on stabilized finite element methods for the reissner mindlin plate model stabilized finite element formulation for the reissner mindlin plate model is considered physical interpretation for the stabilization procedure for low order elements is established explicit interpolation functions for linear and bilinear stabilized mitc elements are derived some numerical examples including buckling and frequency analyses are presented copyright 2007 john wiley sons ltd

analysis of kinematic linked interpolation methods for reissner mindlin plate problems the approximation to the solution of reissner mindlin plate problem is considered in the framework of finite element techniques a general strategy involving a linking operator between rotations and vertical displacements is analyzed an abstract convergence result is provided examples of elements falling into this framework are presented and shown to be stable and locking free numerical tests detail the performances of the elements email lovadina ing unitn it

analysis of some stabilized low order mixed finite element methods for reissner mindlin plates abstract new low order mixed finite element methods are established for the reissner mindlin plate problem under a clamped boundary condition employing equal order bi linear interpolants for the rotation and the lateral displacement and discontinuous constant or constant locally enriched by a special function or linear interpolant for the shear stress where two stabilization terms are introduced one of which is used to control the jump of the normal trace of the shear stress across the interelement boundaries and the other is in essence used to control the rotation by modifying the thickness of the plate when using macro element for the displacement the stabilization term pertaining to the jump of the normal trace of the shear stress can be dropped since the jump can be automatically controlled it is shown that all these methods are stable and optimal convergent including in the l 2 norm for the rotation and the displacement uniform in the thickness of the plate

consistency property of extended least squares parameter estimation for stochastic diffusion equation the extended least squares parameter estimate for stochastic heat diffusion equations is considered the unknown parameter is a heat diffusion coefficient which is a function of a spatial variable almost sure convergence for the estimated parameter is proved a numerical example is demonstrated for supporting the theoretical results developed here

a stable bilinear element for the reissner mindlin plate model abstract in this paper we introduce a new quadrilateral element using isoparametric bilinear basis functions for both components of the rotation vector and the deflection the element is a stable modification of the mitc4 element we report on calculations with this new element the original mitc4 and also the bilinear element with selective reduced integration the numerical results are in accordance with the results of the numerical analysis and they show that i the method with reduced integration is highly unreliable and cannot be recommended ii the mitc4 performs rather well but its instability can lead to a decrease in accuracy for the deflection and especially to an inaccurate and oscillating shear force iii the drawbacks of the mitc4 are not present in the modified method

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

convergence results for continuous time adaptive stochastic filtering algorithms abstract the adaptive stochastic filtering problem for gaussian processes is considered the self tuning synthesis procedure is used to derive two algorithms for this problem almost sure convergence for the parameter estimate and the filtering error will be established the convergence analysis is based on an almost supermartingale convergence lemma that allows a stochastic lyapunov like approach

enumeration of directed site animals on two dimensional lattices studies the problem of directed site animals on the square triangular and hexagonal lattices closed form expressions are proposed for a s the number of animals of size s on the square and triangular lattices these expressions have been checked for s or 33 and s or 10 for the square and triangular lattices respectively by explicit enumeration they imply that a s varies as lambda 2 s 0 for large s where lambda 3 for the square lattice and lambda 4 for the triangular and theta 1 2 for both for the hexagonal lattice a s is found for s or 48 the results are consistent with lambda 2 0252 or 0 0005 and theta 1 2

quasi least squares identification and its strong consistency simple identification algorithms are proposed for both continuous and discrete time systems with correlated noise by a combined method connecting the martingale method with the ordinary differential equation method quite simple conditions are obtained to guarantee strong consistency of the proposed algorithms which give estimates for the unknown coefficients in both the dynamic system and the noise model

locking free finite elements for the reissner mindlin plate two new families of reissner mindlin triangular finite elements are analyzed one family generalizing an element proposed by zienkiewicz and lefebvre approximates for k 1 the transverse displacement by continuous piecewise polynomials of degree k 1 the rotation by continuous piecewise polynomials of degree k 1 plus bubble functions of degree k 3 and projects the shear stress into the space of discontinuous piecewise polynomials of degree k the second family is similar to the first but uses degree k rather than degree k 1 continuous piecewise polynomials to approximate the rotation we prove that for 2 s k 1 the l 2 errors in the derivatives of the transverse displacement are bounded by ch s and the l 2 errors in the rotation and its derivatives are bounded by ch s min 1 ht 1 and ch s 1 min 1 ht 1 respectively for the first family and by ch s and ch s 1 respectively for the second family with c independent of the mesh size h and plate thickness t these estimates are of optimal order for the second family and so it is locking free for the first family while the estimates for the derivatives of the transverse displacement are of optimal order there is a deterioration of order h in the approximation of the rotation and its derivatives for t small demonstrating locking of order h 1 numerical experiments using the lowest order elements of each family are presented to show their performance and the sharpness of the estimates additional experiments show the negative effects of eliminating the projection of the shear stress

flory theory for directed lattice animals and directed percolation the free energies of directed lattice animals in good and theta solvents and the free energy of directed percolation are found by the use of a simple flory type approximation which accounts for the inherent anisotropy of these systems from these free energies the authors obtain the upper critical dimension below which mean field theory breaks down they also calculate closed form dimension dependent expressions for the parallel and perpendicular correlation length exponents which characterise the asymptotic cluster shapes these exponents are in excellent agreement with existing numerical data

an improved reissner mindlin triangular element abstract a modified version of the low order mixed finite element method proposed by onate et al internat j numer method engng 37 1994 2569 for the reissner mindlin plate model is analyzed it is proved that the new method is optimal convergent uniform in the thickness of the plate

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

a mixed finite element for shell model with free edge boundary conditions part 2 the numerical scheme abstract from the mixed variational formulation which was suggested in part 1 we construct a finite element scheme then a mathematical justification concerning the error estimate is developed the most important point is to justify two compatibility conditions between the approximation of the kinematics and the stresses because of the structure of the shell operator they are not obvious at all and several restrictions on the mesh are necessary therefore the classical result known in fluid mechanics for stokes equations cannot be applied directly

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 multigrid method for reissner mindlin plates the numerical solution of the mindlin reissner plate equations by a multigrid method is studied difficulties arise only if the thickness parameter is significantly smaller than the mesh parameter in this case an augmented lagrangian method is applied to transform the given problem into a sequence of problems with relaxed penalty parameter with this a parameter independent iteration is obtained

an additive schwarz method for plate bending problems the additive schwarz method is developed for constructing preconditioner of the linear equation from a discretization of the plate bending problem the condition numbers of the preconditioned systems are shown to be bounded independent of mesh sizes in the case of a generous overlap the number of subdomains and the thickness of the plate

relation between size and shape of isotropic and directed percolation clusters and lattice animals shows that the generalised lattice animal model of family and coniglio 1980 naturally leads to a unified scaling picture for percolation and lattice animals in which the fugacity for occupied elements plays the dual role of a temperature like and a field like variable within this single scaling field description of percolation there is only one independent exponent from which all others can be obtained the author defines a new set of exponents alpha beta and gamma for percolation and finds that they are all related to the cluster number exponent theta through the relation alpha gamma 1 beta 3 theta in analogy with lattice animals to relate the cluster radius exponent nu to the other exponents he uses the generalised ginzburg criteria to obtain a modified hyperscaling relation for isotropic and directed percolation and lattice animals using this relation he finds that theta 1 nu sub perpendicular to d 1 for directed percolation and theta nu perpendicular to d 1 for directed lattice animals where nu sub and nu perpendicular to are exponents characterising the parallel and perpendicular cluster radii respectively using the same approach he obtains the stauffer relation theta 1 d nu and the parisi sourlas relation theta 1 d 2 nu for isotropic percolation and lattice animals respectively the above relations give the following expressions for theta within the flory theory theta percolation 3d 2 d 2 theta directed percolation 6d 5 2d 4 theta animals 7d 6 2d 4 and theta directed animals 9 d 1 4d 8

a multigrid method for a parameter dependent problem in solid mechanics in the finite element calculations of problems in solid mechanics the method of selected reduced integration sri is frequently used to eliminate locking phenomena often sri is equivalent to the application of a mixed method when multigrid methods are applied the formulation as a mixed method is by far superior this is shown by an analysis of the timoshenko beam

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

on the membrane locking of h p finite elements in a cylindrical shell problem we study the performance of high order h p finite clement schemes in approximating the nearly inexlensional deformation state of a thin cylindrical shell roof with both ends free severe locking is demonstrated for both quadratic and cubic elements and even for higher order if the grid is not aligned with the axis of the cylinder carefully designed selective reduced integration is shown to improve the accuracy of the finite element approximation at low and moderately high orders however so far this technique seems to work well only on aligned grids

automatically inf sup compliant diamond mixed finite elements for kirchhoff plates we develop a mixed finite element approximation scheme for kirchhoff plate theory based on the reformulation of kirchhoff plate theory of ortiz and morris 1 in this reformulation the moment equilibrium problem for the rotations is in direct analogy to the problem of incompressible two dimensional elasticity this analogy in turn opens the way for the application of diamond approximation schemes hauret et al 2 to kirchhoff plate theory we show that a special class of meshes derived from an arbitrary triangulation of the domain the diamond meshes results in the automatic satisfaction of the corresponding inf sup condition for kirchhoff plate theory the attendant optimal convergence properties of the diamond approximation scheme are demonstrated by means of the several standard benchmark tests we also provide a reinterpretation of the diamond approximation scheme for kirchhoff plate theory within the framework of discrete mechanics in this interpretation the discrete moment equilibrium problem is formally identical to the classical continuous problem and the two differ only in the choice of differential structures it also follows that the satisfaction of the inf sup condition is a property of the cohomology of a certain discrete transverse differential complex this close connection between the classical inf sup condition and cohomology evinces the important role that the topology of the discretization plays in determining convergence in mixed problems

renormalized field theory of collapsing directed randomly branched polymers we present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition we develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition for the swollen phase we find that by choosing model parameters appropriately our stochastic functional reduces to the one describing the relaxation dynamics near the yang lee singularity edge this corroborates that the scaling behavior of swollen branched polymers is governed by the yang lee universality class as has been known for a long time the main focus of our paper lies on the collapse transition of directed branched polymers we show to arbitrary order in renormalized perturbation theory with ensuremath epsilon expansion that this transition belongs to the same universality class as directed percolation

h and d adaptive fe methods for two dimensional structural problems including post buckling of shells abstract the paper first treats the locking problem of shear elastic plates in bending in the context of multi grid methods a new plate bending element with shape functions of the allman type is presented and used for linear and non linear problems an important issue is the presentation of a flexible mesh generator with different refinement strategies according to a priori criteria different a posteriori criteria for adaptive approximations are given such as a gradient based error with one and two indicators for geometrically non linear load paths the first being residuum based and the second controlling the geometrical nonlinearities branch switching and post buckling deformation processes are investigated adaptively using these indicators and demonstrated with examples another important topic is the automatic dimensional adaptivity of beams and plates within disturbed zones as boundary layers concentrated load areas and sharp changes of thicknesses this d adaptivity is combined with h adaptivity and illustrated by some examples

application of directed lattice animal theory to river networks it is shown that the theory of directed lattice animals is a good candidate for determining the exponents which describe river networks

mixed interpolated elements for reissner mindlin plates dcpartement de mathtmatiyue l nit ersitt 1 aral quthec canado summary we present in this paper a procedure to establish reissner mindlin plate bending elements the procedure is based on the idea to combine known resuits on the approximation of stokes problems with known results on the approximation of elliptic problems the proposed elements satisfy the mathematical conditions of stability and convergence and some of them promise to provide efficient elements for practical solutions

series expansion studies of directed percolation estimates of the correlation length exponents series expansion methods have been used to estimate the longitudinal and transverse correlation length exponents for directed bond percolation on the square lattice the central estimate for the ratio of these exponents phi 1 579 or 0 006 is in good agreement with the value obtained by the phenomenological scaling renormalisation group method

on mixed finite element methods for the reissner mindlin plate model in this paper we analyze the convergence of mixed finite element approximations to the solution of the reissner mindlin plate problem we show that several known elements fall into our analysis thus providing a unified approach we also introduce a low order triangular element which is optimalorder convergent uniformly in the plate thickness

numerical approximation of transverse shearing stress in bent plates after a brief review of the main numerical methods for approximating the bending of plates we discuss the difficulties met in the computation of the transverse shearing stress introducing mixed variational formulations we propose several numerical schemes leading to a good approximation of this quantity finally the opportunity of using such schemes is discussed

a priori and a posteriori analysis for a locking free low order quadrilateral hybrid finite element for reissner mindlin plates this paper proposes a quadrilateral finite element method of the lowest order for reissner mindlin r m plates on the basis of hellinger reissner variational principle which includes variables of displacements shear stresses and bending moments this method uses continuous piecewise isoparametric bilinear interpolation for the approximation of transverse displacement and rotation the piecewiseindependent shear stress bending moment approximation is constructed by following a self equilibrium criterion and a shear stress enhanced condition a priori and reliable a posteriori error estimates are derived and shown to be uniform with respect to the plate thickness t numerical experiments confirm the theoretical results

bending dominated deformation of thin spherical shells analysis and finite element approximation in this paper the bending dominated deformation of a linearly elastic thin spherical shell is considered it is shown that the displacements converge to the solution of a constrained variational problem as the thickness of the shell tends to zero the order of the convergence is estimated and regularity results for the limit problem are derived for the numerical approximation of this limit problem a low order finite element method with a penalty term that generalizes the concept of the discrete kirchhoff triangle elements for plate bending problems is presented the application of the second strang lemma yields error estimates in the energy norm

directed percolation a finite size renormalisation group approach the finite size renormalisation group technique introduced by nightingale 1976 is applied to the directed percolation problem the decay of correlations is anisotropic in this model and finite size scaling is extended to treat such anisotropy precise estimates for critical exponents and percolation probabilities are obtained for site bond and site bond percolation on the square lattice with bonds directed along the positive axes both free boundary conditions for which the results converge linearly with 1 n as n to infinity and helical boundary conditions for which unexpectedly the results converge linearly with 1 n3 are considered

enumeration of directed compact site animals in two dimensions the authors study the problem of directed compact site animals in two dimensions using exact enumeration methods the numerical analysis of the animal number series strongly indicates that the critical exponent theta equals zero they also estimate the non universal growth parameter lambda 2 66185 or 0 00050

hierarchical models of thin elastic structures overview and recent advances in error estimation and adaptivity abstract in the numerical approximation of hierarchical models of thin bodies there are two separate contributions to the total error a modeling error is the error due to dimensional reduction and b discretization error is the error due to the numerical approximation traditionally estimation of these errors has been performed in terms of abstract quantities like the global energy norm which does not give a clear representation of the error in the local features of the solution recently a new class of finite element error estimation techniques has emerged wherein errors in a simulation are measured not in norms but in quantities of interest to the analyst following a brief overview of the literature we focus on extending the theory of a posteriori estimation of the modeling error to local quantities of interest that have physical meaning independent estimates are obtained for the modeling and discretization errors in quantities of interest these local estimates are used to develop goal oriented adaptive modeling strategies in which the model is automatically adapted by controlling the two errors independently and effectively to obtain local quantities of interest to within a preset level of accuracy numerical examples are presented to demonstrate the accuracy of the error estimates and the adaptive strategy

mixed and nonconforming finite element approximations of reissner mindlin plates abstract we consider a mixed finite element approximation of the reissner mindlin plate model which plays an important role in the simulation of plates and shells of small to moderate thickness on triangles and quadrilaterals low order finite elements are proposed the rotation is approximated by conforming isoparametric bi linear elements and the transverse displacement by constant elements and the shear stress by the lowest order raviart thomas elements we prove that the new method satisfies the k ellipticity and the inf sup condition in the abstract framework of the babuska brezzi theory for mixed problems consequently the method is uniformly stable and uniformly optimally convergent independent of the thickness of the plate moreover a local postprocessing approach and the implementation by either the augmented lagrangian algorithm or the hybridization method are discussed including equivalence to some nonconforming methods in particular a new nonconforming method is deduced which can accommodate arbitrary regular quadrilaterals

stability of a class of hybrid linear stochastic systems the objective of the paper is to establish l q stability results for the state processes of a new class of slowly time varying hybrid continuous time linear stochastic systems the systems are hybrid in the sense that jumps both in the dynamics and the state may occur in both cases a jump amounts to resetting to an initial value jump times are defined by a more or less arbitrary point process most of the analysis is based on a carefully organized stochastic lyapunov function argument we motivate our study by a brief summary of some basic problems in continuous time recursive estimation of linear stochastic systems within a framework analogous to the one developed by benveniste et al

a finite element method for the mindlin reissner plate model in this work a finite element method is introduced for the mindlin reissner model that describes the displacement of a plate subject to a transverse load the discretization introduced here is a modification of that proposed by arnold and falk in siam j numer anal 26 1989 pp 1276 1290 the method used here is easier to implement since the internal degrees of freedom are removed thus avoiding the static condensation procedure as in arnold and falk optimal order error estimates are proved with constants independent of the plate thickness and therefore the method is adequate for very thin plates

two lower order nonconforming rectangular elements for the reissner mindlin plate in this paper we propose two lower order nonconforming rectangular elements for the reissner mindlin plate the first one uses the conforming bilinear element to approximate both components of the rotation and the modified nonconforming rotated q 1 element to approximate the displacement whereas the second one uses the modified nonconforming rotated q 1 element to approximate both the rotation and the displacement both elements employ a projection operator to overcome the shear force locking we prove that both methods converge at optimal rates uniformly in the plate thickness t in both the h 1 and l 2 norms and consequently they are locking free

a finite element method with discontinuous rotations for the mindlin reissner plate model we present a continuous discontinuous finite element method for the mindlin reissner plate model based on continuous polynomials of degree k 2 for the transverse displacements and discontinuous polynomials of degree k 1 for the rotations we prove a priori convergence estimates uniformly in the thickness of the plate and thus show that locking is avoided we also derive a posteriori error estimates based on duality together with corresponding adaptive procedures for controlling linear functionals of the error finally we present some numerical results

the problem of membrane locking in finite element analysis of cylindrical shells we analyse the problem of membrane locking in h p finite element models of a thin hemicylindrical shell roof loaded by a smoothly varying normal pressure distribution we show that in the standard finite element method locking occurs especially at low values ofp and when the finite element grid is not aligned with the axis of the cylinder a general strategy of avoiding locking by using modified bilinear forms is introduced and a special implementation of this strategy on aligned rectangular grids is considered

reduction of excessive energy in the four noded membrane quadrilateral element part i linear theory compressible materials abstract the objective of the paper is to set forth in a consistent manner reasons for the appearance of excessive energy in the four noded membrane quadrilateral element and to propose a formulation leading to simple and reliable elements that are less sensitive to distortions of the geometrical shape by presenting the differential geometry emphasis is placed upon those geometrical attributes which are inherently related to the quadrilateral a modified version of the functional of hu washizu is employed for the discretization appropriate approximations for the displacements rotations are chosen and the physical meaning of the various parameters is identified a systematic procedure is followed for the approximation of stress and strain the convergence of the formulation is investigated by examining the inf sup condition and applying the patch test also results of numerical examples and comparisons with other elemental formulations are presented

ϵ expansion for directed animals introduces the problem of directed lattice animals and shows that they are highly anisotropic with two different correlation lengths xi sub and xi perpendicular to parallel and perpendicular to the privileged direction a field theory is introduced and the critical exponents calculated to first order in epsilon dc d where the upper critical dimension dc is 7

on the implementation of mixed methods as nonconforming methods for second order elliptic problems in this paper we show that mixed finite element methods for a fairly general second order elliptic problem with variable coefficients can be given a nonmixed formulation lower order terms are treated so our results apply also to parabolic equations we define an approximation method by incorporating some projection operators within a standard galerkin method which we call a projection finite element method it is shown that for a given mixed method if the projection method s finite element space m h satisfies three conditions then the two approximation methods are equivalent these three conditions can be simplified for a single element in the case of mixed spaces possessing the usual vector projection operator we then construct appropriate nonconforming spaces m h for the known triangular and rectangular elements the lowest order raviart thomas mixed solution on rectangular finite elements in r 2 and r 3 on simplices or on prisms is then implemented as a nonconforming method modified in a simple and computationally trivial manner this new nonconforming solution is actually equivalent to a postprocessed version of the mixed solution a rearrangement of the computation of the mixed method solution through this equivalence allows us to design simple and optimal order multigrid methods for the solution of the linear system

technical communique the convergence of an instrumental variable like recursion the convergence of a modified form of the iv instrumental variable recursion actually a case of the integral adaptation algorithm of landau for the parameters of a scalar transfer function time series model is considered it is known that this algorithm requires at least a positive real condition for its convergence here it is shown that the recursion converges without being monitored in any case the result is disappointing because the positive real condition depends on the transfer function characteristic function

renormalisation group study of fully directed self avoiding walks the author presents a discussion of the critical properties of fully directed self avoiding walks on hypercubic lattices a position space renormalisation group transformation is carried out analytically in two dimensions for any value of the scaling factor b the finite size scaling properties of the transformation are explicitly exhibited including the well known finite size scaling hypothesis v b v approximately 1n b 1 it is shown that the rg transformation in this case is sensitive to v sub thus giving support to existing arguments

shell deformation states and the finite element method a benchmark study of cylindrical shells abstract we demonstrate some of the basic mathematical characteristics of shell deformation states and shell models from the point of view of finite element approximation as benchmark cases we analyze in detail three simple cylindrical shell problems these problems are seemingly similar but turn out to be quite different we 1 compute the exact displacement and strain fields in the model problems both numerically and symbolically using two variants of classical shell models 2 for comparison compute numerically the displacements and strains corresponding to certain higher order dimension reduction models derived from the energy principle 3 demonstrate the dissimilarity of the three benchmark problems as to their asymptotic behaviour in the limit of zero thickness and 4 show both theoretically and experimentally how this diversity is reflected in the accuracy of standard finite element approximations of both low and high order

nonconforming elements in least squares mixed finite element methods in this paper we analyze the finite element discretization for the first order system least squares mixed model for the second order elliptic problem by means of using nonconforming and conforming elements to approximate displacement and stress respectively moreover on arbitrary regular quadrilaterals we propose new variants of both the rotated q1 nonconforming element and the lowest order raviart thomas element

convergence rates of continuous time stochastic els parameter estimation discrete time convergence rates for extended least squares els algorithms are generalized to the continuous time case an essential difference in the estimation is the appropriate prefiltering while in the theory the existence of solutions of the stochastic equations is a concern

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

a uniformly accurate finite element method for the reissner mindlin plate a simple finite element method for the reissner mindlin plate model in the prim itive variables is presented and analyzed the method uses nonconforming linear finite elements for the transverse displacement and conforming linear finite elements enriched by bubbles for the rotation with the computation of the element stiffness matrix modified by the inclusion of a simple elementwise averaging it is proved that the method converges with optimal order uniformly with respect to thickness

an ordinary differential equation technique for continuous time parameter estimation an ordinary differential equation technique is developed via averaging theory and weak convergence theory to analyze the asymptotic behavior of continuous time recursive stochastic parameter estimators this technique is an extension of l ljung s 1977 work in discrete time using this technique the following results are obtained for various continuous time parameter estimators the recursive prediction error method with probability one converges to a minimum of the likelihood function the same is true of the gradient method the extended kalman filter fails with probability one to converge to the true values of the parameters in a system whose state noise covariance is unknown an example of the extended least squares algorithm is analyzed in detail analytic bounds are obtained for the asymptotic rate of convergence of all three estimators applied to this example

a locking free reissner mindlin quadrilateral element on arbitrary regular quadrilaterals a new finite element method for the reissner mindlin plate is proposed where both transverse displacement and rotation are approximated by isoparametric bilinear elements with local bubbles enriching rotation and a local reduction operator is applied to the shear energy term this new method gives optimal error bounds uniform in the thickness of the plate for both transverse displacement and rotation with respect to h1 and l2 norms

wilson s element for the reissner mindlin plate abstract a new method for the reissner mindlin plate has been proposed the nonconforming wilson element is used for transverse displacement rotation is approximated by the usual bilinear element and an orthogonal projection is applied to the shear stress term the uniform convergence with respect to the plate thickness is established numerical results are provided the new method is simple in implementation

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 penalty duality method for the budiansky sanders shell model abstract starting from the budiansky sanders shell model we introduce a perturbed formulation based on a penalty duality argument for which only c finite elements are required an error estimate and numerical procedure for solving the finite element model are given

stabilized finite element formulations for shells in a bending dominated state we consider the design of finite element methods for the naghdi shell model in the case when the deformation is bending dominated two formulations based on stabilizing techniques are introduced and it is proved that they are stable hence free from locking the theoretical estimates are confirmed by numerical benchmark studies

optimal mathcal l 2 error bounds for mitc3 type element in this paper we derive the optimal mathcal l 2 error bounds for the stabilized mitc3 element 3 the min3 type element 7 and the t3bl element 8 in this way we have solved the problem proposed recently in 5 in a positive manner moreover we estimate the difference between stabilized mitc3 and min3 and show it is of order mathcal o h 2 uniform in the plate thickness

a globally convergent adaptive predictor this paper establishes global convergence for an adaptive prediction algorithm key features of the algorithm are i a priori residuals are used in the regression vector ii the input signal need not be persistently exciting iii only an upper bound is required on the system order iv no monitoring or projection procedure is required to guarantee stability and v arbitrary feedback is allowed between output and input

analysis of some mixed finite element methods related to reduced integration we prove error estimates for the following two mixed finite element methods related to reduced integration a method for stokes problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress the main idea of the proof in the case of stokes problem is to combine a weak babuska brezzi type stability estimate for the pressure with a superapproximability property for the velocities a similar technique is used in the case of the plate problem

size and shape of directed lattice animals uses position space renormalisation and exact enumeration methods to study configurational properties of directed lattice animals clusters of directed bonds in which the tail of a new bond must be added to the head of existing bonds exponents are found for the divergence of correlation lengths parallel and perpendicular to the preferred axis in addition an exponent is found that characterises the singularity of the directed animal generating function and critical points are located

on the apparent failure of a flory approximation for directed linear polymers the author discusses the apparent failure of a flory approximation for directed linear polymers commenting on the details implicit in this type of picture the relationship of a standard flory viewpoint to a simplified application of fractal theory is explored and a correspondence is drawn between aspects of both theories

some new families of finite elements for the stokes equations we introduce a way of using the mixed finite element families of raviart thomas and nedelec 13 14 and brezzi et al 5 7 for constructing stable and optimally convergent discretizations for the stokes problem

preconditioners for nonconforming discretizations we prove an abstract norm equivalence for a two level method which allows us to reduce the construction of preconditioners for nonconforming finite element discretizations to known cases of conforming elements

analysis of a mixed finite element method for the reissner mindlin plate problems abstract an analysis of a triangular mixed finite element method proposed by taylor and auricchio cf 13 is presented the method is based on a linked interpolation between deflections and rotations in order to avoid the locking phenomenon cf 15 the analysis shows that the approximated deflections and rotations are first order convergent to the exact solution uniformly in the thickness

a posteriori error analysis of finite element methods for reissner mindlin plates this paper develops an a posteriori error control theory of finite element methods for reissner mindlin plates which states that one can derive a uniformly reliable and efficient a posteriori error estimate for a given scheme by only 1 checking three conditions 2 designing three functions and one parameter 3 bounding the last three terms of the abstract estimator we apply this theory to two classes of methods and achieve robust a posteriori error controls for them

global estimates for mixed methods for second order elliptic equations global error estimates in l2 92 l 9 and h s q 2 in r2 or a re derived for a mixed finite element method for the dirichlet problem for the elliptic operator lp div a grad p bp cp based on the raviart thomas nedelec space vh x wh c h div 92 x l2 g2 optimal order estimates are obtained for the approximation of p and the associated velocity field u a grad p bp in l2 g2 and h s 92 0 6 s k 1 and if q c r2 forp in lv2

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

scaling and critical probabilities for cluster size and la diversity on randomly occupied square lattices using monte carlo simulations we report the behaviour of the total number of clusters the cluster size diversity and the lattice animals la diversity on randomly occupied square lattices the critical probability associated with the maximum of these variables is determined in comparison with the percolation probability pc our simulations indicate that pc and the critical probability of the maximum cluster size diversity pc d s max occur at the same point as indicated in a previous paper tsang i r and tsang i j 1997 j phys a math gen 30 l239 the probability for the maximum number of clusters is obtained at a lower value pc n max 0 27 0 01 we describe the cluster identification algorithm used to count the different la and determined the critical probability for the maximum la diversity pc d f max 0 45 0 02 we derive the exponents characterizing the relation between d s max d f max and n max and several scaling relations between the variables measured the lattice size and the probability of occupation p in addition we show the scaling behaviour of la diversity versus cluster size diversity for each value of p

on the construction of optimal mixed finite element methods for the linear elasticity problem the mixed finite element method for the linear elasticity problem is considered we propose a systematic way of designing methods with optimal convergence rates for both the stress tensor and the displacement the ideas are applied in some examples

directed lattice animals and the lee yang edge singularity the exponents nu perpendicular to gamma of directed animals in d dimensions are shown to equal those for the lee yang problem in d 1 dimensions for d 2 the author obtains the exact results nu perpendicular to theta 1 2 and for d or 7 the scaling relation theta d 1 nu perpendicular to

analysis of some low order quadrilateral reissner mindlin plate elements four quadrilateral elements for the reissner mindlin plate model are considered the elements are the stabilized mitc4 element of lyly stenberg and vihinen 1933 the min4 element of tessler and hughes 1983 the q4bl element of zienkiewicz et al 1993 and the fmin4 element of kikuchi and ishii 1999 for all elements except the q4bl element a unifying variational formulation is introduced and optimal h 1 and l 2 error bounds uniform in the plate thickness are proven moreover we propose a modified q4bl element and show that it admits the optimal h 1 and l 2 error bounds uniform in the plate thickness in particular we study the convergence behavior of all elements regarding the mesh distortion

avoiding locking in reissner mindlin plates with high order hierarchic bubble plus finite elements abstract in this paper we prove that special finite elements of suitable degree do not exhibit any kind of locking phenomenon when used for the numerical solution of reissner mindlin plate bending problems despite its simple approach the discretization of the reissner mindlin model is not straightforward the inclusion of transverse shear strain effect in standard finite element models introduces undesirable numerical effects the approximate solution is very sensitive to the plate thickness and for small thickness it is very far from the true solution the phenomenon is known as locking of the numerical solution the finite element we present is constructed by adding bubble functions to standard serendipity elements the new elements referred to as bubble plus elements from the degree three onwards avoid the numerical locking the mathematical proof of such a good behavior is based on a deep relation between the c 0 bubble plus element of degree three for reissner mindlin plates and the c 1 element for kirchhoff plates known as bogner fox schmit element

the efficiency of the flory approximation the flory approximation 1969 for the self avoiding chain problem is compared with a conventional perturbation theory expansion while in perturbation theory each term is averaged over the unperturbed set of configurations the flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations this imposes restrictions on the integration domain in higher order terms and they can be treated self consistently the accuracy delta nu nu of the flory approximation for self avoiding chain problems is estimated to be 10 1 10 2 for 1 d 4

multigrid methods for a stabilized reissner mindlin plate formulation we consider a stabilized finite element formulation for the reissner mindlin plate bending model the method uses standard basis functions for the deflection and the rotation vector we apply a standard multigrid algorithm to obtain a preconditioner we prove that the condition number of the preconditioned system is uniformly bounded with respect to the mesh size and the thickness parameter in order to apply the abstract multigrid theory we introduce new interpolation norms and prove error estimates in them numerical results confirm the analysis

numerical approximation of mindlin reissner plates we consider a finite element approximation of the so called mindlin reissner formulation for moderately thick elastic plates we show that stability and optimal error bounds hold independently of the value of the thickness 1 introduction the so called mindlin reissner model for moderately thin plates is often used by engineers in connection with plate and shell problems it is well known that many numerical schemes for this model are satisfactory only when the thickness parameter t is not too small for a very small t some bad behavior such as the locking phenomenon might occur here we present a method which is uniformly good as t goes to zero and we prove optimal error estimates for transversal displacement rotations and shear stresses with constants independent of t

site and bond directed branched polymers for arbitrary dimensionality evidence supporting a relation with the lee yang edge singularity parisi and sourlas 1981 have argued that the isotropic branched polymer problem in dimension d 1 is related to the lee yang edge singularity problem in dimension d 1 to test if there is a relation with the directed branched polymer problem the authors calculate the generating functions for both site and bond directed branched polymers for arbitrary dimension d to order smax 10 and bmax 8 their analysis lends support to the proposal that theta d 1 1 theta d d sigma ly d 1 1 where theta and theta d are the critical exponents for lattice animals and directed lattice animals and sigma ly is the lee yang edge singularity exponent they also obtain expansions for the growth parameter in the variable sigma 1 2d 1 1 for bond and site directed lattice animals

iterative solution methods for plate bending problems multigrid and preconditioned cg algorithm the numerical solution of the linear equations arising from a discretization of the plate bending problem based on the zienkiewicz triangle is studied the finite element scheme proceeds from the mindlin reissner formulation with modified shear energy however the kirchhoff condition is imposed on discrete points a multigrid algorithm is analyzed and numerical examples are provided furthermore a suitable preconditioning is established for the use of conjugate gradients

a mixed finite element for shell model with free edge boundary conditions part 1 the mixed variational formulation abstract after a very brief recall on general shell theory we construct a mixed variational formulation based on the introduction of a new unknown the rotation of the normal to the medium surface in koiter shell theory for instance this rotation can be expressed with respect to the three components of the displacement field of the medium surface and their derivatives the lagrange multiplier corresponding to this relation known as the kirchhoff love kinematical assumption is also introduced as an independent unknown there are two main difficulties one is due to the differential geometry of surfaces and is rather technical the other is to define correctly the dual space for the kirchhoff love relation the difficulty is similar to the one met in the characterization of the dual space of the sobolev space h 1 being the medium surface of the shell for which a boundary component appears except for clamped shells which is a very restrictive situation