long time behavior of a model of extensible beams with nonlinear boundary dissipations abstract this paper is concerned with the long time behavior of a model of extensible beams u t t u x x x x m 0 l u x 2 d x u x x h defined in a bounded interval 0 l where m is a continuous nonnegative function and h is a static load to this problem little is known with nonlinear boundary conditions one considers the case where a nonlinear forcing interacts with the shear force at the boundary then the existence of a global attractor is proved with a sole boundary damping

a unifying theory of a posteriori error control for discontinuous galerkin fem a unified a posteriori error analysis is derived in extension of carstensen numer math 100 617 637 2005 and carstensen and hu j numer math 107 3 473 502 2007 for a wide range of discontinuous galerkin dg finite element methods fem applied to the laplace stokes and lame equations two abstract assumptions a1 and a2 guarantee the reliability of explicit residual based computable error estimators the edge jumps are recast via lifting operators to make arguments already established for nonconforming finite element methods available the resulting reliable error estimate is applied to 16 representative dg fems from the literature the estimate recovers known results as well as provides new bounds to a number of schemes

abstract volterra integrodifferential equations with applications to parabolic models with memory in this paper we are concerned with local existence regularity and continuous dependence upon the initial data of epsilon regular mild solutions for the abstract integrodifferential equation 1 2 we also present a result on unique continuation and a blow up alternative for an epsilon regular mild solution of 1 2 finally we apply our results to three interesting models navier stokes equations with memory diffusion equations with memory and a strongly damped plate equation with memory

adaptive stabilization of a kirchhoff s non linear beam with output disturbances abstract this paper is concerned with adaptive stabilization of an undamped non linear beam with disturbed outputs by boundary feedback control the adaptive controller is constructed by the concept of high gain adaptive feedback and the estimation mechanism for the unknown parameters of the measurement noise the global existence and uniqueness of the solution of the closed loop system is justified the stability of the closed loop system is proved such that the convergence of the system state to zero and the convergence of the estimated parameter to the unknown parameter are guaranteed for the smooth and small initial data

global attractors for the extensible thermoelastic beam system abstract this work is focused on the dissipative system t t u x x x x u x x x u l 2 0 1 2 x x u f t x x x x t u g describing the dynamics of an extensible thermoelastic beam where the dissipation is entirely contributed by the second equation ruling the evolution of under natural boundary conditions we prove the existence of bounded absorbing sets when the external sources f and g are time independent the related semigroup of solutions is shown to possess the global attractor of optimal regularity for all parameters r the same result holds true when the first equation is replaced by t t u x x t t u x x x x u x x x u l 2 0 1 2 x x u f with 0 in both cases the solutions on the attractor are strong solutions

local discontinuous galerkin methods for the stokes system in this paper we introduce and analyze local discontinuous galerkin methods for the stokes system for a class of shape regular meshes with hanging nodes we derive a priori estimates for the l2 norm of the errors in the velocities and the pressure we show that optimal order estimates are obtained when polynomials of degree k are used for each component of the velocity and polynomials of degree k 1 for the pressure for any k ge1 we also consider the case in which all the unknowns are approximated with polynomials of degree k and show that although the orders of convergence remain the same the method is more efficient numerical experiments verifying these facts are displayed

adaptive stabilization for a kirchhoff type nonlinear beam under boundary output feedback control abstract in this paper the boundary stabilization for a kirchhoff type nonlinear beam with one end fixed and control at the other end is considered a gain adaptive controller is designed in terms of measured end velocity the existence and uniqueness of the classical solution of the closed loop system are justified the exponential stability of the system is obtained

global attractor for a nonlinear plate equation with supported boundary conditions abstract in this paper we consider a two dimensional nonlinear equation w t t d 2 w e w t n 1 t 2 w x 2 d x d y w x x n 2 t 2 w y 2 d x d y w y y 0 which arises from the model of the viscoelastic thin rectangular plate with four edges supported by virtue of galerkin method combined with the priori estimates we prove the existence and uniqueness of the global solution under initial boundary data for the above equation especially the existence of the bounded absorbing set in space e and the existence of the global attractor of system is also obtained

an hp adaptive mixed discontinuous galerkin fem for nearly incompressible linear elasticity we develop the a posteriori error estimation of mixed hp version discontinuous galerkin finite element methods for nearly incompressible elasticity problems in two space dimensions computable upper and lower bounds on the error measured in terms of a natural mesh dependent energy norm are derived the bounds are explicit in the local mesh sizes and approximation orders and are independent of the locking parameter a series of numerical experiments are presented which demonstrate the performance of the proposed error estimator within an automatic hp adaptive refinement procedure

a study on the linear elastic stability of mindlin plates the debate on the performance of lagrangian and serendipity elements in mindlin s plate theory has been going on for quite some time limited published results for static and vibration analysis based on exact integration demonstrated a drastic deterioration in accuracy as the thickness of the plate decreases and reduced selective integration schemes have been suggested to improve their performance appreciable improvement for lagrangian elements has been recorded but it is only marginal for the serendipity elements on the strength of such observations one would then be tempted to rule out the exact integration schemes and serendipity elements in this paper the above problem is reviewed for stability analysis of plates two elements are chosen from each family one representing the higher order and the other the lower order element contrary to published results all elements can attain very accurate solutions independent of the integration schemes for a sufficiently restrained plate although in general the serendipity elements will require a more refined mesh than the lagrangian ones however for loosely restrained plates the solution failed when integration is performed by reduced selective schemes the failure marks the limitation of the reduced selective schemes which have somehow introduced spurious modes into the system but on the other hand it is ironical that these spurious modes in fact contribute to the improvement of performance of the restrained cases therefore one can equally improve the serendipity elements by a selective scheme which can introduce additional zero modes a scheme based on 5 5 integration points for flexural stiffness and 3 3 integration points for shear stiffness improved the 17se serendipity elements remarkably however because of the lack of bounds in most cases the use of reduced selected schemes is still not recommended finally this paper also proposed an approximate formulation of the geometric stiffness matrices to replace the full formulation such an approximate formulation reduces the number of variables considerably in the eigenvalue search and can still give reasonably accurate results for thin plates with a t 15

a posteriori error estimates for mixed fem in elasticity a residue based reliable and efficient error estimator is established for finite element solutions of mixed boundary value problems in linear planar elasticity the proof of the reliability of the estimator is based on helmholtz type decompositions of the error in the stress variable and a duality argument for the error in the displacements the efficiency follows from inverse estimates the constants in both estimates are independent of the lame constant lambda and so locking phenomena for lambda to infty are properly indicated the analysis justifies a new adaptive algorithm for automatic mesh refinement

a unifying theory of a posteriori finite element error control residual based a posteriori error estimates are derived within a unified setting for lowest order conforming nonconforming and mixed finite element schemes the various residuals are identified for all techniques and problems as the operator norm l of a linear functional of the form in the variable of a sobolev space v the main assumption is that the first order finite element space is included in the kernel ker l of l as a consequence any residual estimator that is a computable bound of l can be used within the proposed frame without further analysis for nonconforming or mixed fe schemes applications are given for the laplace stokes and navier lame equations

global solution and regularizing properties on a class of nonlinear evolution equation abstract in this paper we will consider the equation formula where formula the initial value problem is proved to be locally well posed for initial data taken ind a2 d a3 2 and globally well posed for small data in this case we also show the exponential decay of the solution as time goes to infinity the main result of this paper is to prove that the solution has the smooting effect property on the initial data this means that if the initial data belongs tod a2 d a3 2 then the solutionubelongs toc 0 d ak k n providedm n andrarec function

uniform stabilization of a nonlinear beam by nonlinear boundary feedback we consider the planar motion of a uniform prismatic beam of length l we want to derive a model that reflects the effect of stretching on bending which necessarily leads to nonlinear partial differential equations for the motion of the beam we will however assume that the constitutive equations for bending are linear this is in agreement with existing engineering literature see for example s and the bibliography therein it should be remarked that the effect of stretching on bending becomes significant if in particular a rigid rotation is superimposed on the motion we do not consider such a rotation here even though it could be handled within the present framework we assume that the beam in its reference state occupies the region described in rectangular coordinates by

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

discontinuous galerkin methods for incompressible elastic materials abstract in this paper we introduce and analyze a local discontinuous galerkin method for linear elasticity a simple post processing is introduced which takes advantage of the special structure of the method it allows us to construct an approximation to the displacement which is h div conforming and to enforce the equation that links the pressure to the divergence of the displacement strongly inside each element as a consequence when the material is exactly incompressible the displacement is also exactly incompressible this is achieved without having to deal with the almost impossible task of constructing finite dimensional subspaces of incompressible displacements we provide an error analysis of the method that holds uniformly with respect to the poisson ratio in particular we show that the displacement converges in l2 with order k 1 when polynomials of degree k 0 are used we also display numerical experiments confirming that the theoretical orders of convergence are actually achieved and that they do not deteriorate when the material becomes incompressible

global attractors for von karman equations with nonlinear interior dissipation abstract in this paper we study the asymptotic behavior of weak solutions for von karman equations with nonlinear interior dissipation we prove the existence of a global attractor in the space w 2 2 l 2

global existence for the wave equation with nonlinear boundary damping and source terms abstract the paper deals with local and global existence for the solutions of the wave equation in bounded domains with nonlinear boundary damping and source terms the typical problem studied is u tt u 0 in 0 u 0 on 0 0 u u t m 2 u t u p 2 u on 0 1 u 0 x u 0 x u t 0 x u 1 x on where r n n 1 is a regular and bounded domain 0 1 m 1 2 p r where r 2 n 1 n 2 when n 3 r when n 1 2 and the initial data are in the energy space we prove local existence of the solutions in the energy space when m r r 1 p or n 1 2 and global existence when p m or the initial data are inside the potential well associated to the stationary problem

a posteriori error estimates for a discontinuous galerkin approximation of second order elliptic problems several a posteriori error estimators are introduced and analyzed for a discontinuous galerkin formulation of a model second order elliptic problem in addition to residual type estimators we introduce some estimators that are couched in the ideas and techniques of domain decomposition results of numerical experiments are presented

long time dynamics of an extensible plate equation with thermal memory abstract this work is concerned with long time dynamics of solutions of extensible plate equations with thermal memory the problem corresponds to a model of thermoelasticity based on a theory of non fourier heat flux by considering the case where rotational inertia is present we show that the thermal dissipation is sufficient to stabilize the system and guarantees the existence of a finite dimensional global attractor in addition the existence of exponential attractors is also considered

global attractor for a model of extensible beam with nonlinear damping and source terms abstract this paper is concerned with the existence of a global attractor for the nonlinear beam equation with nonlinear damping and source terms u t t 2 u m u 2 d x u f u g u t h in r where is a bounded domain of r n m is a nonnegative real function and h l 2 the nonlinearities f u and g u t are essentially u u u u and u t r u t respectively with r 0 and this kind of problem models vibrations of extensible beams and plates

energy norm a posteriori error estimation for discontinuous galerkin methods in this paper we present a residual based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous galerkin approximations of elliptic problems the theory is developed for an elliptic model problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed we also present some illustrating numerical examples

on a global solution and asymptotic behaviour for the generalized damped extensible beam equation abstract we prove the existence and uniqueness of global solutions for the cauchy problem concerning the evolution equation u a 2 u m a 1 2 u 2 h au g u 0 suggested by the study of plates and beams where a is a linear operator in a hilbert space h and m and g are real functions we also study the asymptotic behaviour of the solutions under suitable growth assumptions on the nonlinear term g

locking free adaptive discontinuous galerkin fem for linear elasticity problems an adaptive discontinuous galerkin finite element method for linear elasticity problems is presented we develop an a posteriori error estimate and prove its robustness with respect to nearly incompressible materials absence of volume locking furthermore we present some numerical experiments which illustrate the performance of the scheme on adaptively refined meshes

mixed hp dgfem for incompressible flows we consider several mixed discontinuous galerkin approximations of the stokes problem and propose an abstract framework for their analysis using this framework we derive a priori error estimates for hp approximations on tensor product meshes we also prove a new stability estimate for the discrete divergence bilinear form