analysis and discretization of an optimal control problem for the time periodic mhd equations we consider the mathematical formulation and analysis of an optimal control problem associated with the tracking of the velocity and the magnetic field of a viscous incompressible electrically conducting fluid in a bounded two dimensional domain through the adjustment of distributed controls existence of optimal solutions is proved and first order necessary conditions for optimality are used to derive an optimality system of partial differential equations whose solutions provide optimal states and controls semidiscrete in time approximations are defined and their convergence to the exact optimal solutions is shown

the fabry ehrenpreis gap theorem and linear differential equations of infinite order pour comprendre les theoremes de saut de type fabry dans un cadre general on utilise des operateurs de convolution determines par des hyperfonctions supportees par l origine

cloaking via change of variables for the helmholtz equation the transformation optics approach to cloaking uses a singular change of coordinates which blows up a point to the region being cloaked this paper examines a natural regularization obtained by 1 blowing up a ball of radius rather than a point and 2 including a well chosen lossy layer at the inner edge of the cloak we assess the performance of the resulting near cloak as the regularization parameter tends to 0 in the context of dirichlet and neumann boundary measurements for the time harmonic helmholtz equation since the goal is to achieve cloaking regardless of the content of the cloaked region we focus on estimates that are uniform with respect to the physical properties of this region in three space dimensions our regularized construction performs relatively well the deviation from perfect cloaking is of order in two space dimensions it does much worse the deviation is of order 1 log in addition to proving these estimates we give numerical examples demonstrating their sharpness some authors have argued that perfect cloaking can be achieved without losses by using the singular change of variable based construction in our regularized setting the analogous statement is false without the lossy layer there are certain resonant inclusions depending in general on that have a huge effect on the boundary measurements 2010 wiley periodicals inc

optimal control of the free boundary in a two phase stefan problem we present an optimal control approach for the solidification process of a melt in a container the process is described by a two phase stefan problem with the free boundary interface between the two phases modelled as a graph we control the evolution of the free boundary using the temperature on the container wall the control goal consists in tracking a prescribed evolution of the free boundary we achieve this goal by minimizing a appropriate cost functional the resulting minimization problem is solved numerically by a steepest descent method with step size control where the gradient of the cost functional is expressed in terms of the adjoint variables several numerical examples are presented which illustrate the performance of the method the novelty of the approach presented consists in using a sharp interface model for the control of the free boundary this guarantees direct access to the free boundary as optimization variable in terms of its parametrization as a graph moreover at any stage of the optimization process the physical laws constituted by the mathematical model are conserved and the heat flux into the free boundary is variable and thus does not need to be specified a priori in the optimization process this guarantees more flexibility than in the optimization approaches to two phase stefan problems taken so far

on the bezout problem and area of interpolating varieties in cn ii we give an estimate on the growth of the volume of zeros of entire holomorphic maps from c n to c n the methods of li taylor for the estimates for certain holomorphic maps are used to provide the better estimate which applies to general entire holomorphic maps and is shown to be precise by an example

existence theorems for a second order three point boundary value problem abstract letf 0 1 r 2 r be continuous ande c 0 1 let i 0 1 ai r all of theai s having the same sign i 1 2 m 2 0 x t f t x t x t e t t 0 1 e x 0 0 x 1 i 1 m 2 a i x i bc m we discuss existence theorems for the problem e bcm under some sign condition offabout the origin our analysis is based on a nonlinear alternative of leray schauder

optimal control of a free boundary problem with surface tension effects a priori error analysis we present a finite element method along with its analysis for the optimal control of a model free boundary problem with surface tension effects formulated and studied in h antil r h nochetto and p sodre siam j control optim 52 2014 pp 2771 2799 the state system couples the laplace equation in the bulk with the young laplace equation on the free boundary to account for surface tension we first prove that the state and adjoint systems have the requisite regularity for the error analysis strong solutions we discretize the state adjoint and control variables via piecewise linear finite elements and show optimal o h error estimates for all variables including the control this entails using the second order sufficient optimality conditions of h antil r h nochetto and p sodre siam j control optim 52 2014 pp 2771 2799 and the first order necessary optimality conditions for both the continuous and discrete systems we conclude with two numerical examples which exami

on lojasiewicz type inequalities for exponential polynomials abstract let f z n n 1 f n z e i n z be an exponential polynomial that is the coefficients f n z are polynomials in one complex variable we discuss the question of how close distinct roots of the equation f z 0 can get to each other

optimal control for electromagnetic cloaking metamaterial parameters design abstract in this paper we develop an optimal control problem to optimize the permittivity and permeability of the metamaterial which can have the invisible cloaking effect the inverse problem is calibrated as an optimization problem constrained by the time harmonic maxwell s equations proper objective functional is introduced with coefficients of the maxwell s equations as control variables we adopt the discontinuous galerkin method to solve the state equation several two dimensional cloaking benchmark problems are used to test our optimal control method numerical results demonstrate that the optimized permittivity and permeability of the metamaterial can achieve the cloaking effectively

optimal control of quasilinear boldsymbol h mathbf curl elliptic partial differential equations in magnetostatic field problems this paper examines the mathematical and numerical analysis for optimal control problems governed by quasilinear boldsymbol h mathbf curl elliptic partial differential equations we consider a mathematical model involving isotropic materials with magnetic permeability depending strongly on the magnetic field due to the physical and mathematical nature of the problem it is necessary to include divergence free constraints on the state and the control the divergence free control constraint is treated as an explicit variational equality constraint whereas a lagrange multiplier is included in the state equation to deal with the divergence free state constraint we investigate the sensitivity analysis of the control to state operator and establish the associated optimality conditions here the key tool for proving the kkt theory is the helmholtz decomposition an important consequence of the optimality system is a higher regularity result for the optimal control which we prove under the assumption

a second order dispersive fdtd algorithm for transverse electric maxwell s equations with complex interfaces this work overcomes the difficulty of the finite difference time domain fdtd algorithm in solving the transverse electric te maxwell s equations with inhomogeneous dispersive media for such te problems the electric fields are discontinuous across the dispersive interfaces moreover such discontinuities are time variant a novel matched interface and boundary time domain mibtd method is proposed to solve such problems through new developments in both mathematical formulations and numerical algorithms mathematically instead of handling all zeroth and first order jump conditions in a local coordinate we directly construct the te jump conditions which are needed in the fdtd computations in the cartesian coordinate such cartesian direction conditions depend on the time as well as tangential and normal components of the electric flux driven by the jump condition modeling we adopt the standard maxwell s equations in coupling with the debye auxiliary differential equations for the electric flux as the governing equations computationally the leapfrog scheme is employed for integrating the maxwell system and time dependent jump conditions sophisticated interface treatments are developed in both producing the te jump conditions and enforcing them in the fdtd algorithm based on a staggered yee lattice the numerical accuracy stability and efficiency of the proposed scheme are investigated by considering dispersive interfaces of various shapes the mibtd method achieves a spatially second order of convergence in all tests to the best of our knowledge the present mibtd scheme is the first fdtd method in the literature that can restore second order accuracy in treating curved dispersive interfaces for the te maxwell system

a generalized multi point boundary value problem for second order ordinary differential equations let f 0 1 x r 2 r be a function satisfying caratheodory s conditions and e t l 1 0 1 let x i t j 0 1 a i b j r i 1 2 m 2 j 1 2 n 2 0 x 1 x 2 x m 2 1 0 t 1 t 2 t n 2 1 be given this paper is concerned with the problem of existence of a solution for the generalized multi point boundary value problems x t f t x t x t e t 0

error estimates and superconvergence of a mixed finite element method for elliptic optimal control problems abstract in this paper we investigate error estimates and superconvergence of a mixed finite element method for elliptic optimal control problems the gradient for our method belongs to the square integrable space instead of the classical h div space the state and co state are approximated by the p 0 2 p 1 velocity pressure pair and the control variable is approximated by piecewise constant functions first we derive a priori error estimates in h 1 norm for the state and the co state scalar functions a priori error estimates in l 2 2 norm for the state and the co state vector functions and a priori error estimates in l 2 norm for the control function then using postprocessing projection operator we derive a superconvergence result for the control variable next we get a priori error estimates in l 2 norm for the state and the co state scalar functions finally a numerical example is given to demonstrate the theoretical results

seamless integration of global dirichlet to neumann boundary condition and spectral elements for transformation electromagnetics abstract in this paper we present an efficient spectral element method sem for solving general two dimensional helmholtz equations in anisotropic media with particular applications in accurate simulation of polygonal invisibility cloaks concentrators and circular rotators arisen from the field of transformation electromagnetics te in practice we adopt a transparent boundary condition tbc characterised by the dirichlet to neumann dtn map to reduce wave propagation in an unbounded domain to a bounded domain we then introduce a semi analytic technique to integrate the global tbc with local curvilinear elements seamlessly which is accomplished by using a novel elemental mapping and analytic formulas for evaluating global fourier coefficients on spectral element grids exactly from the perspective of te an invisibility cloak is devised by a singular coordinate transformation of maxwell s equations that leads to anisotropic materials coating the cloaked region to render any object inside invisible to observers outside an important issue resides in the imposition of appropriate conditions at the outer boundary of the cloaked region i e cloaking boundary conditions cbcs in order to achieve perfect invisibility following the spirit of yang and wang 2015 we propose new cbcs for polygonal invisibility cloaks from the essential pole conditions related to singular transformations this allows for the decoupling of the governing equations of inside and outside the cloaked regions with this efficient spectral element solver at our disposal we can study the interesting phenomena when some defects and lossy or dispersive media are placed in the cloaking layer of an ideal polygonal cloak

positive solutions for n 1 1 three point boundary value problems with coefficient that changes sign abstract in this paper we establish existence results for positive solutions for the n 1 1 three point boundary value problems consisting of the equation u n a t f u t 0 t 0 1 with one of the following boundary value conditions u 0 u u 1 u u i 0 0 for i 1 2 n 2 and u n 2 0 u n 2 u n 2 1 u n 2 u i 0 0 for i 0 1 n 3 where 0 1 0 0 and a 0 1 r may change sign and r f 0 0 0 is a parameter our approach is based on the leray schauder degree theory this paper is motivated by eloe and henderson nonlinear anal 28 1997 1669 1680

positive solution of singular higher order m point boundary value problem with nonlinearity that changes sign this paper is about a class of singular higher order m point boundary value problems with nonlinearity that changes sign using the fixed point index theory we get a sufficient condition for the existence of positive solution to this problem

global existence for elastic waves with memory we treat the cauchy problem for nonlinear systems of viscoelasticity with a memory term we study the existence and the time decay of the solution to this nonlinear problem the kernel of the memory term includes integrable singularity at zero and polynomial decay at infinity we prove the existence of a global solution for space dimensions n 3 and arbitrary quadratic nonlinearities

twin solutions of boundary value problems for ordinary differential equations and finite difference equations a new twin fixed point theorem is applied first to obtain the existence of at least two positive solutions for the right focal boundary value problem y f ity 0 0 t 1 y 0 y 1 0 it is applied later to obtain the existence of at least two positive solutions for the analogous discrete right focal boundary value problem 2u k g u k 0 k 0 n u 0 u n 1 0

positive solutions of singular sublinear emden fowler boundary value problems abstract this paper is about the dirichlet boundary value problem of singular sublinear emden fowler equations a necessary and sufficient condition for the existence of positive solutions to this problem has been obtained by using the method of lower and upper solutions the uniqueness of positive solutions has also been discussed

a linearized viscous compressible flow plate interaction with non dissipative coupling abstract we address semigroup well posedness for a linear compressible viscous fluid interacting at its boundary with an elastic plate we derive the model by linearizing the compressible navier stokes equations about an arbitrary flow state so the fluid pde includes an ambient flow profile u in contrast to model in 6 we track the effect of this term at the flow structure interface yielding a velocity matching condition involving the material derivative of the structure this destroys the dissipative nature of the coupling of the dynamics we adopt here a lumer phillips approach with a view of associating fluid structure solutions with a c 0 semigroup e a t t 0 on a chosen finite energy space of data given this approach the challenge becomes establishing the maximal dissipativity of an operator a yielding the flow structure dynamics

stabilized interior penalty methods for the time harmonic maxwell equations we propose stabilized interior penalty discontinuous galerkin methods for the indefinite time harmonic maxwell system the methods are based on a mixed formulation of the boundary value problem chosen to provide control on the divergence of the electric field we prove optimal error estimates for the methods in the special case of smooth coefficients and perfectly conducting boundary using a duality approach

analysis of control for a free boundary problem of steady plaques in the artery abstract in the earlier paper of friedman et al a simplified model of plaque growth involving ldl and hdl cholesterols macrophages and foam cells is considered and they satisfy a coupled system of pdes with a free boundary the paper adds some control function to that model allowing the controlled growth of ldl hdl and plaque next the new dual dynamic programming approach for free boundary problem is developed to formulate sufficient optimality conditions for the optimal steering of drugs finally an approximate optimality and numerical calculations are presented

the upper and lower solution method for a class of singular nonlinear second order three point boundary value problems in this paper we develop the upper and lower solution method and the monotone iterative technique for a class of singular nonlinear second order three point boundary value problems a maximum principle is established and some new existence results are obtained

interior penalty dg methods for maxwell s equations in dispersive media in this paper we develop a fully discrete interior penalty discontinuous galerkin method for solving the time dependent maxwell s equations in dispersive media the model is described by a vector integral differential equation our scheme is proved to be unconditionally stable and achieve optimal error estimates in both l 2 norm and energy norm the scheme is implemented and numerical results supporting our analysis are presented

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

on a theorem of polya and levinson abstract in the present paper we prove a variation of the polya levinson interpolation result in the class of entire functions of infraexponential type for the sequences n n 1 satisfying limn n n and n m c n m that is without any condition on the asymptotic directions of the sequence

motion of an elastic solid inside an incompressible viscous fluid the motion of an elastic solid inside an incompressible viscous fluid is ubiquitous in nature mathematically such motion is described by a pde system that couples the parabolic and hyperbolic phases the latter inducing a loss of regularity which has left the basic question of existence open until now in this paper we prove the existence and uniqueness of such motions locally in time when the elastic solid is the linear kirchhoff elastic material the solution is found using a topological fixed point theorem that requires the analysis of a linear problem consisting of the coupling between the time dependent navier stokes equations set in lagrangian variables and the linear equations of elastodynamics for which we prove the existence of a unique weak solution we then establish the regularity of the weak solution this regularity is obtained in function spaces that scale in a hyperbolic fashion in both the fluid and solid phases our functional framework is optimal and provides the a priori estimates necessary for us to employ our fixed point procedure

optimal control of a free boundary problem analysis with second order sufficient conditions we consider a pde constrained optimization problem governed by a free boundary problem the state system is based on coupling the laplace equation in the bulk with a young laplace equation on the free boundary to account for surface tension as proposed by p saavedra and l r scott math comp 57 1991 pp 451 475 this amounts to solving a second order system both in the bulk and on the interface our analysis hinges on a convex control constraint such that the state constraints are always satisfied using only first order regularity we show that the control to state operator is twice continuously frechet differentiable we improve slightly the regularity of the state variables and exploit it to show existence of a control together with second order sufficient optimality conditions

riccati theory and singular estimates for a bolza control problem arising in linearized fluid structure interaction abstract we consider a bolza boundary control problem involving a fluid structure interaction model the aim of this paper is to develop an optimal feedback control synthesis based on riccati theory the model considered consists of a linearized navier stokes equation coupled on the interface with a dynamic wave equation the model incorporates convective terms resulting from the linearization of the navier stokes equation around equilibrium the existence of the optimal control and its feedback characterization via a solution to a riccati equation is established the main mathematical difficulty of the problem is caused by unbounded action of control forces which in turn result in riccati equations with unbounded coefficients and in singular behavior of the gain operator this class of problems has been recently studied via the so called singular estimate control systems secs theory which is based on the validity of the singular estimate se g avalos differential riccati equations for the active control of a problem in structural acoustic j optim theory appl 91 1996 695 728 i lasiecka mathematical control theory of coupled pde s in nsf cmbs lecture notes siam 2002 with unbounded controls i lasiecka a tuffaha riccati equations for the bolza problem arising in boundary point control problems governed by c0 semigroups satisfying a singular estimate j optim theory appl 136 2008 229 246 it is shown that the fluid structure interaction does satisfy the singular estimate se condition this is accomplished by showing that the maximal abstract parabolic regularity is transported via hidden hyperbolic regularity of the boundary traces on the interface thus the established singular estimate allows for the application of recently developed general theory which in turn implies well posedness of the feedback synthesis and of the associated riccati equation moreover the singularities in the optimal control and in the feedback operator at the terminal time are quantitatively described

average growth estimates for hyperplane sections of entire analytic sets suppose x is an analytic subvariety of c a basic problem in value distribution theory is to relate the growth of the volume of x to that of intersections of x with linear subspaces p of with dimx dim p n in contrast to the case where x is algebraic as described by the bezout theorem for a fixed subspace p there is no relationship between the counting functions of x and xnp it is easy to find examples where x n p is empty while x is large on the other hand an example given in 6 shows that x n p can be of infinite order even if x is of order 0 however average transcendental bezout estimates have been given by carlson 1 5 gruman 8 9 and stoll 18 gruman showed that for almost all linear subspaces p x n p has the same order of growth as x and is transcendental ifx is transcendental

modeling viscoelastic behavior of arterial walls and their interaction with pulsatile blood flow fluid structure interaction describing wave propagation in arteries driven by the pulsatile blood flow is a complex problem whenever possible simplified models are called for one dimensional models are typically used in arterial sections that can be approximated by the cylindrical geometry allowing axially symmetric flows although a good first approximation to the underlying problem the one dimensional model suffers from several drawbacks the model is not closed an ad hoc velocity profile needs to be prescribed to obtain a closed system and the model equations are quasi linear hyperbolic oversimplifying the viscous fluid dissipation typically producing shock wave solutions not observed in healthy humans in this manuscript we derived a simple closed reduced model that accounts for the viscous fluid dissipation to the leading order the resulting fluid structure interaction system is of hyperbolic parabolic type arterial walls were modeled by a novel linearly viscoelastic cylindrical koiter shell model and the flow of blood by the incompressible viscous navier stokes equations kelvin voigt type viscoelasticity was used to capture the hysteresis behavior observed in the measurements of the arterial stress strain response using the a priori estimates obtained from an energy inequality together with the asymptotic analysis and ideas from homogenization theory for porous media flows we derived an effective model which is an 2 approximation to the three dimensional axially symmetric problem whereis the aspect ratio of the cylindrical arterial section our model shows two interesting features of the underlying problem bending rigidity often times neglected in the arterial wall models plays a nonnegligible role in the 2 approximation of the original problem and the viscous fluid dissipation imparts long term viscoelastic memory effects on the motion of the arterial walls this does not to the leading order influence the hysteresis behavior of arterial walls the resulting model although two dimensional is in the form that allows the use of one dimensional finite element method techniques producing fast numerical solutions we devised a version of the douglas rachford time splitting algorithm to solve the underlying hyperbolic parabolic problem the results of the numerical simulations were compared with the experimental flow measurements performed at the texas heart institute and with the data corresponding to the hysteresis of the human femoral artery and the canine abdominal aorta excellent agreement was observed

optimal non dissipative discontinuous galerkin methods for maxwells equations in drude metamaterials simulation of electromagnetic wave propagation in metamaterials leads to more complicated time domain maxwells equations than the standard maxwells equations in free space in this paper we develop and analyze a non dissipative discontinuous galerkin dg method for solving the maxwells equations in drude metamaterials previous discontinuous galerkin methods in the literature for electromagnetic wave propagation in metamaterials were either non dissipative but sub optimal or dissipative and optimal our method uses a different and simple choice of numerical fluxes achieving provable non dissipative stability and optimal error estimates simultaneously we prove the stability and optimal error estimates for both semi and fully discrete dg schemes with the leap frog time discretization for the fully discrete case numerical results are given to demonstrate that the dg method can solve metamaterial maxwells equations effectively

superconvergence of triangular raviart thomas mixed finite element methods for a bilinear constrained optimal control problem in this paper we analyze the superconvergence of the bilinear constrained elliptic optimal control problem by triangular raviart thomas mixed finite element methods the state and the co state are approximated by the order k 1 raviart thomas mixed finite elements and the control is approximated by piecewise constant functions we obtain the superconvergence property between average l 2 projection and the approximation of the control variable and the convergence order is h 2 two numerical examples are presented for illustrating the superconvergence results

a sharper condition for the solvability of a three point second order boundary value problem letf 0 1 r2 rbe a function satisfying caratheodory s conditions ande t l1 0 1 let 0 1 r 1 1 be given this paper is concerned with the problem of existence of a solution for the three point boundary value problem formula omitted this problem was studied earlier by gupta ntouyas and tsamatos when 1 and when 1 with 1 in the general case this problem was studied by gupta as a multi point boundary value problem in this paper sharper existence conditions are obtained for the solvability of the above boundary value problem in the general case

a new convergence analysis of finite element methods for elliptic distributed optimal control problems with pointwise state constraints we consider finite element methods for elliptic distributed optimal control problems with pointwise state constraints on two and three dimensional convex polyhedral domains formulated as fourth order variational inequalities we develop a new convergence analysis that is applicable to c 1 finite element methods classical nonconforming finite element methods and discontinuous galerkin methods

optimal control and parameter estimation for stationary fluid structure interaction problems we investigate optimization problems in which the state is given in terms of fluid structure interactions the coupled problem is formulated with the help of the ale arbitrary lagrangian eulerian mapping the solution approach is based on derivative based optimization algorithms in which the derivatives are obtained with the help of the lagrange formalism leading to the so called optimality system the optimality system is then solved with newton s method the focus is on the proper derivation of the adjoint equations guiding the optimization formalism moreover special attention is given to the adjoint information transport between the fluid and structure subproblems numerical tests are used to substantiate the theoretical framework

strong solutions to a nonlinear fluid structure interaction system abstract in this paper we prove the existence of local in time smooth solutions to the nonlinear fluid structure interaction model first introduced in j l lions quelques methodes de resolution des problemes aux limites non lineaires dunod 1969 and considered in v barbu z grujic i lasiecka a tuffaha existence of the energy level weak solutions for a nonlinear fluid structure interaction model in fluids and waves in contemp math vol 440 amer math soc providence ri 2007 pp 55 82 v barbu z grujic i lasiecka a tuffaha smoothness of weak solutions to a nonlinear fluid structure interaction model indiana univ math j 57 3 2008 1173 1207 in particular the strong solutions here are obtained given initial datum for the navier stokes equation in the space h 1 and initial data for the wave equation w 0 and w 1 in the spaces h 2 e and h 1 e respectively

the interaction between quasilinear elastodynamics and the navier stokes equations the interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations coupled to one another along the moving material interface through the continuity of the velocity and traction vectors we prove the existence and uniqueness locally in time of strong solutions in sobolev spaces for quasilinear elastodynamics coupled to the incompressible navier stokes equations unlike our approach in 5 for the case of linear elastodynamics we cannot employ a fixed point argument on the nonlinear system itself and are instead forced to regularize it by a particular parabolic artificial viscosity term we proceed to show that with this specific regularization we obtain a time interval of existence which is independent of the artificial viscosity together with a priori estimates we identify the global solution in both phases as well as the interface motion as a weak limit in strong norms of our sequence of regularized problems

positive solutions of a nonlinear m point boundary value problem let ai 0 for i 1 m 3 and am 2 0 let i satisfy 0 1 2 m 2 1 and m 2i 1 ai i 1 we study the existence of positive solutions to the boundary value problem where a c 0 1 0 and f c 0 0 we show the existence of at least one positive solution if f is either superlinear or sublinear by applying a fixed point theorem in cones

analysis and application of the nodal discontinuous galerkin method for wave propagation in metamaterials in this paper we develop a nodal discontinuous galerkin method for solving the time dependent maxwell s equations when metamaterials are involved both semi and fully discrete schemes are constructed numerical stability and error estimate are proved for both schemes numerical results are presented to demonstrate that the method is not only efficient but also very effective in solving metamaterial maxwell s equations

a stable nonconforming mixed finite element scheme for elliptic optimal control problems a new stable nonconforming mixed finite element mfe scheme is proposed for the constrained optimal control problem ocp governed by elliptic equations the nonconforming fes are employed to approximate the co state the piecewise constant element for the state and control respectively the corresponding optimal order error estimates are derived by full use of the distinguish properties of the nonconforming element i e a the divergence of the function in the fe space is a constant b the consistency error is one order higher than its interpolation error in the broken energy norm finally some numerical results are carried out to verify the theoretical analysis

optimal a priori error estimates of parabolic optimal control problems with pointwise control in this paper we consider a parabolic optimal control problem with a pointwise dirac type control in space but variable in time in two space dimensions to approximate the problem we use the standard continuous piecewise linear approximation in space and the piecewise constant discontinuous galerkin method in time despite low regularity of the state equation we show almost optimal h 2 k convergence rate for the control in l 2 norm this result improves almost twice the previously known estimate in w gong m hinze and z zhou a priori error analysis for finite element approximation of parabolic optimal control problems with pointwise control tech report 2011 07 hamburger beitrage zur angewandten mathematik hamburg germany 2011

interpolating varieties for entire functions of minimal type abstract we obtain both necessary and sufficient conditions for a discrete variety in c n to be an interpolating variety for entire functions of minimal type

minimizing drag in a moving boundary fluid elasticity interaction abstract our goal is to minimize the fluid vorticity in the case of an elastic body moving and deforming inside the fluid using a distributed control this translates into analyzing an optimal control problem subject to a moving boundary fluid structure interaction fsi the fsi is described by the coupling of navier stokes and wave equations the control is inherently a nonlinear control acting as feedback on the moving frame its action depends on the flow map of the domain which is itself defined through the dynamics of the problem a key ingredient in the optimal control problem is represented by the long time behavior of the forced dynamics which was an open problem in the field our main results include existence of solutions for all times with small distributed sources and small initial data as well as existence of optimal control for the problem of minimization of drag in the fluid

positive solutions of m point boundary value problems the second order m point boundary value problem x h x f x 0 0 x 1 0 0 1 i 1m 2ai i is considered under some conditions concerning the first eigenvalue of the relevant linear operator where i 0 1 with 0 1 2 m 2 1 ai 0 with i 1m 2ai 1 h x is allowed to be singular at x 0 and x 1 the existence of positive solutions and multiple positive solutions is obtained by means of fixed point index theory similarly conclusions hold for some other m point boundary value conditions

on well posedness for a free boundary fluid structure model we address a fluid structure interaction model describing the motion of an elastic body immersed in an incompressible fluid we establish a priori estimates for the local existence of solutions for a class of initial data which also guarantees uniqueness

existence of a solution to a fluid multi layered structure interaction problem abstract we study a nonlinear unsteady moving boundary fluid structure interaction fsi problem in which the structure is composed of two layers a thick layer and a thin layer which serves as a fluid structure interface with mass the fluid flow which is driven by the time dependent dynamic pressure data is modeled by the navier stokes equations for an incompressible viscous fluid defined on a 2d cylinder the elastodynamics of the cylinder wall is governed by the 1d linear wave equation modeling the thin structural layer and by the 2d equations of linear elasticity modeling the thick structural layer we prove existence of a weak solution to this nonlinear fsi problem as long as the cylinder radius is greater than zero the spaces of weak solutions presented in this manuscript reveal a striking new feature the presence of a thin fluid structure interface with mass regularizes solutions of the coupled problem

an adaptive edge finite element method for electromagnetic cloaking simulation in this paper we develop an adaptive edge finite element method based on a reliable and efficient recovery type a posteriori error estimator for time harmonic maxwell equations the asymptotically exact a posteriori error estimator is based on the superconvergence result proved for the lowest order edge element on triangular grids where most pairs of triangles sharing a common edge form approximate parallelograms the efficiency and robustness of the proposed method is demonstrated by extensive numerical experiments for electromagnetic cloaking problems with highly anisotropic permittivity and permeability

goal oriented error estimation and adaptivity for free boundary problems the domain map linearization approach in free boundary problems the accuracy of a goal quantity of interest depends on both the accuracy of the approximate solution and the accuracy of the domain approximation we develop duality based a posteriori error estimates for functional outputs of solutions of free boundary problems that include both sources of error the derivation of an appropriate dual problem linearized adjoint is however nonobvious for free boundary problems to derive an appropriate dual problem we present the domain map linearization approach in this approach the free boundary problem is first transformed into an equivalent problem on a fixed reference domain after which the dual problem is obtained by linearization with respect to the domain map we show for a bernoulli type free boundary problem that this dual problem corresponds to a poisson problem with a nonlocal robin type boundary condition furthermore we present numerical experiments that demonstrate the effectivity of the dual based error estimate and its usefulness in goal oriented adaptive mesh refinement

positive solutions of nonlinear three point boundary value problems abstract let a c 0 1 b c 0 1 0 let 1 t be the unique solution of the linear boundary value problem u t a t u t b t u t 0 t 0 1 u 0 0 u 1 1 we study the existence of positive solutions to the nonlinear boundary value problem u t a t u t b t u t h t f u 0 t 0 1 u 0 0 u u 1 where 0 0 and f c 0 0 we show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones

a robust finite element solver for a multiharmonic parabolic optimal control problem this paper presents the analysis of a distributed parabolic optimal control problem in a multiharmonic setting in particular the desired state is assumed to be multiharmonic after eliminating the control from the optimality system we arrive at the reduced optimality system for the state and the co state that is nothing but a coupled system of a forward and a backward parabolic partial differential equation due to the linearity the state and the co state are multiharmonic as well we discretize the fourier coefficients by the finite element method this leads to a large system of algebraic equations which fortunately decouples into smaller systems each of them defining the cosine and sine fourier coefficients for the state and co state with respect to a single frequency for these smaller systems we construct preconditioners resulting in a fast converging minimal residual solver with a parameter independent convergence rate all these systems can be solved totally in parallel

existence of a weak solution to a nonlinear fluid structure interaction problem modeling the flow of an incompressible viscous fluid in a cylinder with deformable walls we study a nonlinear unsteady moving boundary fluid structure interaction fsi problem arising in modeling blood flow through elastic and viscoelastic arteries the fluid flow which is driven by the time dependent pressure data is governed by two dimensional incompressible navier stokes equations while the elastodynamics of the cylindrical wall is modeled by the one dimensional cylindrical koiter shell model two cases are considered the linearly viscoelastic and the linearly elastic koiter shell the fluid and structure are fully coupled two way coupling via the kinematic and dynamic lateral boundary conditions describing continuity of velocity the no slip condition and the balance of contact forces at the fluid structure interface we prove the existence of weak solutions to the two fsi problems the viscoelastic and the elastic case as long as the cylinder radius is greater than zero the proof is based on a novel semi discrete operator splitting numerical scheme known as the kinematically coupled scheme introduced in guidoboni et al j comput phys 228 18 6916 6937 2009 to numerically solve the underlying fsi problems the backbone of the kinematically coupled scheme is the well known marchuk yanenko scheme also known as the lie splitting scheme we effectively prove convergence of that numerical scheme to a solution of the corresponding fsi problem