticity in primal formulation an optimal control problem of static plasticity with linear kinematic hardening and von mises yield condition is studied the problem is treated in its primal formulation where the state system is a variational inequality of the second kind first order necessary optimality conditions are obtained by means of an approximation by a family of control problems with state system regularized by huber type smoothing and a subsequent limit analysis the equivalence of the optimality conditions with the c stationarity system for the equivalent dual formulation of the problem is proved numerical experiments are presented which demonstrate the viability of the huber type smoothing approach

an optimal control problem governed by quasi linear variational inequalities an optimal control problem governed by quasi linear variational inequality is considered the cost functional to be minimized contains the solution of a quasi linear variational inequality to get the existence regularity and necessary condition for the optimal pair a new related control problem is introduced by proving the existence of an optimal pair to such a new problem the existence and regularity of the optimal pair to the original problem are obtained it turns out that the regularity obtained is sharp in general some necessary conditions of the optimal pair are also obtained

maximizing the output energy of a linear channel with a time and amplitude limited input the problem of maximizing the output energy of a linear time invariant channel given that the input signal is time and amplitude limited is considered it is shown that a necessary condition for an input mu to be optimal assuming a unity amplitude constraint is that it satisfy the fixed point equation sgn f mu where the functional f is the convolution of mu with the autocorrelation function of the channel impulse response it is also shown that all solutions to this equation for which mod mu mod 1 almost everywhere correspond to local maxima of the output energy iteratively recomputing mu from the fixed point equation leads to an algorithm for finding local optima numerical results are given for the cases where the transfer function is ideal low pass and has two poles these results support the conjecture that in the ideal low pass case the optimal input signal is a single square pulse a generalization of the preceding fixed point condition is also derived for the problem of maximally separating n outputs of a discrete time linear time invariant channel