mixed finite element method for dirichlet boundary control problem governed by elliptic pdes in this paper we study the finite element approximation of dirichlet boundary control problems governed by elliptic pdes based on a mixed variational scheme we establish a mixed finite element approximation to the underlying optimal control problem we consider the optimal control problems posed on both polygonal and general smooth domains and we derive a priori error estimates for optimal control state and adjoint state the optimal and quasi optimal error estimates are obtained for problems on polygonal and smooth domains respectively numerical experiments are provided to confirm our theoretical results

the approximation for the boundary optimal control problem of burgers fisher equation with constraints this paper deals with the numerical approximation with meshless method for the boundary optimal control problem with some control and state constraints governed by the burgers fisher equation which is a nonlinear evolution equation and is the prototype model for the reaction convection and diffusion phenomena arising in many spatial temporal processes by making use of the element free galerkin efg method the original optimal control problem is discretized spatially to a semi discrete optimal control problem governed by a system of nonlinear ordinary differential equations then by using the control parameterization method the original problem can be reduced to an optimal parameter selection problem governed by a lumped parameter system which can be solved as a nonlinear optimization problems by using the sequential quadratic programming sqp algorithm the numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method

primal dual strategy for constrained optimal control problems an algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed it is based on an active set strategy involving primal as well as dual variables for discretized problems sufficient conditions for convergence in finitely many iterations are given numerical examples are given and the role of the strict complementarity condition is discussed

error analysis for optimal control problem governed by convection diffusion equations dg method in the current paper we study the convergence properties of the dgfe approximation of optimal control problem governed by convection diffusion equations we derive a posteriori error estimates and a priori error estimates for both the states ad joint and the control variable approximation for the optimal control problem these estimates are apparently not available in the literature

quasi norm a priori and a posteriori error estimates for the nonconforming approximation of p laplacian in this paper we derive quasi norm a priori and a posteriori error estimates for the crouzeix raviart type finite element approximation of the p laplacian sharper a priori upper error bounds are obtained for instance for sufficiently regular solutions we prove optimal a priori error bounds on the discretization error in an energy norm when 1 p leq 2 we also show that the new a posteriori error estimates provide improved upper and lower bounds on the discretization error for sufficiently regular solutions the a posteriori error estimates are further shown to be equivalent on the discretization error in a quasi norm

approximations of very weak solutions to boundary value problems standard weak solutions to the poisson problem on a bounded domain have square integrable derivatives which limits the admissible regularity of inhomogeneous data the concept of solution may be further weakened in order to define solutions when data is rough such as for inhomogeneous dirichlet data that is only square integrable over the boundary such very weak solutions satisfy a nonstandard variational form u v g v a galerkin approximation combined with an approximation of the right hand side g defines a finite element approximation of the very weak solution applying conforming linear elements leads to a discrete solution equivalent to the text book finite element solutionto the poisson problem in which the boundary data is approximated by l2 projections the l2 convergence rate of the discrete solution is o hs for some s in 0 1 2 that depends on the shape of the domain assuming a polygonal two dimensional or polyhedral three dimensional domain without slits and only square integr

analysis and finite element approximations for distributed optimal control problems for implicit parabolic equations this work concerns analysis and error estimates for optimal control problems related to implicit parabolic equations the minimization of the tracking functional subject to implicit parabolic equations is examined existence of an optimal solution is proved and an optimality system of equations is derived semi discrete in space error estimates for the finite element approximations of the optimality system are presented these estimates are symmetric and applicable for higher order discretizations finally fully discrete error estimates of arbitrarily high order are presented based on a discontinuous galerkin in time and conforming in space scheme two examples related to the lagrangian moving mesh galerkin formulation for the convection diffusion equation are described

convergence of finite element approximations to state constrained convex parabolic boundary control problems this paper is concerned with the numerical solution of state constrained parabolic boundary control problems by finite element approximations error estimates for the optimal values and in the coercive case for the optimal solutions are derived these estimates are used to prove convergence results under rather weak assumptions in the noncoercive case a bang bang principle is shown to obtain convergence results for the discrete controls also a discussion of several numerical examples concludes the paper

constrained lqr problems in elliptic distributed control systems with point observations in this paper we study bound constrained lqr problems in distributed control systems governed by the elliptic equation with point observations which are motivated by problems in corrosion engineering and contemporary smart materials several regularity and characterization theorems have been established in particular three decomposition formulas are obtained to characterize the optimal control and optimal layer density and are used to direct the numerical computations these results cannot be obtained by the traditional galerkin variational method in the process several useful lemmas are established which are of independent interest we point out that the classical lagrangian multiplier method lmm may fail to provide a reliable numerical algorithm based on our characterization results and the boundary element method two algorithms are proposed to carry out numerical computations it has been shown by our numerical experiments that both algorithms are efficient and insensitive to the partition number of the boundary an adaptive local refinement scheme has also been designed to handle the rough behavior of the optimal solution around sensor locations

counting h colorings of partial k trees the problem of counting all h colorings of a graph g with n vertices is considered while the problem is in general p complete we give linear time algorithms that solve the main variants of this problem when the input graph g is a k tree or in the case where g is directed when the underlying graph of g is a k tree our algorithms remain polynomial even in the case where k o logn or in the case where the size of h is o n our results are easy to implement and imply the existence of polynomial time algorithms for a series of problems on partial k trees such as core checking and chromatic polynomial computation

new elliptic projections and a priori error estimates of h1 galerkin mixed finite element methods for optimal control problems governed by parabolic integro differential equations in this paper we discuss a priori error estimates of h1 galerkin mixed finite element methods for optimal control problems governed by parabolic integro differential equations the state variables and co state variables are approximated by the lowest order raviart thomas mixed finite element and linear finite element and the control variable is approximated by piecewise constant functions both semidiscrete and fully discrete schemes are considered based on some new elliptic projections we derive a priori error estimates for the control variable the state variables and the adjoint state variables the related a priori error estimates for the new projections error are also established a numerical example is given to demonstrate the theoretical results

approximation of boundary control problems on curved domains in this paper we consider boundary control problems associated to a semilinear elliptic equation defined in a curved domain omega the dirichlet and neumann cases are analyzed to deal with the numerical analysis of these problems the approximation of omega by an appropriate domain omega h typically polygonal is required here we do not consider the numerical approximation of the control problems instead we formulate the corresponding infinite dimensional control problems in omega h and we study the influence of the replacement of omega by omega h on the solutions of the control problems our goal is to compare the optimal controls defined on gamma partial omega with those defined on gamma h partial omega h and to derive some error estimates the use of a convenient parametrization of the boundary is needed for such estimates

error analysis for a finite element approximation of elliptic dirichlet boundary control problems we consider the galerkin finite element approximation of an elliptic dirichlet boundary control model problem governed by the laplacian operator the analytical setting of this problem uses l 2 controls and a very weak formulation of the state equation however the corresponding finite element approximation uses standard continuous trial and test functions for this approximation we derive a priori error estimates of optimal order which are confirmed by numerical experiments the proofs employ duality arguments and known results from the l p error analysis for the finite element dirichlet projection

finite element approximation of parabolic time optimal control problems the numerical approximation of a parabolic time optimal control problem via piecewise linear splines is considered at each stage of the approximation a bang bang approximate control is selected by solving for its switching times as the solution of a constrained nonlinear least squares optimization problem the well posedness of the approximation scheme is shown and the rate of convergence to the exact solution investigated numerical results for some one and two dimensional parabolic control problems are given

adaptive finite element methods for optimal control of partial differential equations basic concept a new approach to error control and mesh adaptivity is described for the discretization of optimal control problems governed by elliptic partial differential equations the lagrangian formalism yields the first order necessary optimality condition in form of an indefinite boundary value problem which is approximated by an adaptive galerkin finite element method the mesh design in the resulting reduced models is controlled by residual based a posteriori error estimates these are derived by duality arguments employing the cost functional of the optimization problem for controlling the discretization error in this case the computed state and costate variables can be used as sensitivity factors multiplying the local cell residuals in the error estimators this results in a generic and simple algorithm for mesh adaptation within the optimization process this method is developed and tested for simple boundary control problems in semiconductor models

adaptive finite element approximation for distributed elliptic optimal control problems in this paper sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems these error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adjustments and can save substantial computational work

a posteriori error estimates for discontinuous galerkin time stepping method for optimal control problems governed by parabolic equations in this paper we examine the discontinuous galerkin dg finite element approximation to convex distributed optimal control problems governed by linear parabolic equations where the discontinuous finite element method is used for the time discretization and the conforming finite element method is used for the space discretization we derive a posteriori error estimates for both the state and the control approximation assuming only that the underlying mesh in space is nondegenerate for problems with control constraints of obstacle type which are the kind most frequently met in applications further improved error estimates are obtained

a posteriori error estimates for control problems governed by stokes equations in this paper we derive a posteriori error estimates for the finite element approximation of distributed optimal control problems governed by the stokes equations we obtain a posteriori error estimators for both the state and the control approximation in the l2 norm and the h1 norm these estimates can be used to construct reliable adaptive finite element approximation for the control problems

a simple computational homogenization method for structures made of linear heterogeneous viscoelastic materials in this paper a numerical multiscale method is proposed for computing the response of structures made of linearly non aging viscoelastic and highly heterogeneous materials in contrast with most of the approaches reported in the literature the present one operates directly in the time domain and avoids both defining macroscopic internal variables and concurrent computations at micro and macro scales the macroscopic constitutive law takes the form of a convolution integral containing an effective relaxation tensor to numerically identify this tensor a representative volume element rve for the microstructure is first chosen relaxation tests are then numerically performed on the rve correspondingly the components of the effective relaxation tensor are determined and stored for different snapshots in time at the macroscopic scale a continuous representation of the effective relaxation tensor is obtained in the time domain by interpolating the data with the help of spline functions the convolution integral characterizing the time dependent macroscopic stress strain relation is evaluated numerically arbitrary local linear viscoelastic laws and microstructure morphologies can be dealt with implicit algorithms are provided to compute the time dependent response of a structure at the macroscopic scale by the finite element method accuracy and efficiency of the proposed approach are demonstrated through 2d and 3d numerical examples and applied to estimate the creep of structures made of concrete

generalization of the jensen inequality for pseudo integral generalizations of the jensen integral inequality for the pseudo integral are proven there are considered two cases of the real semiring with pseudo operations one when pseudo operations are defined by monotone and continuous function g then the pseudo integral reduces on g integral and the second semiring a b max where the pseudo multiplication is generated

analysis and finite element approximation of an optimal control problem in electrochemistry with current density controls an optimal control problem for impressed cathodic systems in electrochemistry is studied the control in this problem is the current density on the anode a matching objective functional is considered we first demonstrate the existence and uniqueness of solutions for the governing partial differential equation with a nonlinear boundary condition we then prove the existence of an optimal solution next we derive a necessary condition of optimality and establish an optimality system of equations finally we define a finite element algorithm and derive optimal error estimates

ritz galerkin approximation of the time optimal boundary control problem for parabolic systems with dirichlet boundary conditions this paper deals with ritz galerkin approximations of the following two problems i boundary value problems with l 2 boundary data given in the form of dirichlet boundary conditions ii time optimal control problems for parabolic systems with control acting on the boundary in both cases optimal rates of convergence of approximation are obtained also the specialization is considered to approximating with nonconformal elements which are not required to satisfy boundary conditions corresponding rates of convergence are also proved

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

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

an efficient algorithm for the evaluation of convolution integrals we propose an algorithm for the numerical evaluation of convolution integrals of the form 0 xk x y f y x dy for x 0 x our method is especially suitable in situations where the fundamental interval 0 x is very long and the kernel function k is expensive to calculate separate versions are provided where the forcing function f is known in advance and where it must be determined step by step along the solution path these methods are efficient with respect to both run time and memory requirements

a high accuracy nfem for constrained optimal control problems governed by elliptic equations in this paper a new nonconforming finite element method nfem is proposed for the constrained optimal control problems ocps governed by elliptic equations the state and co state are approximated by the nonconforming eq 1 rot element and the control is approximated by the piecewise constant element respectively the superclose properties for the above three variables are obtained moreover for the state and co state the superconvergence results are achieved in a broken energy norm by using the post processing technique lastly some numerical examples are provided to verify the theoretical analysis

idempotent integral as limit of g integrals we show that sup and inf decomposable measures can be obtained as limits of families of pseudo additive measures with respect to generated pseudo additions the corresponding integrals with respect to sup or inf decomposable measures can be obtained as limits of families of g integrals

new methods for 3 sat decision and worst case analysis abstract we prove the worst case upper bound 1 5045 n for the time complexity of 3 sat decision where n is the number of variables in the input formula introducing new methods for the analysis as well as new algorithmic techniques we add new 2 and 3 clauses called blocked clauses generalizing the extension rule of extended resolution our methods for estimating the size of trees lead to a refined measure of formula complexity of 3 clause sets and can be applied also to arbitrary trees

finite element approximations of parabolic optimal control problems with controls acting on a lower dimensional manifold this paper is devoted to the study of finite element approximations to parabolic optimal control problems with controls acting on a lower dimensional manifold the manifold can be a point a curve or a surface which may be independent of time or evolve in the time horizon and is assumed to be strictly contained in the space domain at first we obtain the first order optimality conditions for the control problems and the corresponding regularity results then for the control problems we consider the fully discrete finite element approximations based on the piecewise constant discontinuous galerkin scheme for time discretization and piecewise linear finite elements for space discretization and variational discretization to the control variable a priori error estimates are finally obtained for the fully discretized control problems and supported by numerical examples

a superconvergent hybridizable discontinuous galerkin method for dirichlet boundary control of elliptic pdes we begin an investigation of hybridizable discontinuous galerkin hdg methods for approximating the solution of dirichlet boundary control problems governed by elliptic pdes these problems can involve atypical variational formulations and often have solutions with low regularity on polyhedral domains these issues can provide challenges for numerical methods and the associated numerical analysis we propose an hdg method for a dirichlet boundary control problem for the poisson equation and obtain optimal a priori error estimates for the control specifically under certain assumptions for a 2d convex polygonal domain we show the control converges at a superlinear rate we present 2d and 3d numerical experiments to demonstrate our theoretical results

pseudo additive measures and integrals abstract we suggest pseudo additive measures based on a pseudo addition and discuss integrals with respect to pseudo additive measures a pseudo additive measure is a special type of fuzzy measures to define an integral a multiplication corresponding to a pseudo addition is introduced the resulting integral is an extension of the lebesgue integral in this context radon nikodym like theorems are shown

general chebyshev type inequalities for sugeno integrals chebyshev type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the real line and product operation

adaptive finite element method for elliptic optimal control problems convergence and optimality in this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints we use variational discretization concept to discretize the control variable and piecewise linear and continuous finite elements to approximate the state variable based on the well established convergence theory of afem for elliptic boundary value problems we rigorously prove the convergence and quasi optimality of afem for optimal control problems with respect to the state and adjoint state variables by using the so called perturbation argument numerical experiments confirm our theoretical analysis

weak boundary penalization for dirichlet boundary control problems governed by elliptic equations abstract this paper concerns the finite element approximation of dirichlet boundary control problems governed by elliptic equations different from the existing literatures in which standard finite element method mixed finite element method or robin penalization method are used to deal with the underlying problems we adopt an alternative penalization approach introduced by nitsche called weak boundary penalization compared with the above methods our discrete scheme not only keeps consistency and avoids penalization error but also can be analyzed and computed conveniently as neumann boundary control problems based on the weak boundary penalization method we establish a finite element approximation to the dirichlet boundary control problems and derive the a priori error estimates for the control state and adjoint state numerical experiments are provided to confirm our theoretical results

adaptive space time finite element methods for parabolic optimization problems in this paper we derive a posteriori error estimates for space time finite element discretizations of parabolic optimization problems the provided error estimates assess the discretization error with respect to a given quantity of interest and separate the influences of different parts of the discretization time space and control discretization this allows us to set up an efficient adaptive algorithm which successively improves the accuracy of the computed solution by construction of locally refined meshes for time and space discretizations

counting models for 2 sat and 3 sat formulae we here present algorithms for counting models and max weight models for 2sat and 3sat formulae they use polynomial space and run in o 1 2561n and o 1 6737n time respectively where n is the number of variables this is faster than the previously best algorithms for counting nonweighted models for 2sat and 3sat which run in o 1 3247n and o 1 6894n time respectively in order to prove these time bounds we develop new measures of formula complexity allowing us to conveniently analyze the effects of certain factors with a large impact on the total running time we also provide an algorithm for the restricted case of separable 2sat formulae with fast running times for well studied input classes for all three algorithms we present interesting applications such as computing the permanent of sparse 0 1 matrices

the complexity of counting in sparse regular and planar graphs we show that a number of graph theoretic counting problems remain cal np hard indeed cal p complete in very restricted classes of graphs in particular we prove that the problems of counting matchings vertex covers independent sets and extremal variants of these all remain hard when restricted to planar bipartite graphs of bounded degree or regular graphs of constant degree we obtain corollaries about counting cliques in restricted classes of graphs and counting satisfying assignments to restricted classes of monotone 2 cnf formulae to achieve these results a new interpolation based reduction technique which preserves properties such as constant degree is introduced

number of models and satisfiability of sets of clauses abstract we present a way of calculating the number of models of propositional formulas represented by sets of clauses the complexity of such a procedure is o n k where k is the length of clauses and n is the number of variables in the clauses the value of 2 is approximately 1 619 value of 3 is approximately 1 840 and the value of k approaches 2 when k is large further we apply the theory on satisfiability problems especially on the 3 sat problems the complexity of the 3 sat problems is o n where n is the number of variables in the clauses the value of is approximately 1 571 which is better than the results in schiermeyer 1993 and monien and schiermeyer 1985

some a posteriori error estimators for elliptic partial differential equations we present three new a posteriori error estimators in the energy norm for finite element solutions to elliptic partial differential equations the estimators are based on solving local neumann problems in each element the estimators differ in how they enforce consistency of the neumann problems we prove that as the mesh size decreases under suitable assumptions two of the error estimators approach upper bounds on the norm of the true error and all three error estimators are within multiplicative constants of the norm of the true error we present numerical results in which one of the error estimators appears to converge to the norm of the true error

jensen and chebyshev inequalities for pseudo integrals of set valued functions set valued functions are an important mathematical notion and play a crucial role in several practical areas at the same time pseudo analysis as a background allows extension of some classical mathematical notions to the forms that are highly applicable in some nonstandard situations this paper focuses on pseudo integration of set valued functions which is generalization of aumann s research and corresponding extensions of the jensen and chebyshev integral inequalities to the set valued case since the integral inequalities in question are widely used in various aspects of mathematics the main motivation for the presented research lies in the possibility of expanding the applicability of these inequalities by combining the properties of set valued functions with pseudo analysis

a stabilized mixed finite element approximation of bilinear state optimal control problems abstract we propose a stabilized mixed finite element approximation for optimal control problems governed by bilinear state equations it is proved that the resulting mixed bilinear formulation is coercive and also continuous which avoids the difficulty in choosing the mixed finite element spaces i e the ladyzhenkaya babuska brezzi matching condition for the mixed finite element spaces is unnecessary under pointwise bilateral constraint on the control variable we deduce the optimality conditions at both continuous and discrete levels for the optimal control problems under consideration then an a priori error analysis in a weighted norm is discussed with relatively low regularity requirements for the solutions to the optimal control problems finally numerical experiments are given to confirm the efficiency and reliability of the proposed stabilized mixed finite element method

a posteriori error estimates for hp finite element solutions of convex optimal control problems in this paper we present a posteriori error analysis for hp finite element approximation of convex optimal control problems we derive a new quasi interpolation operator of clement type and a new quasi interpolation operator of scott zhang type that preserves homogeneous boundary condition the scott zhang type quasi interpolation is suitable for an application in bounding the errors in l 2 norm then hp a posteriori error estimators are obtained for the coupled state and control approximations such estimators can be used to construct reliable adaptive finite elements for the control problems

a partial k arboretum of graphs with bounded treewidth the notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies this survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class also some mutual relations between such classes are discussed

a priori and a posteriori error estimates of h 1 galerkin mixed finite element methods for optimal control problems governed by pseudo hyperbolic integro differential equations abstract in this paper we investigate a priori and a posteriori error estimates of h1 galerkin mixed finite element methods for optimal control problems governed by pseudo hyperbolic integro differential equations the state variables and co state variables are approximated by the lowest order raviart thomas mixed finite element and linear finite element and the control variable is approximated by piecewise constant functions based on two new elliptic projections we derive a priori error estimates both for the control variable the state variable and the co state variable the related a priori error estimates for the new projections error are also established moreover a posteriori error estimates for all variables are derived via energy method such a posteriori error estimates which are apparently not available in the literature are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem

chebyshev type inequalities for pseudo integrals abstract chebyshev type inequalities for two classes of pseudo integrals are shown one of them concerning the pseudo integrals based on a function reduces on the g integral where pseudo operations are defined by a monotone and continuous function g another one concerns the pseudo integrals based on a semiring a b max where is generated moreover a strengthened version of chebyshev s inequality for pseudo integrals is proved

a chebyshev type inequality for fuzzy integrals abstract in this paper we prove a chebyshev type inequality for fuzzy integrals more precisely we show that 0 1 fg d 0 1 f d 0 1 g d where is the lebesgue measure on r and f g 0 1 0 are two continuous and strictly monotone functions both increasing or both decreasing also some examples and applications are presented

semidiscrete approximations of optimal robin boundary control problems constrained by semilinear parabolic pde an optimal robin boundary control problem associated with semilinear parabolic partial differential equations is considered existence of an optimal solution is proved and an optimality system of equations is derived semidiscrete finite element approximations of the optimality system are defined and error estimates are obtained

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

error estimates for the numerical approximation of dirichlet boundary control for semilinear elliptic equations we study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control the control is the trace of the state on the boundary of the domain which is assumed to be a convex polygonal open set in mathbb r 2 piecewise linear finite elements are used to approximate the control as well as the state we prove that the error estimates are of order o h 1 1 p for some p 2 which is consistent with the w 1 1 p p gamma regularity of the optimal control

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

a priori and a posteriori error analysis of edge stabilization galerkin method for the optimal control problem governed by convection dominated diffusion equation in this paper we study an edge stabilization galerkin approximation scheme for the constrained optimal control problem governed by convection dominated diffusion equation the method uses least square stabilization of the gradient jumps across element edges a priori and a posteriori error estimates are derived for both the state co state and the control the theoretical results are illustrated by two numerical experiments

generalized pseudo convolution in the theory of probabilistic metric spaces information fuzzy numbers optimization system theory a notion of the generalized pseudo convolution of functions based on pseudo operations is introduced it is proved that such general pseudo convolution is commutative associative operation that in some cases has a unit element we present that the generalized pseudo convolution occurs as a basic notion in many different theories as probabilistic metric spaces information theory fuzzy numbers optimization system theory

finite dimensional approximation of a class of constrained nonlinear optimal control problems an abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed nonlinearities occur in both the objective functional and the constraints the framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces an approximate problem posed on finite dimensional spaces together with a number of hypotheses concerning the two problems the framework is used to show that optimal solutions exist to show that lagrange multipliers may be used to enforce the constraints to derive an optimality system from which optimal states and controls may be deduced and to derive existence results and error estimates for solutions of the approximate problem the abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods the first involves the von k arm an plate equations of nonlinear elasticity the second the ginzburg landau equations of superconductivity and the third the navier stokes equations for incompressible viscous flows

boundary value problems and optimal boundary control for the navier stokes system the two dimensional case we study optimal boundary control problems for the two dimensional navier stokes equations in an unbounded domain control is effected through the dirichlet boundary condition and is sought in a subset of the trace space of velocity fields with minimal regularity satisfying the energy estimates an objective of interest is the drag functional we first establish three important results for inhomogeneous boundary value problems for the navier stokes equations namely we identify the trace space for the velocity fields possessing finite energy we prove the existence of a solution for the navier stokes equations with boundary data belonging to the trace space and we identify the space in which the stress vector along the boundary of admissible solutions is well defined then we prove the existence of an optimal solution over the control set finally we justify the use of lagrange multiplier principles derive an optimality system of equations in the weak sense from which optimal states and controls may be determined and prove that the optimality system of equations satisfies in appropriate senses a system of partial differential equations with boundary values

an observer s information dynamics acquisition of information and the origin of the cognitive dynamics conventional information science considers an information process but traditionally uses the probability measure for random states and shannon s entropy as the uncertainty function of these states this paper presents a new approach based on an integral information measure of the random process an entropy functional ef on the trajectories of the process accumulates and encodes the process inner connections between the information states the application of a variation principle vp to the ef determines the process information path functional ipf whose extremal trajectories describe the informational dynamics of this process information dynamics with the vp invariant relations evaluate the information content of a random process expose its information code and reveal a conserved hidden information produced at an acquisition of the process information by introducing both objective and subjective information observers we consider the observers information cognitive dynamics and neurodynamics based on the ef ipf approach the universal nature of information process dynamics and regularities discovered in the information observers have many applications not only in cognitive and intelligent systems but also in different biological social and economic systems

a posteriori error estimates for nonlinear problems l r o t p ω error estimates for finite element discretizations of parabolic equations using the abstract framework of 9 we analyze a residual a posteriori error estimator for space time finite element discretizations of quasilinear parabolic pdes the estimator gives global upper and local lower bounds on the error of the numerical solution the finite element discretizations in particular cover the so called 0 scheme which includes the implicit and explicit euler methods and the crank nicholson scheme

numerics and hydrodynamic stability toward error control in computational fluid dynamics we critically review the available error analysis in computational fluid dynamics cfd and come to the conclusion that the existing error estimates are meaningless in most cases of interest we propose a new approach to error analysis in cfd aiming at reliable and efficient adaptive quantitative error control this is based on a precise analysis of hydrodynamic stability coupled with galerkin orthogonality we prove a priori and a posteriori type error estimates in a model case for pipe flow formulate corresponding adaptive algorithms and discuss the potential of this approach for adaptive error control in cfd

finite element approximation of dirichlet boundary control for elliptic pdes on two and three dimensional curved domains we consider the variational discretization of elliptic dirichlet optimal control problems with constraints on the control the underlying state equation which is considered on smooth two and three dimensional domains is discretized by linear finite elements taking into account domain approximation the control variable is not discretized we obtain optimal error bounds for the optimal control in two and three space dimensions and prove a superconvergence result in two dimensions provided that the underlying mesh satisfies some additional condition we confirm our analytical findings by numerical experiments

pseudo fractional integral inequality of chebyshev type in this paper we give a general version of chebyshev type inequality for pseudo convolution integral on a semiring a b our result is flexible enough to support both pseudo integral and convolution integral e g fractional integral thus closing the series of papers it includes the corresponding results of agahi et al 1 as a special case finally some concluding remarks are drawn and some open problems for further investigations are given

approximations of elliptic optimal control problems with controls acting on a lower dimensional manifold in this paper we study finite element approximations to some elliptic optimal control problems with controls acting on a lower dimensional manifold which can be a point a curve or a surface we use piecewise linear finite elements to approximate state variables while utilizing the variational discretization to approximate control variables we derive several a priori error estimates for optimal controls from different cases depending on the dimensions of the computational domain and the manifold where controls act we ends up with extensive numerical experiments which confirm our theoretical findings