a posteriori error estimation and adaptive mesh refinement techniques abstract we analyse three different a posteriori error estimators for elliptic partial differential equations they are based on the evaluation of local residuals with respect to the strong form of the differential equation on the solution of local problems with neumann boundary conditions and on the solution of local problems with dirichlet boundary conditions we prove that all three are equivalent and yield global upper and local lower bounds for the true error thus adaptive mesh refinement techniques based on these estimators are capable to detect local singularities of the solution and to appropriately refine the grid near these singularities some numerical examples prove the efficiency of the error estimators and the mesh refinement techniques

on the asymptotic exactness of error estimators for linear triangular finite elements this paper deals with a posteriori error estimates for piecewise linear finite element approximations of elliptic problems we analyze two estimators based on recovery operators for the gradient of the approximate solution by using superconvergence results we prove their asymptotic exactness under regularity assumptions on the mesh and the solution one of the estimators can be easily computed in terms of the jumps of the gradient of the finite element approximation this estimator is equivalent to the error in the energy norm under rather general conditions however we show that for the asymptotic exactness the regularity assumption on the mesh is not merely technical while doing this we analyze the relation between superconvergence and asymptotic exactness for some particular examples

a new paradigm for parallel adaptive meshing algorithms we present a new approach to the use of parallel computers with adaptive finite element methods this approach addresses the load balancing problem in a new way requiring far less communication than current approaches it also allows existing sequential adaptive pde codes such as pltmg and mc to run in a parallel environment without a large investment in recoding in this new approach the load balancing problem is reduced to the numerical solution of a small elliptic problem on a single processor using a sequential adaptive solver without requiring any modifications to the sequential solver the small elliptic problem is used to produce a posteriori error estimates to predict future element densities in the mesh which are then used in a weighted recursive spectral bisection of the initial mesh the bulk of the calculation then takes place independently on each processor with no communication using possibly the same sequential adaptive solver each processor adapts its region of the mesh independently and a nearly load balanced mesh distribution is usually obtained as a result of the initial weighted spectral bisection only the initial fan out of the mesh decomposition to the processors requires communication two additional steps requiring boundary exchange communication may be employed after the individual processors reach an adapted solution namely the construction of a global conforming mesh from the independent subproblems followed by a final smoothing phase using the subdomain solutions as an initial guess we present a series of convincing numerical experiments which illustrate the effectiveness of this approach the justification of the initial refinement prediction step as well as the justification of skipping the two communication intensive steps is supported by some recent j xu and a zhou math comp to appear and not so recent j a nitsche and a h schatz math comp 28 1974 pp 937 958 a h schatz and l b wahlbin math comp 31 1977 pp 414 442 a h schatz and l b wahlbin math comp 64 1995 pp 907 928 results on local a priori and a posteriori error estimation

a general algorithm for limit solutions of plane stress problems a computational approach to limit solutions is considered most challenging for two major reasons a limit solution is likely to be non smooth such that certain non differentiable functions are perfectly admissible and make physical and mathematical sense moreover the possibility of non unique solutions makes it difficult to analyze the convergence of an iterative algorithm or even to define a criterion of convergence in this paper we use two mathematical tools to resolve these difficulties a duality theorem defines convergence from above and from below the exact solution a combined smoothing and successive approximation applied to the upper bound formulation perturbs the original problem into a smooth one by a small parameter e as e 0 the solution of the original problem is recovered this general computational algorithm is robust such that from any initial trial solution the first iteration falls into a convex hull that contains the exact solution s of the problem unlike an incremental method thut invariably renders the limit problem ill conditioned the algorithm is numerically stable limit analysis itself is a highly efficient concept which bypasses the tedium of the intermediate elastic plastic deformation and seeks the most important information directly with the said algorithm we have produced many limit solutions of plane stress problems certain non smooth characters of the limit solutions are shown in the examples presented two well known as well as one parametric family of yield functions are used to allow comparison with some classical solutions

swelling collapse transition of self attracting walks we study the structural properties of self attracting walks in d dimensions using scaling arguments and monte carlo simulations we find evidence of a transition analogous to the theta transition of polymers above a critical attractive interaction u c the walk collapses and the exponents nu and k characterizing the scaling with time t of the mean square end to end distance approximately t 2nu and the average number of visited sites approximately t k are universal and given by nu 1 d 1 and k d d 1 below u c the walk swells and the exponents are as with no interaction i e nu 1 2 for all d k 1 2 for d 1 and k 1 for d 2 at u c the exponents are found to be in a different universality class

computation of limit loads for computing the collapse state of a perfect plastic continuum we suggest a mixed finite element approximation to the infinite dimensional mathematical programming problem of limit analysis the convergence of the limit load to the exact solution is discussed as well as solution methods for the discrete problem finally the method is applied to a classical problem in plane strain

an algorithm for shakedown analysis with nonlinear yield functions abstract this paper is devoted to propose an algorithm to solve the discrete form of the shakedown analysis problem with a nonlinear yield function firstly variational formulations for shakedown analysis of structures under variable loads are considered secondly the corresponding discrete forms are briefly recalled then the algorithm is derived by combining a newton formula based on the discrete equality conditions with a return mapping procedure focusing plastic admissibility the proposed numerical procedure can be applied to finite element models with large number of degrees of freedom because the algorithm is specially designed to take advantage of the structure of such models the numerical procedure is applied to a square plate with a circular hole under variable traction in two directions and the obtained approximations are compared with available results finally a rectangular plate with two small holes is considered in both plane strain and plane stress conditions all application use the mises condition without linearization

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

an upper bound limit analysis of mindlin plates using cs dsg3 method and second order cone programming the paper presents a numerical procedure for kinematic limit analysis of mindlin plate governed by von mises criterion the cell based smoothed discrete shear gap method cs dsg3 is combined with a second order cone optimization programming socp for determining the upper bound limit load of the mindlin plates the limit analysis problem of mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work this minimization problem is then transformed into an explicit form suitable for the solution using the socp the numerical results of some benchmark problems show that the proposal procedure can provide the reliable upper bound collapse multipliers for the mindlin plates cs dsg3 is combined with socp for determining upper bound limit load of mindlin plates limit analysis problem is transformed into an explicit form suitable for solution using socp and cs dsg3 numerical results show that cs dsg3 is free of shear locking and can provide reliable upper bound collapse multipliers for mindlin plates

computation of collapse states with von mises type yield condition a new computational approach to the problem of limit analysis with quadratic yield condition is developed and tested the problem is solved with the exact convex yield condition and the general case of unbounded yield set corresponding to unrestricted hydrostatic pressure is treated the solution method simultaneously approximates the collapse fields for stresses and flow the approach consists of two separate steps first the continuous problem is discretized by the finite element method into a finite dimensional optimization problem which turns out to be of a very specific form then this problem is solved by a suitable optimization method this way it is not necessary to be an expert in optimization in order to solve collapse problems and we can take advantage of the rapid development in optimization methods for large sparse problems without changing the discretization program the efficiency and accuracy of the method for large problems is demonstrated by solving a classical problem in the plane strain model approximately 90000 finite element nodes with 3 stress components and 2 velocity components at each node in two space dimensions this may be overkill but it shows that we are able to solve problems in three space dimensions

correlation effects in a discrete quantum random walk we introduce memory dependent discrete time quantum random walk models by adding uncorrelated memory terms and also by modifying the hamiltonian of the walker to include couplings with memory keeping agents we next study numerically the correlation effects in these models we also propose a correlation exponent as a relevant and promising tool for investigation of correlation or memory hence non markovian effects our analysis can easily be applied to more realistic models in which different regimes may emerge because of competition between different underlying physical mechanisms

a posteriori error estimates for the stokes problem an a posteriors error estimate is derived and analyzed for the mini element discretization of the stokes equations the estimate is based on the solution of a local stokes problem in each element of the finite element mesh using spaces of quadratic bump functions for both velocity and pressure errors this results in solving a 9 times 9 system which reduces to two easily invertible 3 times 3 systems comparisons with other estimates based on a petrov galerkin solution are used in this analysis which shows that it provides a reasonable approximation of the actual discretization error numerical experiments clearly show the efficiency of such an estimate in the solution of self adaptive mesh refinement procedures

a primal dual algorithm for shakedown analysis of structures abstract the paper describes a primal dual algorithm for shakedown analysis of structures with the use of kinematically admissible finite elements starting from koiter kinematic theorem a primal dual optimization condition is established by adopting static terms as complementary variables newton like iterations are performed to give both upper and quasi lower bounds of the load factor that converge rapidly to the accurate solution of shakedown limit

mesh adaptive computation of upper and lower bounds in limit analysis summary an efficient procedure to compute strict upper and lower bounds for the exact collapse multiplier in limit analysis is presented with a formulation that explicitly considers the exact convex yield condition the approach consists of two main steps first the continuous problem under the form of the static principle of limit analysis is discretized twice one per bound using particularly chosen finite element spaces for the stresses and velocities that guarantee the attainment of an upper or a lower bound the second step consists of solving the resulting discrete non linear optimization problems these are reformulated as second order cone programs which allows for the use of primal dual interior point methods that optimally exploit the convexity and duality properties of the limit analysis model to benefit from the fact that collapse mechanisms are typically highly localized a novel method for adaptive meshing is introduced the method first decomposes the total bound gap as the sum of positive contributions from each element in the mesh and then refines those elements with higher contributions the efficiency of the methodology is illustrated with applications in plane stress and plane strain problems copyright q 2008 john wiley sons ltd

a general non linear optimization algorithm for lower bound limit analysis the non linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided the algorithm is an interior point method and is completely general in the sense that no particular finite element discretization or yield criterion is required as with interior point methods for linear programming the number of iterations is affected only little by the problem size some practical implementation issues are discussed with reference to the special structure of the common lower bound load optimization problem and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non linear yield criteria copyright 2002 john wiley sons ltd

maximum norm a posteriori error estimates for a one dimensional convection diffusion problem a singularly perturbed quasi linear two point boundary value problem with an exponential boundary layer is discretized on arbitrary nonuniform meshes using first and second order difference schemes including upwind schemes we give first and second order maximum norm a posteriori error estimates that are based on difference derivatives of the numerical solution and hold true uniformly in the small parameter numerical experiments support the theoretical results

lower bound limit analysis with adaptive remeshing the objective of this work is to present an adaptive remeshing procedure for lower bound limit analysis with application to soil mechanics unlike conventional finite element meshes a lower bound grid incorporates statically admissible stress discontinuities between adjacent elements these discontinuities permit large stress jumps over an infinitesimal distance and reduce the number of elements needed to predict the collapse load accurately in general the role of the discontinuities is crucial as their arrangement and distribution has a dramatic influence on the accuracy of the lower bound solution limit analysis and soil plasticity 1975 to ensure that the discontinuities are positioned in an optimal manner requires an error estimator and mesh adaptation strategy which accounts for the presence of stress singularities in the computed stress field recently borges et al int j solids struct 2001 38 1707 1720 presented an anisotropic mesh adaptation strategy for a mixed limit analysis formulation which used a directional error estimator in the present work this strategy has been tailored to suit a discontinuous lower bound formulation which employs the stresses and body forces as primary unknowns the adapted mesh has a maximum density of discontinuities in the direction of the maximum rate of change in the stress field for problems involving strong stress singularities in the boundary conditions e g a strip footing the automatic generation of discontinuity fans centred on the singular points has been implemented the efficiency of the proposed technique is demonstrated by analysis of two classical soil mechanics problems namely the bearing capacity of a rigid strip footing and the collapse of a vertical cut copyright 2005 john wiley sons ltd

a cell based smoothed finite element method for kinematic limit analysis this paper presents a new numerical procedure for kinematic limit analysis problems which incorporates the cell based smoothed finite element method with second order cone programming the application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort the non smooth optimization problem is formulated as a problem of minimizing a sum of euclidean norms ensuring that the resulting optimization problem can be solved by an efficient second order cone programming algorithm plane stress and plane strain problems governed by the von mises criterion are considered but extensions to problems with other yield criteria having a similar conic quadratic form or 3d problems can be envisaged

access control in user hierarchy based on elliptic curve cryptosystem this work proposes a novel key management method based on elliptic curve cryptosystem and one way hash function to solve dynamic access problems in a user hierarchy the proposed scheme attempts to derive the secret key of successors efficiently and non redundantly it includes functions such as insertion and removal of classes updating of their relationships and changing of secret keys the method utilizes a central authority which enables a user to change the secret key at will conveniently since the proposed method uses the elliptic curve cryptosystem which has a low computational cost and small key size its performance in terms of both security and efficiency is quite commendable therefore it can be anticipated that its use will be extended to wireless communication in the future

multiparticle random walks on a deformable medium multiparticle random walks on a deformable medium have been investigated in 2 1 dimensions the time evolution of the particle distribution is studied the results show that the randomly distributed particles in the beginning will be self organized into a cluster pattern in the intermediate stage and then return to the random distribution pattern in the late stage the dependence of the clustering degree on the stiffness parameter of medium ensuremath alpha stability parameter of systems ensuremath beta and average particle density ensuremath rho 0 is also investigated there exists an optimal clustering stability ensuremath beta p at which the system has the strongest clustering ability and corresponds to a maximum clustering coefficient ensuremath gamma p the dependence of the optimal clustering coefficient ensuremath gamma p on the stiffness ensuremath alpha and particle density ensuremath rho 0 is obtained and the landscape of the medium generated by particles is also investigated

an a posteriori error estimate and adaptive timestep control for a backward euler discretization of a parabolic problem a simple algorithm for adaptive timestep control is presented for a backward euler discretization of a linear parabolic problem the algorithm is based on an a posteriori error estimate involving the computed approximate solution it is proved that with only very rough a priori information on the exact solution the algorithm will choose a sequence of timesteps for which the error will be controlled up to a constant uniformly in time on a given tolerance level

a computational homogenization approach for limit analysis of heterogeneous materials summary the macroscopic strength domain and failure mode of heterogeneous or composite materials can be quantitatively determined by solving an auxiliary limit analysis problem formulated on a periodic representative volume element in this paper a novel numerical procedure based on kinematic theorem and homogenization theory for limit analysis of periodic composites is developed the total velocity fields instead of fluctuating periodic velocity at microscopic level are approximated by finite elements ensuring that the resulting optimization problem is similar to the limit analysis problem formulated for structures except for additional constraints which are periodic boundary conditions and averaging relations the optimization problem is then formulated in the form of a standard second order cone programming problem to be solved by highly efficient solvers effects of loading condition representative volume element architecture and fiber air void volume fraction on the macroscopic strength of perforated and fiber reinforced composites are studied in numerical examples copyright 2017 john wiley sons ltd

a non linear programming method approach for upper bound limit analysis this paper presents a finite element model based on mathematical non linear programming in order to determine upper bounds of colapse loads of a mechanical structure the proposed formulation is derived within a kinematical approach framework employing two simultaneous and independent field approximations for the velocity and strain rate fields the augmented lagrangian is used to establish the compatibility between these two fields in this model only continuous velocity fields are used uzawa s minimization algorithm is applied to determine the optimal kinematical field that minimizes the difference between external and dissipated work rate the use of this technique allows to bypass the complexity of the non linear aspects of the problem since non linearity is addressed as a set of small local subproblems of optimization for each finite element the obtained model is quite versatile and suitable for solving a wide range of collapse problems this paper studies 3d strut and tie structures 2d plane strain stress and 3d solid problems copyright 2007 john wiley sons ltd

reliability and efficiency of an anisotropic zienkiewicz zhu error estimator abstract in this paper we study the efficiency and the reliability of an anisotropic a posteriori error estimator in the case of the poisson problem supplied with mixed boundary conditions the error estimator may be classified as a residual based one but its novelty is twofold firstly it employs anisotropic estimates of the interpolation error for linear triangular finite elements and secondly it makes use of the zienkiewicz zhu recovery procedure to approximate the gradient of the exact solution finally we describe the adaptive procedure used to obtain a numerical solution satisfying a given accuracy and we include some numerical test cases to assess the robustness of the proposed numerical algorithm

a posteriori error estimators for the stokes equations ii non conforming discretizations we present an a posteriori error estimator for the non conforming crouzeix raviart discretization of the stokes equations which is based on the local evaluation of residuals with respect to the strong form of the differential equation the error estimator yields global upper and local lower bounds for the error of the finite element solution it can easily be generalized to the stationary incompressible navier stokes equations and to other non conforming finite element methods numerical examples show the efficiency of the proposed error estimator

limit analysis of plates using the efg method and second order cone programming the meshless element free galerkin efg method is extended to allow computation of the limit load of plates a kinematic formulation that involves approximating the displacement field using the moving least squares technique is developed only one displacement variable is required for each efg node ensuring that the total number of variables in the resulting optimization problem is kept to a minimum with far fewer variables being required compared with finite element formulations using compatible elements a stabilized conforming nodal integration scheme is extended to plastic plate bending problems the evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions difficulties imposing essential boundary conditions are overcome by enforcing displacements at the nodes directly the formulation can be expressed as the problem of minimizing a sum of euclidean norms subject to a set of equality constraints this non smooth minimization problem can be transformed into a form suitable for solution using second order cone programming the procedure is applied to several benchmark beam and plate problems and is found in practice to generate good upper bound solutions for benchmark problems

adaptive frame methods for nonlinear variational problems in this paper we develop adaptive numerical solvers for certain nonlinear variational problems the discretization of the variational problems is done by a suitable frame decomposition of the solution i e a complete stable and redundant expansion the discretization yields an equivalent nonlinear problem on the space of frame coefficients the discrete problem is then adaptively solved using approximated nested fixed point and richardson type iterations we investigate the convergence stability and optimal complexity of the scheme a theoretical advantage for example with respect to adaptive finite element schemes is that convergence and complexity results for the latter are usually hard to prove the use of frames is further motivated by their redundancy which at least numerically has been shown to improve the conditioning of the discretization matrices also frames are usually easier to construct than riesz bases we present a construction of divergence free wavelet frames suitable for applications in fluid dynamics and magnetohydrodynamics

an efficient key assignment scheme for access control in a large leaf class hierarchy the employees of an organization are usually divided into different security classes to authorize the information retrieval and the number of leaf classes is substantially larger than the number of non leaf classes additionally the alternations in leaf classes are more frequent than in non leaf classes we proposed a new key assignment scheme for controlling the access right in a large poset partially ordered set hierarchy to reduce the required computation for key generation and derivation with the storage amount of data decreased

analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements this paper adresses the problem of determining upper and lower bounds for the effectivity index on the a posteriori estimate of the error in the finite element method these bounds are given explicitly for a certain concrete estimator for linear elements and unstructured triangular meshes they depend strongly on the geometry of the triangles and relatively weakly on the smoothness of the solution an example shows that the bounds are not over pessimistic in babuska plank and rodriguez 4 detailed numerical experimentation is given

a secure effective key management scheme for dynamic access control in a large leaf class hierarchy lo et al 2011 proposed an efficient key assignment scheme for access control in a large leaf class hierarchy where the alternations in leaf classes are more frequent than in non leaf classes in the hierarchy their scheme is based on the public key cryptosystem and hash function where operations like modular exponentiations are very much costly compared to symmetric key encryptions and decryptions and hash computations their scheme performs better than the previously proposed schemes however in this paper we show that lo et al s scheme fails to preserve the forward security property where a security class c x can also derive the secret keys of its successor classes c j s even after deleting the security class c x from the hierarchy we aim to propose a new key management scheme for dynamic access control in a large leaf class hierarchy which makes use of symmetric key cryptosystem and one way hash function we show that our scheme requires significantly less storage and computational overheads as compared to lo et al s scheme and other related schemes through the informal and formal security analysis we further show that our scheme is secure against all possible attacks including the forward security in addition our scheme supports efficiently dynamic access control problems compared to lo et al s scheme and other related schemes thus higher security along with low storage and computational costs make our scheme more suitable for practical applications compared to other schemes

a posteriori error estimators for the stokes equations we present two a posteriori error estimators for the mini element discretization of the stokes equations one is based on a suitable evaluation of the residual of the finite element solution the other one is based on the solution of suitable local stokes problems involving the residual of the finite element solution both estimators are globally upper and locally lower bounds for the error of the finite element discretization numerical examples show their efficiency both in estimating the error and in controlling an automatic self adaptive mesh refinement process the methods presented here can easily be generalized to the navier stokes equations and to other discretization schemes

a posteriori error estimator and error control for contact problems in this paper we consider two error estimators for one body contact problems the first error estimator is defined in terms of h div conforming stress approximations and equilibrated fluxes while the second is a standard edge based residual error estimator without any modification with respect to the contact we show reliability and efficiency for both estimators more over the error is bounded by the first estimator with a constant one plus a higher order data oscillation term plus a term arising from the contact that is shown numerically to be of higher order the second estimator is used in a control based afem refinement strategy and the decay of the error in the energy is shown several numerical tests demonstrate the performance of both estimators

edge residuals dominate a posteriori error estimates for low order finite element methods we prove that up to higher order perturbation terms edge residuals yield global upper and local lower bounds on the error of linear finite element methods both in h1 and l2 norms we present two proofs one uses the standard l2 projection and the other relies on a new weighted clement type interpolation operator

kinematic limit analysis of frictional materials using nonlinear programming abstract in this paper a nonlinear numerical technique is developed to calculate the plastic limit loads and failure modes of frictional materials by means of mathematical programming limit analysis and the conventional displacement based finite element method the analysis is based on a general yield function which can take the form of the mohr coulomb or drucker prager criterion by using an associated flow rule a general nonlinear yield criterion can be directly introduced into the kinematic theorem of limit analysis without linearization the plastic dissipation power can then be expressed in terms of kinematically admissible velocity fields and a nonlinear optimization formulation is obtained the nonlinear formulation only has one constraint and requires considerably less computational effort than a linear programming formulation the calculation is based entirely on kinematically admissible velocities without calculation of the stress field the finite element formulation of kinematic limit analysis is developed and solved as a nonlinear mathematical programming problem subject to a single equality constraint the objective function corresponds to the plastic dissipation power which is then minimized to give an upper bound to the true limit load an effective direct iterative algorithm for kinematic limit analysis is proposed in this paper to solve the resulting nonlinear mathematical programming problem the effectiveness and efficiency of the proposed method have been illustrated through a number of numerical examples

a fundamental class of stress elements in lower bound limit analysis there is a major restriction in the formulation of rigorous lower bound limit analysis by means of the finite element method once the stress field has been discretized the yield criterion and the

a stabilized discrete shear gap finite element for adaptive limit analysis of mindlin reissner plates summary this paper presents a numerical formulation for computation of collapse load of mindlin reissner plates that uses stabilized discrete shear gap finite elements and second order cone programming displacement fields are approximated using the discrete shear gap in combination with a stabilized strain smoothing technique ensuring that shear locking problem can be avoided and that accurate solutions can be obtained the underlying optimization problem is formulated in the form of a standard second order cone programming so that it can be solved using highly efficient primal dual interior point algorithm an error indicator based on plastic dissipation will be used in the adaptive refinement scheme various plates with arbitrary geometries and boundary conditions are examined to illustrate the performance of the proposed procedure copyright 2013 john wiley sons ltd

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

automatic mesh refinement in limit analysis a strategy for automatic mesh refinement in limit analysis is combined with a recently developed computational method in the absence of estimates of the local error the strategy can be based on the deformations and on slack in the yield condition the approach is tested on standard problems in plane strain including the classical punch problem very accurate results are obtained with the use of moderate computational power

galerkin least squares finite element method for the obstacle problem we construct a consistent multiplier free method for the finite element solution of the obstacle problem the method is based on an augmented lagrangian formulation in which we eliminate the multip

a polytree based adaptive approach to limit analysis of cracked structures abstract we in this paper present a novel adaptive finite element scheme for limit analysis of cracked structures the key idea is to develop a general refinement algorithm based on a so called polytree mesh structure the method is well suited for arbitrary polygonal elements and furthermore traditional triangular and quadrilateral ones which are considered as special cases also polytree meshes are conforming and can be regarded as a generalization of quadtree meshes for the aim of this paper we restrict our main interest in plane strain limit analysis to von mises type materials yet its extension to a wide class of other solid mechanics problems and materials is completely possible to avoid volumetric locking we propose an approximate velocity field enriched with bubble functions using wachspress coordinates on a primal mesh and design carefully strain rates on a dual mesh level an adaptive mesh refinement process is guided by an l 2 norm based indicator of strain rates through numerical validations we show that the present method reaches high accuracy with low computational cost this allows us to perform large scale limit analysis problems favorably

a stabilized nitsche overlapping mesh method for the stokes problem we develop a nitsche based formulation for a general class of stabilized finite element methods for the stokes problem posed on a pair of overlapping non matching meshes by extending the least squares stabilization to the overlap region we prove that the method is stable consistent and optimally convergent to avoid an ill conditioned linear algebra system the scheme is augmented by a least squares term measuring the discontinuity of the solution in the overlap region of the two meshes as a consequence we may prove an estimate for the condition number of the resulting stiffness matrix that is independent of the location of the interface finally we present numerical examples in three spatial dimensions illustrating and confirming the theoretical results

an adaptive finite element strategy for the three dimensional time dependent navier stokes equations abstract an adaptive strategy for three dimensional time dependent problems in the context of the fem is presented the basic tools are a mechanism for local refinement and coarsening of simplicial meshes and an unexpensive error estimator the algorithm for local grid modification is based on bisecting tetrahedra the method is applied to the navier stokes equations

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

an interior point algorithm for elastoplasticity the problem of small deformation rate independent elastoplasticity is treated using convex programming theory and algorithms a finite step variational formulation is first derived after which the relevant potential is discretized in space and subsequently viewed as the lagrangian associated with a convex mathematical program next an algorithm based on the classical primal dual interior point method is developed several key modifications to the conventional implementation of this algorithm are made to fully exploit the nature of the common elastoplastic boundary value problem the resulting method is compared to state of the art elastoplastic procedures for which both similarities and differences are found finally a number of examples are solved demonstrating the capabilities of the algorithm when applied to standard perfect plasticity hardening multisurface plasticity and problems involving softening copyright 2006 john wiley sons ltd

adaptive hpq finite element methods for the analysis of 3d based models of complex structures part 2 a posteriori error estimation abstract this is the second paper out of a series of papers devoted to model and hpq adaptive finite element methods assigned for the modeling and analysis of elastic structures of complex mechanical description in our previous publication we investigated the issue of hierarchical models and approximations of such structures we applied 3d or 3d based mechanical models hierarchical modeling and hierarchical approximations within the proposed finite element formulation furthermore we assumed that the mechanical model and discretization parameters such as the size h of the element and the longitudinal and transverse approximation orders p and q could vary locally i e they could be different in each finite element the a posteriori error estimation discussed in the present paper is based on the generalization of the residual equilibration method on the models with internal constraints the generalized method is applied to the assessment of the total and approximation errors while the modeling error is calculated as the difference between the former two errors the corresponding error controlled adaptive procedures are based on a three step strategy with possible iterations of h and p steps

a note on upper bound formulations in limit analysis summary in this paper we study some recent formulations for the computation of upper bounds in limit analysis we show that a previous formulation presented by the authors does not guarantee the strictness of the upper bound nor does it provide a velocity field that satisfies the normality rule everywhere we show that these deficiencies are related to the quadrature employed for the evaluation of the dissipation power we derive a formulation that furnishes a strict upper bound of the load factor which in fact coincides with a formulation reported in the literature from the analysis of these formulations we propose a post process which consists in computing exactly the dissipation power for the optimum upper bound velocity field this post process may further reduce the strict upper bound of the load factor in particular situations finally we also determine the quadratures that must be used in the elemental and edge gap contributions so that they are always positive and their addition equals the global bound gap copyright 2012 john wiley sons ltd

the finite element method for parabolic equations ii a posteriori error estimation and adaptive approach abstract we extend in this paper the analysis of a posteriori estimates of the space discretization error presented in a previous paper 3 for time independent space meshes in the context of the model problem studied there results are given relating the effectivity of the error estimator to properties of the solution space meshes and manner in which the meshes change a procedure based upon this theory is presented for the adaptive construction of time dependent meshes the results of some computational experiments show that this procedure is practically very effective and suggest that it can be used to control the space discretization error in more general problems author

quadratic velocity linear stress interpolations in limit analysis summary we compare a family of mixed interpolations on triangles with straight edges as applied to limit analysis the aim of this paper is to prove theoretically that the approximate collapse factors obtained with these finite elements always comply with certain inequalities that exist among them two of these interpolations are used in limit analysis for the first time in this article the inequalities in the proposition are also demonstrated via numerical applications to this end the most frequently used benchmark problems in limit analysis are revisited and discussed with respect to the results computed with these finite elements copyright 2014 john wiley sons ltd

a two stage feasible directions algorithm for nonlinear constrained optimization we present a feasible directions algorithm based on lagrangian concepts for the solution of the nonlinear programming problem with equality and inequality constraints at each iteration a descent direction is defined by modifying it we obtain a feasible descent direction the line search procedure assures the global convergence of the method and the feasibility of all the iterates we prove the global convergence of the algorithm and apply it to the solution of some test problems although the present version of the algorithm does not include any second order information like quasi newton methods these numerical results exhibit a behavior comparable to that of the best methods known at present for nonlinear programming

an adaptive approach to limit analysis abstract the main objective of this paper is to propose an adaptive mesh refinement procedure for finite element models in limit analysis we use an a posteriori indicator based on the local directional interpolation error and a recovering scheme to compute second derivatives of the finite element solution the proposed mesh adaptation process gives improved results in localizing regions of rapid or abrupt variations of the variables whose location is not known a priori limit analysis of bodies in plane strain and plane stress is considered in the applications

convergence of simple adaptive galerkin schemes based on h h 2 error estimators we discuss several adaptive mesh refinement strategies based on h h 2 error estimation this class of adaptive methods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead we prove that under the saturation assumption these adaptive algorithms are convergent our framework applies not only to finite element methods but also yields a first convergence proof for adaptive boundary element schemes for a finite element model problem we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general

computation of limit and shakedown loads using a node based smoothed finite element method summary this paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node based smoothed fem in combination with a primal dual algorithm an associated primal dual form based on the von mises yield criterion is adopted the primal dual algorithm together with a newton like iteration are then used to solve this associated primal dual form to determine simultaneously both approximate upper and quasi lower bounds of the plastic collapse limit and the shakedown limit the present formulation uses only linear approximations and its implementation into finite element programs is quite simple several numerical examples are given to show the reliability accuracy and generality of the present formulation compared with other available methods copyright 2011 john wiley sons ltd

a posteriori error estimates for nonlinear problems finite element discretizations of elliptic equations we give a general framework for deriving a posteriori error estimates for approximate solutions of nonlinear problems in a first step it is proven that the error of the approximate solution can be bounded from above and from below by an appropriate norm of its residual in a second step this norm of the residual is bounded from above and from below by a similar norm of a suitable finite dimensional approximation of the residual this quantity can easily be evaluated and for many practical applications sharp explicit upper and lower bounds are readily obtained the general results are then applied to finite element discretizations of scalar quasi linear elliptic partial differential equations of 2nd order the eigenvalue problem for scalar linear elliptic operators of 2nd order and the stationary incompressible navier stokes equations they immediately yield a posteriori error estimates which can easily be computed from the given data of the problem and the computed numerical solution and which give global upper and local lower bounds on the error of the numerical solution

adaptive element free galerkin method applied to the limit analysis of plates the implementation of an h adaptive element free galerkin efg method in the framework of limit analysis is described the naturally conforming property of meshfree approximations with no nodal connectivity required facilitates the implementation of h adaptivity nodes may be moved discarded or introduced without the need for complex manipulation of the data structures involved with the use of the taylor expansion technique the error in the computed displacement field and its derivatives can be estimated throughout the problem domain with high accuracy a stabilized conforming nodal integration scheme is extended for use in error estimation and results in an efficient and truly meshfree adaptive method to demonstrate its effectiveness the procedure is then applied to plates with various boundary conditions

cryptanalysis and improvement of an access control in user hierarchy based on elliptic curve cryptosystem in a key management scheme for hierarchy based access control each security class having higher clearance can derive the cryptographic secret keys of its other security classes having lower clearances in 2008 chung et al proposed an efficient scheme on access control in user hierarchy based on elliptic curve cryptosystem information sciences 178 1 2008 230 243 their scheme provides solution of key management efficiently for dynamic access problems however in this paper we propose an attack on chung et al s scheme to show that chung et al s scheme is insecure against the exterior root finding attack we show that under this attack an attacker adversary who is not a user in any security class in a user hierarchy attempts to derive the secret key of a security class by using the root finding algorithm in order to remedy this attack we further propose a simple improvement on chung et al s scheme overall the main theme of this paper is very simple a security flaw is presented on chung et al s scheme and then a fix is provided in order to remedy the security flaw found in chung et al s scheme

an iterative algorithm for limit analysis with nonlinear yield functions abstract a mathematical programming algorithm is proposed for the general limit analysis problem plastic behavior is described by a set of linear or nonlinear yield functions abstract formulations of limit analysis are first considered and a quasi newton strategy for solving the optimality conditions is then sketched the structure of the problem arising from a finite element discretization is taken into account in order that the algorithm should be able to solve large scale problems

formulation and solution of some plasticity problems as conic programs abstract the application of conic programming to some traditionally difficult plasticity problems is considered convenient standard forms for conic programming of both limit and incremental elastoplastic analysis are given the types of yield criteria that can be treated by conic programming is discussed and it is shown that the three dimensional mohr coulomb criterion can be cast as a set of conic constraints thus facilitating efficient treatment by dedicated algorithms finally the performance of a number of mixed finite elements is evaluated together with a state of the art second order cone programming algorithm

an edge based finite element method es fem with adaptive scaled bubble functions for plane strain limit analysis abstract this paper deals with critical roles of cubic bubble functions for the edge based finite element method es fem formulation within the framework of the kinematic theorem for predicting the plastic collapse loads of structures we show that the bubble function can be scaled by a non zero coefficient alpha while the volumetric locking is entirely eliminated based on this finding the present method is designed in a very small value with a bubble function that is maximum at the center of the element this can lead to the loss of the partition of unity for easy reference the present method is termed as bes fem the significant advantage of the present method lies in the rigorous treatment of the volumetric locking free that can occur in the fully plastic range the bes fem works well with high efficiency by using triangular meshes it achieves both simplicity and computational efficiency for implementation into packages of plastic limit analyses in case of bes fem the locking issue can be solved conveniently by two schemes 1 the usual piecewise linear displacements enriched with a cubic bubble function on a primal mesh of triangular elements and 2 a projection operator of strain rates through a dual mesh associated with the edges in the mesh the optimization formulation of finite element limit analysis is written in the form of a second order cone programming socp the well established interior point solvers can be exploited efficiently the bes fem using a small number of integration points enables to solve the large scale optimization problems efficiently in addition an adaptive meshing procedure based on an alternative indicator of dissipation is also derived to further enhance the quality of the solution without increasing significantly the number of degrees of freedom of the model numerical results show the robustness of the proposed method

a posteriori error estimation for elasto plastic problems based on duality theory abstract in this paper we introduce a new approach to a posteriori error estimation for elasto plastic problems based on the duality theory of the calculus of variations we show that in spite of the prevailing view duality methods provide a viable way for obtaining computable a posteriori error estimates for nonlinear boundary value problems without directly solving the dual problem rigorous mathematical analysis leads to what we call duality error estimators consisting of two parts the error in the constitutive law and the error in the equilibrium equations this representation is both physically meaningful and computationally important the duality error estimators hold for any conforming approximation of the exact solution regardless of whether or not they satisfy the galerkin orthogonality condition in particular they encompass the familiar smoothening or gradient averaging techniques commonly used in practice we prove that the duality error estimators are equivalent to the error when the approximate solution is the exact solution of the discretised problem moreover in the case of linear elasticity the known residual type error estimators can be obtained from the duality error estimators numerical results for a model elasto plastic problem show the accuracy of the duality error estimators

the superconvergent patch recovery and a posteriori error estimates part 2 error estimates and adaptivity in this second part of the paper the issue of a posteriori error estimation is discussed in particular we derive a theorem showing the dependence of the effectivity index for the zienkiewicz zhu error estimator on the convergence rate of the recovered solution this shows that with superconvergent recovery the effectivity index tends asymptotically to unity the superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the zienkiewicz zhu error estimator to demonstrate accurate estimation of the exact error attainable numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient stress error estimation several examples of the performance of the error estimator in adaptive mesh refinement are also presented

algorithms for refining triangular grids suitable for adaptive and multigrid techniques two general algorithms for refining triangular computational meshes based on the bisection of triangles by the longest side are presented and discussed the algorithms can be applied globally or locally for selective refinement of any conforming triangulation and always generate a new conforming triangulation after a finite number of interactions even when locally used the algorithms also ensure that all angles in subsequent refined triangulations are greater than or equal to half the smallest angle in the original triangulation the shape regularity of all triangles is maintained and the transition between small and large triangles is smooth in a natural way proofs of the above properties are presented the second algorithm is a simpler improved version of the first which retains most of the properties of the latter the algorithms can be used either for constructing irregular computational meshes or for locally refining any given triangulation in this sense they can be adequately combined with adaptive and or multigrid techniques for solving finite element systems examples of the application of the algorithms are given and two possible generalizations are pointed out

a priori and a posteriori error analyses of a pseudostress based mixed formulation for linear elasticity in this paper we present the a priori and a posteriori error analyses of a non standard mixed finite element method for the linear elasticity problem with non homogeneous dirichlet boundary conditions more precisely the approach introduced here is based on a simplified interpretation of the pseudostress displacement formulation originally proposed in arnold and falk 1988 which does not require symmetric tensor spaces in the finite element discretization in addition physical quantities such as the stress the strain tensor of small deformations and the rotation are computed through a simple postprocessing in terms of the pseudostress variable furthermore we also introduce a second element by element postprocessing formula for the stress which yields an optimally convergent approximation of this unknown with respect to the broken h div norm we apply the classical babuska brezzi theory to prove that the corresponding continuous and discrete schemes are well posed in particular raviart thomas spaces of order k 0 for the pseudostress and piecewise polynomials of degree k for the displacement can be utilized moreover we remark that in the 3d case the number of unknowns behaves approximately as 9 times the number of elements tetrahedra of the triangulation when k 0 this factor increases to 12 5 when one uses the classical peers next we derive a reliable and efficient residual based a posteriori error estimator for the mixed finite element scheme finally several numerical results illustrating the performance of the method confirming the theoretical properties of the estimator and showing the expected behaviour of the associated adaptive algorithm are provided

lower bound limit analysis of cohesive frictional materials using second order cone programming the formulation of limit analysis by means of the finite element method leads to an optimization problem with a large number of variables and constraints here we present a method for obtaining strict lower bound solutions using second order cone programming socp for which efficient primaldual interior point algorithms have recently been developed following a review of previous work we provide a brief introduction to socp and describe how lower bound limit analysis can be formulated in this way some methods for exploiting the data structure of the problem are also described including an efficient strategy for detecting and removing linearly dependent constraints at the assembly stage the benefits of employing socp are then illustrated with numerical examples through the use of an effective algorithm software very large optimization problems with up to 700 000 variables are solved in minutes on a desktop machine the numerical examples concern plane strain conditions and the mohr coulomb criterion however we show that socp can also be applied to any other problem of lower bound limit analysis involving a yield function with a conic quadratic form notable examples being the drucker prager criterion in 2d or 3d and nielsen s criterion for plates

numerical assessment of the macroscopic strength criterion of reinforced soils using semidefinite programming summary the macroscopic strength properties of reinforced soils regarded as periodic composite materials are investigated by means of a fem based formulation of both static and kinematic approaches of yield design applied to the reinforced soil s unit cell because the reinforced soil s individual constituents obey a 3d mohr coulomb strength condition such a numerical problem can be treated through an optimization procedure using semidefinite programming the whole numerical procedure is applied to the derivation of both lower bound and upper bound estimates to the macroscopic yield surface of a soil reinforced either by columnar inclusions stone columns or a double array of trenches cross trench reinforcement the so obtained results highlight the efficiency of the proposed numerical method copyright 2014 john wiley sons ltd

a new discontinuous upper bound limit analysis formulation summary a new upper bound formulation of limit analysis of two and three dimensional solids is presented in contrast to most discrete upper bound methods the present one is formulated in terms of stresses rather than velocities and plastic multipliers however by means of duality theory it is shown that the formulation does indeed result in rigorous upper bound solutions also kinematically admissible discontinuities which have previously been shown to be very efficient are given an interpretation in terms of stresses this allows for a much simpler implementation and in contrast to existing formulations extension to arbitrary yield criteria in two and three dimensions is straightforward finally the capabilities of the new method are demonstrated through a number of examples copyright 2005 john wiley sons ltd

the finite element method for parabolic equations in this first of two papers computable a posteriori estimates of the space discretization error in the finite element method of lines solution of parabolic equations are analyzed for time independent space meshes the effectiveness of the error estimator is related to conditions on the solution regularity mesh family type and asymptotic range for the mesh size for clarity the results are limited to a model problem in which piecewise linear elements in one space dimension are used the results extend straight forwardly to systems of equations and higher order elements in one space dimension while the higher dimensional case requires additional considerations the theory presented here provides the basis for the analysis and adaptive construction of time dependent space meshes which is the subject of the second paper computational results show that the approach is practically very effective and suggest that it can be used for solving more general problems

on the construction and analysis of high order locally conservative finite volume type methods for one dimensional elliptic problems locally conservative finite volume type methods based on continuous piecewise polynomial functions of degree r ge 2 are introduced and analyzed in the context of indefinite elliptic problems in one space dimension the new methods extend and generalize the classical finite volume method based on piecewise linear functions we derive a priori error estimates in the l2 h1 and l infty norm and discuss superconvergence effects for the error and its derivative explicit residual based a posteriori error bounds in the l2 and energy norm are also derived we compute the experimental order of convergence and show the results of an adaptive algorithm based on the a posteriori error estimates

upper and lower bounds in limit analysis adaptive meshing strategies and discontinuous loading summary upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimisation problems the membership constraints for von mises and mohrcoulomb plasticity criteria are written as a set of quadratic constraints which permits to solve the optimisation problem using specific algorithms for second order conic program socp from the stress field at the lower bound and the velocities at the upper bound we construct a novel error estimate based on elemental and edge contributions to the bound gap these contributions are employed in an adaptive remeshing strategy that is able to reproduce fan type mesh patterns around points with discontinuous surface loading the solution of this type of problems is analysed in detail and from this study some additional meshing strategies are also described we particularise the resulting formulation and strategies to two dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature copyright c 2007 john wiley sons ltd

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner