a characterization of hybridized mixed methods for second order elliptic problems in this paper we give a new characterization of the approximate solution given by hybridized mixed methods for second order self adjoint elliptic problems we apply this characterization to obtain an explicit formula for the entries of the matrix equation for the lagrange multiplier unknowns resulting from hybridization we also obtain necessary and sufficient conditions under which the multipliers of the raviart thomas and the brezzi douglas marini methods of similar order are identical

a superconvergent ldg hybridizable galerkin method for second order elliptic problems we identify and study an ldg hybridizable galerkin method which is not an ldg method for second order elliptic problems in several space dimensions with remarkable convergence properties unlike all other known discontinuous galerkin methods using polynomials of degree k 0 for both the potential as well as the flux the order of convergence in l 2 of both unknowns is k 1 moreover both the approximate potential as well as its numerical trace superconverge in l 2 like norms to suitably chosen projections of the potential with order k 2 this allows the application of element by element postprocessing of the approximate solution which provides an approximation of the potential converging with order k 2 in l 2 the method can be thought to be in between the hybridized version of the raviart thomas and that of the brezzi douglas marini mixed methods

godement jacquet l functions and full theta lifts we relate poles of local godement jacquet l functions to distributions on matrix spaces with singular supports as an application we show the irreducibility of the full theta lifts to mathrm gl n mathrm f of generic irreducible representations of mathrm gl n mathrm f where mathrm f is an arbitrary local field

unified hybridization of discontinuous galerkin mixed and continuous galerkin methods for second order elliptic problems we introduce a unifying framework for hybridization of finite element methods for second order elliptic problems the methods fitting in the framework are a general class of mixed dual finite element methods including hybridized mixed continuous galerkin nonconforming and a new wide class of hybridizable discontinuous galerkin methods the distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements since the associated matrix is sparse symmetric and positive definite these methods can be efficiently implemented moreover the framework allows in a single implementation the use of different methods in different elements or subdomains of the computational domain which are then automatically coupled finally the framework brings about a new point of view thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom

smoothed projections in finite element exterior calculus the development of smoothed projections constructed by combining the canonical interpolation operators defined from the degrees of freedom with a smoothing operator have proved to be an eective tool in finite element exterior calculus the advan tage of these operators is that they are l 2 bounded projections and still they commute with the exterior derivative in the present paper we generalize the construction of these smoothed projections such that also non quasi uniform meshes and essential boundary conditions are covered the new tool introduced here is a space dependent smoothing operator which commutes with the exterior derivative

on the tempered l functions conjecture we give a general proof of shahidi s tempered l function conjecture which has previously been known in all but one case one of the consequences is the standard module conjecture for p adic groups which means that the langlands quotient of a standard module is generic if and only if the standard module is irreducible and the inducing data generic we have also included the result that every generic tempered representation of a p adic group is a sub representation of a representation parabolically induced from a generic supercuspidal representation with a non negative real central character 1 introduction let f be a non archimedean local field of characteristic 0 let g be the group of points of a quasi split connected reductive f group by a parabolic subgroup borel subgroup levi subgroup torus split torus of g we will mean the group of points of an f parabolic subgroup f borel subgroup f levi subgroup f torus f split torus of the algebraic group under lying g fix a borel subgroup b tu of g a nd lett0 t be the maximal split torus in t i fm is any semi standard levi subgroup of g i e a levi subgroup which contains t0 a standard parabolic subgroup of m will be a parabolic subgroup of m which contains b m denote by w the weyl group of g defined with respect to t0 and by w g the longest element in w by sh3 section 3 we can fix a non degenerate character of u which for every levi subgroup m is compatible with w g 0 w m we will still denote by the restriction of to m u every generic representation of m becomes generic with respect to after changing the splitting in u let p mu be a standard parabolic subgroup of g and tm the maximal split torus in the center of m we will write a for the dual of the real lie algebra am of tm a c for its complexification and a m for the positive weyl chamber in a defined with respect to p following w we define a map hm m am such that m f q hm m for every f rational character a of m i f is a smooth representation of m and a c we denote by the smooth rep resentation of m defined by m q hm m m remark that although the sign in the definition of hm has been changed compared to the one due to harish chandra the meaning of is unchanged the symbol i g will denote the

the quantum state diffusion model applied to open systems a model of a quantum system interacting with its environment is proposed in which the system is represented by a state vector that satisfies a stochastic differential equation derived from a density operator equation such as the bloch equation and consistent with it the advantages of the numerical solution of these equations over the direct numerical solution of the density operator equations are described the method is applied to the nonlinear absorber cascades of quantum transitions second harmonic generation and a measurement reduction process the model provides graphic illustrations of these processes with statistical fluctuations that mimic those of experiments the stochastic differential equations originated from studies of the measurement problem in the foundations of quantum mechanics the model is compared with the quantum jump model of dalibard 1992 carmichael and others which originated among experimenters looking for intuitive pictures and rules of computation

locking free optimal discontinuous galerkin methods for timoshenko beams in this paper we consider the so called hp version of discontinuous galerkin methods for timoshenko beams we prove that when the numerical traces are properly chosen the methods display optimal convergence uniformly with respect to the thickness of the beam these methods are thus free from shear locking we also prove that when polynomials of degree p are used all the numerical traces superconverge with a rate of order h 2p 1 p 2p 1 numerical experiments verifying the above mentioned theoretical results are shown

higher order pathwise numerical approximations of spdes with additive noise in this article the pathwise numerical approximation of semilinear parabolic stochastic partial differential equations spdes driven by additive noise is considered a new numerical scheme for the time and space discretization of such spdes is proposed and this scheme is shown to converge for such spdes faster than standard numerical schemes such as the linear implicit euler scheme or the linear implicit crank nicholson scheme the suggested scheme takes advantage of the smoothing effect of the dominant linear operator and of two linear functionals of the noise process of the spde the abstract setting under which the scheme is analyzed includes spdes driven by fractional brownian motions too

mixed finite elements for second order elliptic problems in three variables two families of mixed finite elements one based on simplices and the other on cubes are introduced as alternatives to the usual raviart thomas nedelec spaces these spaces are analogues of those introduced by brezzi douglas and marini in two space variables error estimates inl2 andh s are derived

a mixed method for the biharmonic problem based on a system of first order equations we introduce a new mixed method for the biharmonic problem the method is based on a formulation where the biharmonic problem is rewritten as a system of four first order equations a hybrid form of the method is introduced which allows us to reduce the globally coupled degrees of freedom to only those associated with lagrange multipliers which approximate the solution and its derivative at the faces of the triangulation for k ge 1 a projection of the primal variable error superconverges with order k 3 while the error itself converges with order k 1 only this fact is exploited by using local postprocessing techniques that produce new approximations to the primal variable converging with order k 3 we provide numerical experiments that validate our theoretical results

virtual element for the buckling problem of kirchhoff love plates abstract in this paper we develop a virtual element method vem of high order to solve the fourth order plate buckling eigenvalue problem on polygonal meshes we write a variational formulation based on the kirchhoff love model depending on the transverse displacement of the plate we propose a c 1 conforming virtual element discretization of arbitrary order k 2 and we use the so called babuska osborn abstract spectral approximation theory to show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates for the buckling modes eigenfunctions and a double order for the buckling coefficients eigenvalues finally we report some numerical experiments illustrating the behavior of the proposed scheme and confirming our theoretical results on different families of meshes

sufficient conditions for conservativity of minimal quantum dynamical semigroups abstract the conservativity of a minimal quantum dynamical semigroup is proved whenever there exists a generalized subharmonic operator bounded from below by the dissipative part of the infinitesimal generator we discuss applications of this criteria in mathematical physics and quantum probability

eigenvalue approximation by mixed and hybrid methods note univ maryland dept math college pk md 20742 ecole polytech ctr math appl f 91128 palaiseau france univ paris 6 f 75230 paris 05 france mercier b cea limeil f 94190 villeneuve france isi document delivery no lq584times cited 29cited reference count 44 reference asn article 1981 005doi 10 2307 2007651 record created on 2006 08 24 modified on 2017 05 12

numerical solution of stochastic quantum master equations using stochastic interacting wave functions abstract we develop a new approach for solving stochastic quantum master equations with mixed initial states first we obtain that the solution of the jump diffusion stochastic master equation is represented by a mixture of pure states satisfying a system of stochastic differential equations of schrodinger type then we design three exponential schemes for these coupled stochastic schrodinger equations which are driven by brownian motions and jump processes hence we have constructed efficient numerical methods for the stochastic master equations based on quantum trajectories the good performance of the new numerical integrators is illustrated by simulations of two quantum measurement processes

locking free finite element method for a bending moment formulation of timoshenko beams in this paper we study a finite element formulation for timoshenko beams it is known that standard finite elements applied to this model lead to wrong results when the thickness of the beam is small here we consider a mixed formulation in terms of the transverse displacement rotation shear stress and bending moment by using the classical babuska brezzi theory it is proved that the resulting variational formulation is well posed we discretize it by continuous piecewise linear finite elements for the shear stress and bending moment and discontinuous piecewise constant finite elements for the displacement and rotation we prove an optimal linear order of convergence in terms of the mesh size for the natural norms and a double order quadratic in l 2 norms for the shear stress and the bending moment these estimates involve constants and norms of the solution that are proved to be bounded independently of the beam thickness which ensures the locking free character of the method numerical tests are reported in order to support our theoretical results

a family of c 0 finite elements for kirchhoff plates i error analysis a new finite element formulation for the kirchhoff plate model is presented the method is a displacement formulation with the deflection and the rotation vector as unknowns and it is based on ideas stemming from a stabilized method for the reissner mindlin model r stenberg in asymptotic methods for elastic structures p ciarlet l trabucho and j m viano eds de gruyter berlin 1995 and a method to treat a free boundary p destuynder and t nevers rairo model math anal numer 22 1988 pp 217 242 optimal a priori and a posteriori error estimates are derived

the hellan herrmann johnson method some new error estimates and postprocessing analyse du comportement de la methode mixte de hellan herrmann johnson pour la resolution du probleme biharmonique 2 f etablissement d un resultat de superconvergence

first order solutions for the buckling loads of weakened timoshenko columns in this work closed form expressions for the buckling loads of weakened timoshenko columns with different boundary conditions and shear force approaches proportional to the bending rotation or to the total slope are presented the crack model used promotes discontinuities in both transversal displacements and rotation due to bending to solve the buckling problem the perturbation method is used considering that the solutions for both the cracked and the uncracked columns are slightly different this procedure leads to first order closed form expressions for the buckling loads of the timoshenko cracked column which were compared with those found by directly solving the corresponding eigenvalue problem establishing validity limits for these solutions

an optimal c 0 finite element algorithm for the 2d biharmonic problem theoretical analysis and numerical results the aim of this paper is to give a new method for the numerical approximation of the biharmonic problem this method is based on the mixed method given by ciarlet raviart and have the same numerical properties of the glowinski pironneau method the error estimate associated to these methods are of order o h k 1 for k geq 2 the algorithm proposed in this paper converges even for k geq 1 without any regularity condition on omega or psi we have an error estimate of order o h k in case of regularity

analysis of the dpg method for the poisson equation we give an error analysis of the recently developed dpg method applied to solve the poisson equation and a convection diffusion problem we prove that the method is quasioptimal error estimates in terms of both the mesh size h and the polynomial degree p for various element shapes can be derived from our results results of extensive numerical experiments are also presented

on dissipative stochastic equations in a hilbert space a general existence and uniqueness theorem for solutions of linear dissipative stochastic differential equation in a hilbert space is proved the dual equation is introduced and the duality relation is established proofs take inspirations from quantum stochastic calculus however without using it solutions of both equations provide classical stochastic representation for a quantum dynamical semigroup describing quantum markovian evolution the problem of the mean square norm conservation closely related to the unitality non explosion of the quantum dynamical semigroup is considered and a hyperdissipativity condition ensuring such conservation is discussed comments are given on the existence of solutions of a nonlinear stochastic differential equation introduced and discussed recently in physical literature in connection with continuous quantum measurement processes

superconvergent discontinuous galerkin methods for second order elliptic problems we identify discontinuous galerkin methods for second order elliptic problems in several space dimensions having superconvergence properties similar to those of the raviart thomas and the brezzi douglas marini mixed methods these methods use polynomials of degree k 0 for both the potential as well as the flux we show that the approximate flux converges in l2 with the optimal order of k 1 and that the approximate potential and its numerical trace superconverge in l2 like norms to suitably chosen projections of the potential with order k 2 we also apply element by element postprocessing of the approximate solution to obtain new approximations of the flux and the potential the new approximate flux is proven to have normal components continuous across inter element boundaries to converge in l2 with order k 1 and to have a divergence converging in l2 also with order k 1 the new approximate potential is proven to converge with order k 2 in l2 numerical experiments validating these theoretical results are presented

regular decomposition and a framework of order reduced methods for fourth order problems this paper is devoted to the construction of order reduced method of fourth order problems a constructive framework is presented such that a problem on the high regularity space can be deduced to an equivalent system on three low regularity spaces which are connected by a regular decomposition corresponding to a decomposition of the regularity of the high order space the generated numerical schemes based on the deduced problems can be of lower complicacy and the framework is fit for various fourth order problems three fourth order problems are then discussed under the framework including one in two dimension and two in three dimension they are each corresponding to a regular decomposition and thus are discretised based on the discretised analogues of the regular decomposition optimal error estimates are given

heisenberg evolution of quantum observables represented by unbounded operators this paper deals with open quantum systems in particular we focus on the adjoint quantum master equations with initial conditions given by unbounded operators examples of this type of initial data are the position and momentum operators of quantum oscillators and the occupation number operator in many body particle systems the article establishes the existence and uniqueness of solutions of the operator equations governing the motion of unbounded observables under the born markov approximations to this end we develop the relation between operator evolution equations arising in quantum mechanics and stochastic evolutions equations of schrodinger type furthermore we examine quantum dynamical semigroup properties of the heisenberg evolutions of general classes of observables

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

analysis of the discontinuous petrov galerkin method with optimal test functions for the reissner mindlin plate bending model we analyze the discontinuous petrov galerkin dpg method with optimal test functions when applied to solve the reissner mindlin model of plate bending we prove that the hybrid variational formulation underlying the dpg method is well posed stable with a thickness dependent constant in a norm encompassing the l 2 norms of the bending moment the shear force the transverse deflection and the rotation vector we then construct a numerical solution scheme based on quadrilateral scalar and vector finite elements of degree p we show that for affine meshes the discretization inherits the stability of the continuous formulation provided that the optimal test functions are approximated by polynomials of degree p 3 we prove a theoretical error estimate in terms of the mesh size h and polynomial degree p and demonstrate numerical convergence on affine as well as non affine mesh sequences

transcending classical invariant theory let sp2 r sp2 sp be the real symplectic group of rank n let sp denote the two fold cover of sp there is a unitary representation constructed by shale sh and weil wa of sp that is of considerable interest in the theory of automorphic forms we denote this representation by co and call it the oscillator representation the purpose of this paper is to establish about c a fact that should be useful for clarifying the structure of spaces of automorphic forms constructed using co we begin by formulating the result let e be a reductive subgroup of sp and let e denote the inverse image of e in sp denote by r e the set of infinitesimal equivalence classes of continuous irreducible admissible representations of e on locally convex spaces let co be the smooth representation of sp associated to co let co be realized on a hilbert space and let the subspace of smooth vectors on which space co is defined be written denote by r9 e co the set of elements of e which are realized as quotients by co e invariant closed subspaces of t g consider a reductive dual pair g g c sp h2 it is not hard to show that g and g commute with one another hence we may regard co i g g as a representation of gx g it is well known f that r gx g s9 g xr9 g the identification associates to p e r g and p e i g the tensor product p x p we note that p x p is not defined as a topological vector space nevertheless the infinitesimal equivalence class of p op is well defined select p x p e g x g suppose that in fact p p e 9 g g c then clearly p e r g c and p e 9 g c hence g co defines the graph of a correspondence between certain subsets of r9 g cv and j g co in fact the situation is quite precise

discretization by finite elements of a model parameter dependent problem the discretization by finite elements of a model variational problem for a clamped loaded beam is studied with emphasis on the effect of the beam thickness which appears as a parameter in the problem on the accuracy it is shown that the approximation achieved by a standard finite element method degenerates for thin beams in contrast a large family of mixed finite element methods are shown to yield quasioptimal approximation independent of the thickness parameter the most useful of these methods may be realized by replacing the integrals appearing in the stiffness matrix of the standard method by gauss quadratures

a posteriori error estimates for maxwell equations maxwell equations are posed as variational boundary value problems in the function space h curl and are discretized by nedelec finite elements in beck et al 2000 a residual type a posteriori error estimator was proposed and analyzed under certain conditions onto the domain in the present paper we prove the reliability of that error estimator on lipschitz domains the key is to establish new error estimates for the commuting quasi interpolation operators recently introduced in j schoberl commuting quasi interpolation operators for mixed finite elements similar estimates are required for additive schwarz preconditioning to incorporate boundary conditions we establish a new extension result

numerical efficiency locking and unlocking of nurbs finite elements abstract the strategy of using finite elements with nurbs shape functions for approximation of both geometry and displacements isogeometric approach is investigated from the point of view of finite element technology convergence rates are compared to those of classical finite element approaches utilizing standard lagrange shape functions moreover typical locking phenomena are examined it is found that higher order inter element continuity within the nurbs approach results in identical convergence rates but smaller absolute errors compared to c 0 continuous approaches however nurbs finite elements suffer from the same locking problems as finite elements using lagrange shape functions the discrete shear gap dsg method a general framework for formulation of locking free elements is applied to develop a new class of nurbs finite elements the resulting nurbs dsg elements are absolutely free from locking and preserve the property of improved accuracy compared with standard locking free finite elements the method is exemplified for the timoshenko beam model but may be applied to more general cases

computation of natural frequencies of shear deformable beams and plates by an rbf pseudospectral method a study of free vibration of timoshenko beams and mindlin plates is presented the analysis is based on a new numerical scheme where collocation by radial basis functions and pseudospectral methods are combined to produce highly accurate results numerical results are presented and discussed for various thickness to length ratios

approximation of the buckling problem for reissner mindlin plates this paper deals with the approximation of the buckling coefficients and modes of a clamped plate modeled by the reissner mindlin equations these coefficients are the reciprocals of the eigenvalues of a noncompact operator we give a spectral characterization of this operator and show that the relevant buckling coefficients correspond to isolated nondefective eigenvalues then we consider the numerical computation of these coefficients and their corresponding modes for the finite element approximation of reissner mindlin equations it is well known that some kind of reduced integration or mixed interpolation has to be used to avoid locking in particular we consider duran liberman elements which have been already proved to be locking free for load and vibration problems we adapt the classical approximation theory for noncompact operators to obtain optimal order error estimates for the eigenfunctions and a double order for the eigenvalues these estimates are valid with constants independent of the plate thickness we report some numerical experiments confirming the theoretical results finally we refine the analysis in the case of a uniformly compressed plate

bending moment mixed method for the kirchhoff love plate model we deal with the kirchhoff love model for a bending thin plate with physical boundary conditions we propose here a new mixed formulation based on a decomposition of the bending moment for its discretization we employ classical low order conforming finite elements then the discrete formulation allows us to obtain directly an approximation of the bending moment while the deflection is recovered by solving an additional second order elliptic problem we establish optimal error estimates which prove that the method is unconditionally convergent moreover its convergence rate is optimal whenever the exact solution is sufficiently smooth

discretization of the timoshenko beam problem by thep and theh p versions of the finite element method in this paper the discretization of the timoshenko beam problem by thep and theh p versions of the finite element method is considered optimal error estimates are established the locking phenomenon disappears as the thickness of the beam decreases

discontinuous petrov galerkin method with optimal test functions for thin body problems in solid mechanics we study the applicability of the discontinuous petrov galerkin dpg variational framework for thin body problems in structural mechanics our numerical approach is based on discontinuous piecewise polynomial finite element spaces for the trial functions and approximate local computation of the corresponding optimal test functions in the timoshenko beam problem the proposed method is shown to provide the best approximation in an energy type norm which is equivalent to the l2 norm for all the unknowns uniformly with respect to the thickness parameter the same formulation remains valid also for the asymptotic euler bernoulli solution as another one dimensional model problem we consider the modelling of the so called basic edge effect in shell deformations in particular we derive a special norm for the test space which leads to a robust method in terms of the shell thickness finally we demonstrate how a posteriori error estimator arising directly from the discontinuous variational framework can be utilized to generate an optimal hp mesh for resolving the boundary layer

design principles and error analysis for reduced shear plate bending finite elements in this paper we consider the problem of designing plate bending elements which are free of shear locking this phenomenon is known to afflict several elements for the reissner mindlin plate model when the thickness d of the plate is small due to the inability of the approximating subspaces to satisfy the kirchhoff constraint to avoid locking a reduction operator is often applied to the stress to modify the variational formulation and reduce the effect of this constraint we investigate the conditions required on such reduction operators to ensure that the approximability and consistency errors are of the right order a set of sufficient conditions is presented under which optimal errors can be obtained these are derived directly without transforming the problem via a hemholtz decomposition or considering it as a mixed method our analysis explicitly takes into account boundary layers and their resolution and we prove via an asymptotic analysis that convergence of the finite element approximations will occur uniformly as d rightarrow 0 even on quasiuniform meshes the analysis is carried out in the case of a free boundary where the boundary layer is known to be strong we also propose and analyze a simple post processing scheme for the shear stress our general theory is used to analyze the well known mitc elements for the reissner mindlin plate as we show the theory makes it possible to analyze both straight and curved elements we also analyze some other elements

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

a piecewise linear finite element method for the buckling and the vibration problems of thin plates the aim of this paper is to analyze a piecewise linear finite element method to approximate the buckling and the vibration problems of a thin plate the method is based on a conforming discretization of a bending moment formulation for the kirchhoff love model the analysis restricts to simply connected polygonal clamped plates not necessarily convex the method is proved to converge with optimal order for both spectral problems including an improved order for the eigenvalues numerical experiments are reported to assess its performance and to compare it with other low order finite element methods

continuous discontinuous finite element approximations of fourth order elliptic problems in structural and continuum mechanics with applications to thin beams and plates and strain gradient elasticity abstract a new finite element method for fourth order elliptic partial differential equations is presented and applied to thin bending theory problems in structural mechanics and to a strain gradient theory problem the method combines concepts from the continuous galerkin cg method the discontinuous galerkin dg method and stabilization techniques a brief review of the cg method the dg method and stabilization techniques highlights the advantages and disadvantages of these methods and suggests a new approach for the solution of fourth order elliptic problems a continuous discontinuous galerkin c dg method is proposed which uses c 0 continuous interpolation functions and is formulated in the primary variable only the advantage of this formulation over a more traditional mixed approach is that the introduction of additional unknowns and related difficulties can be avoided in the context of thin bending theory the c dg method leads to a formulation where displacements are the only degrees of freedom and no rotational degrees of freedom need to be considered the main feature of the c dg method is the weak enforcement of continuity of first and higher order derivatives through stabilizing terms on interior boundaries consistency stability and convergence of the method are shown analytically numerical experiments verify the theoretical results and applications are presented for bernoulli euler beam bending poisson kirchhoff plate bending and a shear layer problem using toupin mindlin strain gradient theory

fully discrete dpg methods for the kirchhoff love plate bending model abstract we extend the analysis and discretization of the kirchhoff love plate bending problem from fuhrer et al in press in two aspects first we present a well posed formulation and quasi optimal dpg discretization that include the gradient of the deflection second we construct fortin operators that prove the well posedness and quasi optimal convergence of lowest order discrete schemes with approximated test functions for both formulations our results apply to the case of non convex polygonal plates where shear forces can be less than l 2 regular numerical results illustrate expected convergence orders

avoiding shear locking for the timoshenko beam problem via isogeometric collocation methods in this work we study isogeometric collocation methods for the timoshenko beam problem considering both mixed and displacement based formulations in particular we show that locking free solutions are obtained for mixed methods independently on the approximation degrees selected for the unknown fields moreover several numerical tests are provided in order to support our theoretical results and to show the good behavior and the flexibility of isogeometric collocation methods in this context

a locking free fem in active vibration control of a timoshenko beam in this paper we analyze the numerical approximation of an active vibration control problem of a timoshenko beam in order to avoid locking we focus on the finite element method used to compute the beam vibration to minimize it optimal order error estimates are obtained for the control variable which is the amplitude of secondary forces modeled as dirac s delta distributions these estimates are valid with constants that do not depend on the thickness of the beam in order to assess the performance of the method numerical tests are reported

analysis of some low order finite element schemes for mindlin reissner and kirchhoff plates we set up a framework for analyzing mixed finite element methods for the plate problem using a mesh dependent energy norm which applies both to the kirchhoff and to the mindlin reissner formulation of the problem the analysis techniques are applied to some low order finite element schemes where three degrees of freedom are associated to each vertex of a triangulation of the domain the schemes proceed from the mindlin reissner formulation with modified shear energy

numerical simulation of stochastic evolution equations associated to quantum markov semigroups we address the problem of approximating numerically the solutions x t t 0 t of stochastic evolution equations on hilbert spaces h with respect to brownian motions arising in the unraveling of backward quantum master equations in particular we study the computation of mean values of x t ax t where a is a linear operator first we introduce estimates on the behavior of x t then we characterize the error induced by the substitution of x t with the solution x t n of a convenient stochastic ordinary differential equation it allows us to establish the rate of convergence of e to e where x t n denotes the explicit euler method finally we consider an extrapolation method based on the euler scheme an application to the quantum harmonic oscillator system is included

a projection based error analysis of hdg methods for timoshenko beams in this paper we give the first a priori error analysis of the hybridizable discontinuous galerkin hdg methods for timoshenko beams the analysis is based on the use of a projection especially designed to fit the structure of the numerical traces of the hdg method this property allows to prove in a very concise manner that the projection of the errors is bounded in terms of the distance between the exact solution and its projection the study of the influence of the stabilization function on the approximation is then reduced to the study of how they affect the approximation properties of the projection in a single element surprisingly and unlike any other discontinuous galerkin method this can be done without assuming any positivity property of the stabilization function of the hdg method we apply this approach to hdg methods using polynomials of degree k 0 in all the unknowns and show that the projection of the error in each of them superconverges with order k 2 when k 1 and converges with order 1 for k 0 as a result we show that the hdg methods converge with optimal order k 1 for all the unknowns and that they are free from shear locking finally we show that all the numerical traces converge with order 2k 1 numerical experiments validating these results are shown

a finite element method for the buckling problem of simply supported kirchhoff plates the aim of this paper is to develop a finite element method to approximate the buckling problem of simply supported kirchhoff plates subjected to general plane stress tensor we introduce an auxiliary variable w u with u representing the displacement of the plate to write a variational formulation of the spectral problem we propose a conforming discretization of the problem where the unknowns are approximated by piecewise linear and continuous finite elements we show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates for the eigenfunctions and a double order for the eigenvalues finally we present some numerical experiments supporting our theoretical results