a stabilized mixed finite element method for darcy flow we develop new stabilized mixed finite element methods for darcy flow stability and an a priori error estimate in the stability norm are established a wide variety of convergent finite elements present themselves unlike the classical galerkin formulation which requires highly specialized elements an interesting feature of the formulation is that there are no mesh dependent parameters numerical tests confirm the theoretical results 2002 elsevier science b v all rights reserved

admissibility analysis of stochastic singular systems with poisson switching abstract this paper addresses the mean square admissibility problem for a class of stochastic singular systems with poisson switching by using h representation approach we show the equivalence between mean square admissibility and robust admissibility of a deterministic system which is an extension of the result in the case of deterministic system 1 based on multiple lyapunov functions and matrix decomposition approaches some easily verifiable sufficient conditions without equality constraint are established and can be conveniently used to state feedback controller design some admissibility criteria are constructed for linear singular systems with poisson switching three examples including a rlc circuit and a mass spring damper system are introduced to demonstrate the validity of the theoretical results

convergence in the incompressible limit of finite element approximations based on the hu washizu formulation the classical hu washizu mixed formulation for plane problems in elasticity is examined afresh with the emphasis on behavior in the incompressible limit the classical continuous problem is embedded in a family of hu washizu problems parametrized by a scalar for which alpha lambda big mu corresponds to the classical formulation with and being the lame parameters uniform well posedness in the incompressible limit of the continuous problem is established for 1 finite element approximations are based on the choice of piecewise bilinear approximations for the displacements on quadrilateral meshes conditions for uniform convergence are made explicit these conditions are shown to be met by particular choices of bases for stresses and strains and include bases that are well known as well as newly constructed bases though a discrete version of the spherical part of the stress exhibits checkerboard modes it is shown that a independent a priori error estimate for the displacement can be established furthermore a independent estimate is established for the post processed stress the theoretical results are explored further through selected numerical examples

observer based controller design for stochastic descriptor systems with brownian motions in the paper a complete proof of the properness and mean square exponential stability for stochastic brownian systems is firstly addressed which lays a solid foundation for system analysis and control synthesis for this kind of stochastic systems observer based controller for the descriptor system with brownian motions is then investigated it is noticed that the system dynamics and observer dynamics are both subjected to state brownian fluctuation which makes it challenging either to design observer gain and controller gain simultaneously or design the observer and control gains by using a complete separation design technique a sequential design technique is proposed to calculate the control and observer gains by solving linear matrix inequalities the proposed design methods are readily extended to the case for stochastic descriptor systems with multiple brownian motions a numerical example is finally given to illustrate the design techniques and simulated results have demonstrated the efficiency

f bar based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids part i formulation and benchmarking this paper proposes a new technique which allows the use of simplex finite elements linear triangles in 2d and linear tetrahedra in 3d in the large strain analysis of nearly incompressible solids the new technique extends the f bar method proposed by de souza neto et al int j solids and struct 1996 33 3277 3296 and is conceptually very simple it relies on the enforcement of near incompressibility over a patch of simplex elements rather than the point wise enforcement of conventional displacement based finite elements within the framework of the f bar method this is achieved by assuming for each element of a mesh a modified f bar deformation gradient whose volumetric component is defined as the volume change ratio of a pre defined patch of elements the resulting constraint relaxation effectively overcomes volumetric locking and allows the successful use of simplex elements under finite strain near incompressibility as the original f bar procedure the present methodology preserves the displacement based structure of the finite element equations as well as the strain driven format of standard algorithms for numerical integration of path dependent constitutive equations and can be used regardless of the constitutive model adopted the new elements are implemented within an implicit quasi static environment in this context a closed form expression for the exact tangent stiffness of the new elements is derived this allows the use of the full newton raphson scheme for equilibrium iterations the performance of the proposed elements is assessed by means of a comprehensive set of benchmarking two and three dimensional numerical examples

adaptivity for parameter identification of incompressible hyperelastic materials using stabilized tetrahedral elements abstract this work is concerned with the identification of material parameters for isotropic incompressible hyperelastic material models besides the principal stretch based strain energy function by ogden an invariant based strain energy function by rivlin saunders is considered for which parameter sensitivities are derived the identification is formulated as a least squares minimization problem based on the finite element method to account for inhomogeneous states of stresses and strains in the experimental data which is obtained by optical measurements for the finite element method low order tetrahedral elements in a mixed displacement pressure formulation with stabilization are considered special attention is payed to an adaptive mesh refinement based on a goal oriented a posteriori error indicator to gain reliable material parameters to approximate error terms an element wise recovery technique based on enhanced gradients is introduced

from the hu washizu formulation to the average nodal strain formulation abstract we present a stabilized finite element method for the hu washizu formulation of linear elasticity based on simplicial meshes leading to the stabilized nodal strain formulation or node based uniform strain elements we show that the finite element approximation converges uniformly to the exact solution for the nearly incompressible case

analysis of new augmented lagrangian formulations for mixed finite element schemes two new augmented lagrangian formulations for mixed finite element schemes are presented the methods lead in some cases to an improvement in the order of the approximation an error analysis is provided together with some interesting examples of applications

gradient schemes for linear and non linear elasticity equations the gradient scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations we show in this paper that the gradient scheme framework can be adapted to elasticity equations and provides error estimates for linear elasticity and convergence results for non linear elasticity we also establish that several classical and modern numerical methods for elasticity are embedded in the gradient scheme framework which allows us to obtain convergence results for these methods in cases where the solution does not satisfy the full h 2 h 2 regularity or for non linear models

robust h sub spl infin filter design of uncertain descriptor systems with discrete and distributed delays the robust h sub spl infin filtering problem for a class of continuous time uncertain linear descriptor systems with time varying discrete and distributed delays is investigated the time delays are assumed to be constant and known the uncertainties under consideration are norm bounded and possible time varying uncertainties sufficient condition for the existence of an h sub spl infin filter is expressed in terms of strict linear matrix inequalities lmis instead of using decomposition technique a unified form of lmis is proposed to show the exponential stability of the augmented systems the condition for assuring the stability of the fast subsystem is implied from the unified form of lmis which is shown to be less conservative than the characteristic equation based conditions or matrix norm based conditions the suitable filter is derived through a convex optimization problem a numerical example is given to show the effectiveness of the method

stability analysis for semi markovian switched singular stochastic systems abstract the stability problem is investigated for switched singular stochastic systems with semi markovian switching signals considering the inherent mode dependent state jumps at the switching instants sufficient conditions of stochastic stability exponential stability in the mean square and almost surely exponential stability are obtained by using the stochastic analysis theory and lyapunov function method finally an example is provided to illustrate the effectiveness of the proposed results

a stabilized nodally integrated tetrahedral a stabilized nodally integrated linear tetrahedral is formulated and analysed it is well known that linear tetrahedral elements perform poorly in problems with plasticity nearly incompressible materials and acute bending for a variety of reasons low order tetrahedral elements are preferable to quadratic tetrahedral elements particularly for nonlinear problems but the severe locking problems of tetrahedrals have forced analysts to employ hexahedral formulations for most nonlinear problems on the other hand automatic mesh generation is often not feasible for building many 3d hexahedral meshes a stabilized nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity nearly incompressible materials and acute bending the formulation is analytically and numerically shown to be stable and optimally convergent for the compressible case provided sufficient smoothness of the exact solution u c2 h1 3 future work may extend the formulation to the incompressible regime and relax the regularity requirements nonetheless the results demonstrate that the method is not susceptible to locking and performs quite well in several standard linear and nonlinear benchmarks published in 2006 by john wiley sons ltd

division algebras over henselian fields in this chapter we focus on the tame division algebras d with center a field f with henselian valuation v as usual we approach this by first obtaining results for graded division algebras then lifting back from operatorname mathsf gr d to d this is facilitated by results in 8 1 on existence and uniqueness of lifts of tame subalgebras from operatorname mathsf gr d to d in 8 2 we describe four fundamental canonical up to conjugacy subalgebras of d that reflect its valuative structure the rest of the chapter is devoted to brauer group factorizations of d corresponding to the noncanonical direct product decomposition of operatorname mathit br t f given in cor 7 85 the factor operatorname mathit hom c operatorname mathcal g overline f mathbb t gamma f is represented by a type of division algebra n called decomposably semiramified defined in 8 3 and characterized by the property that n contains a maximal subfield inertial over f and another totally ramified over f we show in 8 4 that every tame division algebra d is brauer equivalent to some s f t where s is inertially split and t is tame and totally ramified over f we show further that every inertially split division algebra s is brauer equivalent to some i f n where i is inertial over f and n is decomposably semiramified the classes overline i for the i appearing in the i f n decompositions of s are shown to range over a single coset of mathit dec z overline s overline f in operatorname mathit br overline f called the specialization coset of s in the final subsection 8 4 6 we summarize what happens in the special case that v is discrete of rank 1 where substantial simplifications occur

stability of singular stochastic systems with markovian switching in recent years singular hybrid systems have received considerable attention however few results are concerned with stability of singular hybrid stochastic systems based on a stability result for singular hybrid systems this note studies mean square stability of singular hybrid stochastic systems it is found that the diffusions and the markov chain may play important roles in system analysis in mean square sense as a special case a criterion for mean square stability of hybrid stochastic systems is developed by the frequency domain approach

stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications this papers summarizes two linear tetrahedral fe formulations that have been recently proposed to overcome volumetric locking in nearly incompressible explicit dynamic applications in particular the average nodal pressure anp technique described by bonet and burton communications in numerical methods in engineering 1998 14 437 449 is briefly reviewed in addition the split based formulation proposed by zienkiewicz et al international journal for numerical methods in engineering 1998 43 565 583 is described here in terms of a time integration of the nodal jacobian this will make it simple to compare both techniques and will enable a new combined method to be presented the paper will then discuss the stability constraints that each technique places on the timestep size a von neuman stability analysis on simple 1 d uniform meshes will show that the anp element permits the use of much larger timesteps than the split based formulations finally numerical examples corroborating in 3 d this analytical conclusions will be presented copyright 2001 john wiley sons ltd

uniform convergence and a posteriori error estimators for the enhanced strain finite element method enhanced strain elements frequently employed in practice are known to improve the approximation of standard non enhanced displacement based elements in finite element computations the first contribution in this work towards a complete theoretical explanation for this observation is a proof of robust convergence of enhanced element schemes it is shown that such schemes are locking free in the incompressible limit in the sense that the error bound in the a priori estimate is independent of the relevant lame constant the second contribution is a residual based a posteriori error estimate the l 2 norm of the stress error is estimated by a reliable and efficient estimator that can be computed from the residuals

stabilisation of hybrid stochastic differential equations by delay feedback control this paper is concerned with the exponential mean square stabilisation of hybrid stochastic differential equations also known as stochastic differential equations with markovian switching by delay feedback controls although the stabilisation by non delay feedback controls for such equations has been discussed by several authors there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap to make our theory more understandable as well as to avoid complicated notations we will restrict our underlying hybrid stochastic differential equations to a relatively simple form however our theory can certainly be developed to cope with much more general equations without any difficulty

volume averaged nodal projection method for nearly incompressible elasticity using meshfree and bubble basis functions we present a displacement based galerkin meshfree method for the analysis of nearly incompressible linear elastic solids where low order simplicial tessellations i e 3 node triangular or 4 node tetrahedral meshes are used as a background structure for numerical integration of the weak form integrals and to get the nodal information for the computation of the meshfree basis functions in this approach a volume averaged nodal projection operator is constructed to project the dilatational strain into an approximation space of equal or lower order than the approximation space for the displacement field resulting in a locking free method the stability of the method is provided via bubble like basis functions because the notion of an element or cell is not present in the computation of the meshfree basis functions such low order tessellations can be used regardless of the order of the approximation spaces desired first and second order meshfree basis functions are chosen as a particular case in the proposed method numerical examples are provided in two and three dimensions to demonstrate the robustness of the method its ability to avoid volumetric locking in the nearly incompressible regime and its improved performance when compared to the mini finite element scheme on the simplicial mesh

stabilization of singular t s fuzzy markovian jump system with mode dependent derivative term coefficient via sliding mode control abstract this paper introduces sliding mode control for singular takagi sugeno t s fuzzy markovian jump system with mode dependent derivative term coefficient firstly a new continuous switching function is designed then sufficient conditions about admissibility of sliding motion under the case of completely known transition rate and uncertain transition rate are presented respectively the obtained conditions are strict linear matrix inequalities furthermore a sliding mode controller is presented finally an example is given to illustrate the effectiveness of the obtained results in this paper

stabilization of singular markovian jump systems with generally uncertain transition rates this note is devoted to investigating the stability and stabilization problems for continuous time singular markovian jump systems smjss with generally uncertain transition rates gutrs in this gutr singular model each transition rate can be completely unknown or only its estimate value is known in terms of a set of coupled linear matrix inequalities lmis a sufficient condition is established to ensure the systems to be regular impulse free and stochastically stable moreover the corresponding sufficient condition on the existence of a mode dependent state feedback controller is derived to guarantee the closed loop systems stochastically admissible by applying the lmi technique finally a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method

linear finite element methods for planar linear elasticity a linear nonconforming conforming displacement finite element method for the pure displacement pure traction problem in two dimensional linear elasticity for a homogeneous isotropic elastic material is considered in the case of a convex polygonal configuration domain error estimates in the energy l sup 2 norm are obtained the convergence rate does not deteriorate for nearly incompressible material furthermore the convergence analysis does not rely on the theory of saddle point problems 22 refs

robust h sliding mode control for nonlinear stochastic t s fuzzy singular markovian jump systems with time varying delays abstract in this paper the robust h stabilization problem for stochastic t s fuzzy singular markovian jump systems with time delays is investigated by using integral sliding mode control a novel fuzzy integral type sliding surface function is designed by fully taking the singular derivative matrix into account by the utilization of linear matrix inequality technique a delay dependent criterion is derived which guarantees the sliding mode dynamics to be stochastically admissible with a prescribed h performance moreover a suitable sliding mode law is synthesized to ensure the stochastic admissibility of the resulting closed loop system and the proposed sliding mode control law can steer the trajectories of the controlled system to the specified sliding surface in finite time finally three examples are provided to illustrate the effectiveness of the proposed method

robust h 2 control of descriptor system with time varying uncertainty for a descriptor system with time varying structured uncertainty this paper considers the robust h 2 control problem of finding a controller satisfying the prescribed h 2 performance level against all possible uncertainty under the constraint of robust stability a sufficient condition for the robust h2 performance is derived in terms of a linear matrix inequality lmi based on this lmi condition we develop a design method of a descriptor variable feedback controller achieving the robust performance the present design method can solve the robust h 2 control problem for a wider class of plants than the state space approach a numerical example is also included to show the applicability of the present method

l2 l consensus of stochastic delayed multi agent systems with adt switching interaction topologies abstract this paper investigates the l 2 l consensus for a class of stochastic delayed multi agent systems subject to switching interaction topologies via utilizing an observer based control protocol the switching between the interaction topologies is assumed to have the average dwell time adt constraint with the aid of a simple model transformation the l 2 l consensus issue is transformed into the problem of weighted stochastic l 2 l control analysis results on the weighted stochastic l 2 l control are proposed by constructing lyapunov krasovskii functional and employing stochastic analysis methods then an approach is developed to determine the desired observer based consensus protocol finally an illustrative numerical example is given to show the usefulness of our design method

essential dimension of finite p groups we prove that the essential dimension and p dimension of a p group g over a field f containing a primitive p th root of unity is equal to the least dimension of a faithful representation of g over f

admissibility and stabilization of stochastic singular markovian jump systems with time delays abstract this paper deals with the admissibility analysis and stabilization of stochastic singular markovian jump systems ssmjss with time delays more general conditions for the existence and uniqueness of the impulse free solution to delayed ssmjss are presented consequently by constructing stochastic lyapunov krasovskii functional and applying generalized ito formula new sufficient conditions for the stability of ssmjss and delayed ssmjss are obtained in terms of strict linear matrix inequalities state feedback controller is designed to ensure stabilization of the delayed ssmjss three illustrative examples including an r l c circuit network and an oil catalytic cracking process are employed to verify the effectiveness and usefulness of the obtained results

a mixed finite element method for nearly incompressible elasticity and stokes equations using primal and dual meshes with quadrilateral and hexahedral grids we consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and stokes equations the finite element method is based on quadrilateral and hexahedral triangulation using primal and dual meshes we use the standard bilinear and trilinear finite element space enriched with element wise defined bubble functions with respect to the primal mesh for the displacement or velocity whereas the pressure space is discretized by using a piecewise constant finite element space with respect to the dual mesh

brief paper stability and stabilization of continuous time singular hybrid systems in this paper the problems of stability and state feedback stabilization for a class of continuous time singular hybrid systems are investigated a new sufficient and necessary condition for a continuous time singular hybrid system to be regular impulse free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities lmis moreover a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities finally a numerical example is given to illustrate the effectiveness of the obtained theoretical results

on the accuracy of the finite volume element method based on piecewise linear polynomials we present a general error estimation framework for a finite volume element fve method based on linear polynomials for solving second order elliptic boundary value problems this framework treats the fve method as a perturbation of the galerkin finite element method and reveals that regularities in both the exact solution and the source term can affect the accuracy of fve methods in particular the error estimates and counterexamples in this paper will confirm that the fve method cannot have the standard o h2 convergence rate in the l2 norm when the source term has the minimum regularity only being in l2 even if the exact solution is in h2

a volume averaged nodal projection method for the reissner mindlin plate model abstract we introduce a novel meshfree galerkin method for the solution of reissner mindlin plate problems that is written in terms of the primitive variables only i e rotations and transverse displacement and is devoid of shear locking the proposed approach uses linear maximum entropy basis functions for field variables approximation and is built variationally on a two field potential energy functional wherein the shear strain written in terms of the primitive variables is computed via a volume averaged nodal projection operator that is constructed from the kirchhoff constraint of the three field mixed weak form the meshfree approximation is constructed over a set of scattered nodes that are obtained from an integration mesh of three node triangles on which the meshfree stiffness matrix and nodal force vector are numerically integrated the stability of the method is rendered by adding bubble like enrichment to the rotation degrees of freedom some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses

reformulation of nodally integrated continuum elements to attain insensitivity to distortion summary the nodally integrated continuum element nice formulation is an assumed strain finite element technique derived from a weighted residual statement that weakly enforces both the balance equation and the kinematic equation the original nice formulation has a number of desirable attributes e g resistance to volumetric locking but similar to classical finite elements it is sensitive to a geometrical distortion of the finite element mesh the present work analyzes the nice technique from this viewpoint the source of the sensitivity to the shape of the element is identified and an improvement of the nice formulation is proposed we illustrate the performance of the revised nice formulation on extremely distorted meshes the tetrahedral meshes contain zero volume or negative volume elements including slivers and the new nice formulation is shown to have the condition number of the stiffness matrix under control even in the presence of slivers furthermore insensitivity to distortions is demonstrated for quadratic and cubic hexahedral elements the proposed improvement confers robustness to all element shapes treated by the nice formulation the approximation properties of the original nice formulation are preserved in particular the improved version is also locking free and at the same time the need for stabilization also carries over copyright 2011 john wiley sons ltd

a finite element method for a three field formulation of linear elasticity based on biorthogonal systems abstract we consider a mixed finite element method based on simplicial triangulations for a three field formulation of linear elasticity the three field formulation is based on three unknowns displacement stress and strain in order to obtain an efficient discretization scheme we use a pair of finite element bases forming a biorthogonal system for the strain and stress the biorthogonality relation allows us to statically condense out the strain and stress from the saddle point system leading to a symmetric and positive definite system the strain and stress can be recovered in a post processing step simply by inverting a diagonal matrix moreover we show a uniform convergence of the finite element approximation in the incompressible limit numerical experiments are presented to support the theoretical results

some remarks on stability of stochastic singular systems with state dependent noise this paper discusses the stability for stochastic singular systems with state dependent noise in both continuous time and discrete time cases firstly the condition for the existence and uniqueness of the solution to stochastic singular systems is given based on this condition the stochastic ito singular system is transformed into a deterministic standard singular system by means of h representation method secondly new sufficient conditions for the stability of systems considered are derived in terms of strict linear matrix inequalities finally an example is given to illustrate the effectiveness of the obtained theoretical results

meshfree enriched simplex elements with strain smoothing for the finite element analysis of compressible and nearly incompressible solids abstract this paper presents a meshfree enriched finite element formulation for triangular and tetrahedral elements in the analysis of two and three dimensional compressible and nearly incompressible solids the new formulation is first established in two dimensional case by introducing a meshfree approximation into a linear triangular finite element with an enriched node the interpolation functions of the four noded triangular element are constructed by the meshfree convex approximations and are completed to a polynomial of degree one the reference mapping using the constructed interpolation functions is shown to be invertible everywhere in the element and the global element area is proven to be conserved under a standard three point integration rule the triangular element formulation is extendable to the tetrahedral element in three dimensional case to provide a locking free analysis for the nearly incompressible materials an area weighted strain smoothing is developed in conjunction with the enriched interpolation functions to yield a discrete divergence free property at the integration point the resultant element formulation with strain smoothing is shown to pass the patch test to introduce the smoothed strain into galerkin formulation a modified hu washizu variational principle is adopted to formulate the discrete equations since the kronecker delta property in element interpolation is held along the element boundary using meshfree convex approximation boundary conditions can be treated in a standard way several numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed method

stabilization of stochastic singular nonlinear hybrid systems abstract this paper deals with the control of the class of singular nonlinear stochastic hybrid systems under some appropriate assumptions results on stochastic stability and stochastic stabilization are developed two state feedback controllers linear and nonlinear that stochastically stabilize the class of systems we are considering are designed lmi sufficient conditions are developed to compute the gains of these controllers