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

feasible and noninterior path following in constrained minimization with low multiplier regularity primal dual path following methods for constrained minimization problems in function space with low multiplier regularity are introduced and analyzed regularity properties of the path are proved the path structure allows us to define approximating models which are used for controlling the path parameter in an iterative process for computing a solution of the original problem the moreau yosida regularized subproblems of the new path following technique are solved efficiently by semismooth newton methods the overall algorithmic concept is provided and numerical tests including a comparison with primal dual path following interior point methods for state constrained optimal control problems show the efficiency of the new concept

the primal dual active set strategy as a semismooth newton method this paper addresses complementarity problems motivated by constrained optimal control problems it is shown that the primal dual active set strategy which is known to be extremely efficient for this class of problems and a specific semismooth newton method lead to identical algorithms the notion of slant differentiability is recalled and it is argued that the max function is slantly differentiable in lp spaces when appropriately combined with a two norm concept this leads to new local convergence results of the primal dual active set strategy global unconditional convergence results are obtained by means of appropriate merit functions

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

semismooth newton methods for optimal control of the wave equation with control constraints in this paper optimal control problems governed by the wave equation with control constraints are analyzed three types of control action are considered distributed control neumann boundary control and dirichlet control and proper functional analytic settings for them are discussed for treating inequality constraints semismooth newton methods are discussed and their convergence properties are investigated in the case of distributed and neumann control superlinear convergence is shown for dirichlet boundary control superlinear convergence is proved for a strongly damped wave equation for numerical realization a space time finite element discretization is discussed numerical examples illustrate the results

reduced basis approximation of parametrized optimal flow control problems for the stokes equations this paper extends the reduced basis method for the solution of parametrized optimal control problems presented in negri et al 2013 to the case of noncoercive elliptic equations such as the stokes equations we discuss both the theoretical properties with particular emphasis on the stability of the resulting double nested saddle point problems and on aggregated error estimates and the computational aspects of the method then we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three dimensional flow through boundary control demonstrating the effectivity of the methodology

constrained dirichlet boundary control in l 2 for a class of evolution equations optimal dirichlet boundary control based on the very weak solution of a parabolic state equation is analyzed this approach allows us to consider the boundary controls in l 2 which has advantages over approaches which consider control in sobolev spaces involving fractional derivatives pointwise constraints on the boundary are incorporated by the primal dual active set strategy its global and local superlinear convergences are shown a discretization based on space time finite elements is proposed and numerical examples are included

representation of computations in concurrent automata by dependence orders abstract an automaton with concurrency relations a is a labelled transition system with a collection of binary relations indicating when two actions in a given state of the automaton can occur independently of each other the concurrency relations induce a natural equivalence relation for finite computation sequences we investigate two graph theoretic representations of the equivalence classes of computation sequences and obtain that under suitable assumptions on a they are isomorphic furthermore the graphs are shown to carry a monoid operation reflecting precisely the composition of computations this generalizes fundamental graph theoretical representation results due to mazurkiewicz in trace theory

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

an energy space finite element approach for elliptic dirichlet boundary control problems in this paper we present a finite element analysis for a dirichlet boundary control problem where the dirichlet control is considered in a convex closed subspace of the energy space h 1 2 gamma h 1 2 as an equivalent norm in h 1 2 gamma h 1 2 we use the energy norm induced by the so called steklov poincare operator which realizes the dirichlet to neumann map and which can be implemented by using standard finite element methods the presented stability and error analysis of the discretization of the resulting variational inequality is based on the mapping properties of the solution operators related to the primal and adjoint boundary value problems and their finite element approximations some numerical results are given which confirm on one hand the theoretical estimates but on the other hand indicate the differences when modelling the control in l 2 gamma l 2

defect structures in sine gordon like models abstract we investigate several models described by real scalar fields searching for topological defects some models are described by a single field and support one or two topological sectors and others are two field models which support several topological sectors almost all the defect structures that we find are stable and finite energy solutions of first order differential equations that solve the corresponding equations of motion in particular for the double sine gordon model we show how to find small and large bps solutions as deformations of the bps solution of the 4 model and also for most of the two field models we find the corresponding integrating factors which lead to the complete set of bps solutions nicely unveiling how they bifurcate among the several topological sectors

error estimates for variational normal derivatives and dirichlet control problems with energy regularization this article deals with error estimates for the finite element approximation of variational normal derivatives and as a consequence error estimates for the finite element approximation of dirichlet boundary control problems with energy regularization the regularity of the solution is carefully carved out exploiting weighted sobolev and holder spaces this allows to derive a sharp relation between the convergence rates for the approximation and the structure of the geometry more precisely the largest opening angle at the vertices of polygonal domains numerical experiments confirm that the derived convergence rates are sharp

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

on the regularity of the solutions of dirichlet optimal control problems in polygonal domains a linear quadratic dirichlet control problem governed by an elliptic equation posed on a possibly nonconvex polygonal domain is analyzed detailed regularity results are provided in classical sobolev slobodetski spaces in particular it is proved that in the presence of pointwise control constraints the optimal control is continuous despite the nonconvexity of the domain

invariance results for delay and volterra equations in fractional order sobolev spaces on deduit l invariance des trajectoires d equations de type volterra et a retard infini dans des espaces de sobolev d ordre fractionnaire pour des hypotheses minimales sur les donnees du probleme

edge stabilization for galerkin approximations of convection diffusion reaction problems n this paper we recall a stabilization technique for finite element methods for convection diffusion reaction equations originally proposed by j douglas jr and t dupont in computing methods in applied sciences second internat sympos versailles 1975 207 216 lecture notes in phys 58 springer berlin 1976 mr0440955 55 13823 the method uses least square stabilization of the gradient jumps across element boundaries we prove that the method is stable in the hyperbolic limit and prove optimal a priori error estimates we address the question of monotonicity of discrete solutions and present some numerical examples illustrating the theoretical results

optimal control of the convection diffusion equation using stabilized finite element methods in this paper we analyze the discretization of optimal control problems governed by convection diffusion equations which are subject to pointwise control constraints we present a stabilization scheme which leads to improved approximate solutions even on corse meshes in the convection dominated case moreover the in general different approaches optimize then discretize and discretize then optimize coincide for the proposed discretization scheme this allows for a symmetric optimality system at the discrete level and optimal order of convergence

theory of traces abstract the theory of traces originated by a mazurkiewicz in 1977 is an attempt to provide a mathematical description of the behavior of concurrent systems its aim is to reconcile the sequential nature of observations of the system behavior on the one hand and the nonsequential nature of causality between the actions of the system on the other hand one can see the theory of traces to be rooted in formal string language theory with the notion of partial commutativity playing the central role alternatively one can see the theory of traces to be rooted in the theory of labeled acyclic directed graphs or even in the theory of labeled partial orders this paper attempts to present a major portion of the theory of traces in a unified way however it is not a survey in the sense that a number of new notions are introduced and a number of new results are proved although traditionally most of the development in the theory of traces follows the string language theoretic line we try to demonstrate to the reader that the graph theoretic point of view may be more appropriate the paper essentially consists of two parts the first one sections 1 through 4 is concerned with the basic theory of traces the second one section 5 presents applications of the theory of traces to the theory of the behavior of concurrent systems where the basic system model we have chosen is the condition event system introduced by c a petri

recognizable languages in concurrency monoids automata with concurrency relations a are labelled transition systems with a collection of binary relations indicating when two actions in a given state of the automaton are concurrent we investigate concurrency monoids m a comprising all finite computation sequences of a modulo a canonical congruence induced by the concurrency relations with composition as monoid operation under suitable assumptions on a we obtain a kleene type characterization of the recognizable languages of m a this generalizes results of cori metivier perrin and ochmanski in trace theory

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

finite element error estimates in non energy norms for the two dimensional scalar signorini problem this paper is concerned with error estimates for the piecewise linear finite element approximation of the two dimensional scalar signorini problem on a convex polygonal domain varomega using a cea type lemma a supercloseness result and a non standard duality argument we prove w 1 p varomega l infty varomega w 1 infty varomega and h 1 2 partial varomega error estimates under reasonable assumptions on the regularity of the exact solution and l p varomega error estimates under comparatively mild assumptions on the involved contact sets the obtained orders of convergence turn out to be optimal for problems with essentially bounded right hand sides our results are accompanied by numerical experiments which confirm the theoretical findings

galerkin approximations of abstract parabolic boundary value problems with rough boundary data l p theory etude des approximations de galerkin d un probleme aux valeurs limites parabolique abstrait avec des donnees aux limites grossieres determination des vitesses de convergence optimales dans les normes lp

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

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

aspects of sine gordon solitons defects and gates it was recently noted how the classical sine gordon theory can support discontinuities or defects and yet maintain integrability by preserving sufficiently many conservation laws since soliton number is not preserved by a defect a possible application to the construction of logical gates is suggested

synchronization expressions with extended join operation synchronization expressions are high level constructs used for specifying minimal synchronization constraints of parallel processes their semantics is defined by the corresponding synchronization language the original definition of synchronization expressions 12 13 forces the languages to be closed under rewriting rules that for instance do not preserve regularity here we propose an extension of the syntactic definition of synchronization expressions and an appropriate modification of their semantics the extended definition has the advantage that it allows us to eliminate the less well motivated transformations rewriting rules describing properties of synchronization languages we show that the modified rewriting rules preserve regularity of the languages also we obtain a characterization of finite synchronization languages as the family consisting of languages satisfying the start termination property and closed under three types of simple rewriting rules

a semi smooth newton method for control constrained boundary optimal control of the navier stokes equations abstract in this paper we study optimal control of the navier stokes equations when the control acts as a pointwise constrained boundary condition of dirichlet type the problem is analyzed in the control space h 00 1 2 the optimality system and second order sufficient optimality conditions are derived for the numerical solution we apply a semi smooth newton method to a regularized version of the original problem and show convergence properties of the method and of the regularized solutions towards the original one

finite element approximation of optimal control problems governed by time fractional diffusion equation in this paper galerkin finite element approximation of optimal control problems governed by time fractional diffusion equations is investigated piecewise linear polynomials are used to approximate the state and adjoint state while the control is discretized by variational discretization method a priori error estimates for the semi discrete approximations of the state adjoint state and control are derived furthermore we also discuss the fully discrete scheme for the control problems a finite difference method developed in lin and xu 2007 is used to discretize the time fractional derivative fully discrete first order optimality condition is developed based on first discretize then optimize approach the stability and truncation error of the fully discrete scheme are analyzed numerical example is given to illustrate the theoretical findings

the velocity tracking problem for navier stokes flows with boundary control we present some systematic approaches to the mathematical formulation and numerical approximation of the time dependent optimal control problem of tracking the velocity for navier stokes flows in a bounded two dimensional domain with boundary control we study the existence of optimal solutions and derive an optimality system from which optimal solutions may be determined we also define and analyze semidiscrete in time and full space time discrete approximations of the optimality system and a gradient method for the solution of the fully discrete system the results of some computational experiments are provided

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

classical behavior of deformed sine gordon models abstract in this work we deform the 4 model with distinct deformation functions to propose a diversity of sine gordon like models we investigate the proposed models and we obtain all the topological solutions that they engender in particular we introduce non polynomial potentials which support some exotic two kink solutions

analysis of a robust finite element approximation for a parabolic equation with rough boundary data the approximation of parabolic equations with nonhomogeneous dirichlet boundary data by a numerical method that consists of finite elements for the space discretization and the backward euler time discretization is studied the boundary values are assumed in a least squares sense it is shown that this method achieves an optimal rate of convergence for rough only l2 boundary data and for smooth data as well the results of numerical computations which confirm the robust theoretical error estimates are also presented

a c0 interior penalty method for the dirichlet control problem governed by biharmonic operator an energy space based dirichlet boundary control problem governed by biharmonic equation is investigated and subsequently a c0 interior penalty method is proposed and analyzed an abstract a priori error estimate is derived under the minimal regularity conditions the abstract error estimate guarantees optimal order of convergence whenever the solution is sufficiently regular further an optimal order l2 norm error estimate is derived numerical experiments illustrate the theoretical findings

adaptivity with dynamic meshes for space time finite element discretizations of parabolic equations in this paper we develop an error estimator and an adaptive algorithm for efficient solution of parabolic partial differential equations the error estimator assesses the discretization error with respect to a given quantity of physical interest and separates the influence of the time and space discretizations this allows us to set up an efficient adaptive strategy producing economical locally refined meshes for each time step and an adapted time discretization the space and time discretization errors are equilibrated leading to an efficient method

the primal dual active set method for nonlinear optimal control problems with bilateral constraints the primal dual active set method has proved to be an efficient numerical tool in the context of diverse applications so far it has been investigated mainly for linear problems this paper is devoted to the study of global convergence of the primal dual active set method for nonlinear problems with bilateral constraints utilizing the close relationship between the primal dual active set method and semismooth newton methods local superlinear convergence of the method is investigated as well