efficient parallel resolution of the simplified transport equations in mixed dual formulation a reactivity computation consists of computing the highest eigenvalue of a generalized eigenvalue problem for which an inverse power algorithm is commonly used very fine modelizations are difficult to treat for our sequential solver based on the simplified transport equations in terms of memory consumption and computational time a first implementation of a lagrangian based domain decomposition method brings to a poor parallel efficiency because of an increase in the power iterations 1 in order to obtain a high parallel efficiency we improve the parallelization scheme by changing the location of the loop over the subdomains in the overall algorithm and by benefiting from the characteristics of the raviart thomas finite element the new parallel algorithm still allows us to locally adapt the numerical scheme mesh finite element order however it can be significantly optimized for the matching grid case the good behavior of the new parallelization scheme is demonstrated for the matching grid case on several hundreds of nodes for computations based on a pin by pin discretization

practical output regulation for bounded linear infinite dimensional state space systems we develop the mathematical foundations of practical state space output regulation for bounded infinite dimensional linear systems by practical output regulation we mean asymptotic tracking of references and rejection of disturbances with a given accuracy our main results are general upper bounds for the norms perturbations to the parameters of the exosystem the plant and a controller which achieves exact output regulation these bounds depend explicitly on the desired tracking accuracy e 0 in this paper all perturbations are assumed to be bounded additive and linear our results apply for both feedforward and error feedback controllers and for arbitrary bounded uniformly continuous reference disturbance signals

first order transitions in spherical models finite size scaling finite size behavior near the first order phase boundary of ferromagnetic spherical models is investigated for block and cylinder shaped systems ind dimensions the bulk thermodynamic singularities are rounded and asymptotically for large size obey appropriate scaling laws both short range interactions and long range couplings decaying like 1 rd with 0 are analyzed the short range results agree precisely with a recently developed scaling theory foro n symmetric systems in the limitn more generally the scaling functions are universal depending only on explicit aspects of the shape and interactions enter only in the spin wave or goldstone mode contributions which appear technically as corrections to scaling an appendix analyzes the truncation error in the approximation by many fold sums of multivariate integrals with integrands diverging like jaj j2 as 0

non matching mesh gluing by meshless interpolation an alternative to lagrange multipliers rewards of using non matching meshes are great in many aspects sub meshing a complex structure in a sub structure wise manner separately and or in parallel selective local refinement unlimited scalability guarantee for generating meshes in increasingly large scale finite element simulation etc however when meshes do not match a gluing algorithm is required to enforce inter domain continuity non matching terminologically originates from mesh discretization in nature and the non matching mesh issue is therefore avoidable or does not exist in a node based or meshless discretization in meshless methods motivated by this a gluing algorithm is developed based on meshless interpolation the gluing is accomplished by continuous trial and test functions across non matching meshes constructed using nodes only the developed gluing algorithm is tested in static and wave propagation problems in two and three dimensions it is demonstrated that the gluing algorithm does not deteriorate convergence and accuracy compared with the one piece conforming mesh compared with lagrange multiplier gluing one of the most common approaches the current algorithm has two significant benefits 1 easier implementation in any dimension and 2 positive definite banded system matrices not acting against equation solvers and hence better suited for large scale finite element analysis

interface element method iem for a partitioned system with non matching interfaces abstract a novel method for non matching interfaces on the boundaries of finite elements in partitioned domains is presented by introducing interface elements in this paper the interface element method iem satisfies the continuity conditions exactly through interface element domains without recourse to lagrange multiplier technique the interface elements take an interpolation scheme used in meshless methods to join partitioned domains the moving least square mls approximations in the present study are implemented to construct the shape functions of the interface elements the compatibility of displacements on the boundaries of the finite elements and the interface elements is always preserved in this method and the completeness of the shape functions of the interface elements transfers rigid body motions and strain fields correctly moreover alignment of the boundaries of sub domains in the mls approximations and integration domains provides a consistent numerical integration the numerical examples show that the iem is a useful tool for the analysis of a partitioned system and for a global local analysis

error estimates for the combinedh andp versions of the finite element method in theh version of the finite element method convergence is achieved by refining the mesh while keeping the degree of the elements fixed on the other hand thep version keeps the mesh fixed and increases the degree of the elements in this paper we prove estimates showing the simultaneous dependence of the order of approximation on both the element degrees and the mesh in addition it is shown that a proper design of the mesh and distribution of element degrees lead to a better than polynomial rate of convergence with respect to the number of degrees of freedom even in the presence of corner singularities numerical results comparing theh version p version and combinedh p version for a one dimensional problem are presented

a computational multilevel approach for solving 2d navier stokes equations over non matching grids a multilevel approach with parallel implementation is developed for obtaining fast solutions of the navier stokes equations solved on domains with non matching grids the method relies on computing solutions over different subdomains with different multigrid levels by using multiple processors a local vanka type relaxation operator for the multigrid solution of the navier stokes system allows solutions to be computed at the element level the natural implementation on a multiprocessor architecture results in a straightforward and flexible algorithm numerical computations are presented using benchmark applications in order to support the method parallelization is discussed to achieve proper accuracy load balancing and computational efficiency between different processors 2005 elsevier b v all rights reserved

output regulation of periodic signals for dps an infinite dimensional signal generator in this note we consider output regulation and disturbance rejection of periodic signals via state feedback in the setting of exponentially stabilizable linear infinite dimensional systems we show that if an infinite dimensional exogenous system is generating periodic reference signals solvability of the state feedback regulation problem is equivalent to solvability of the so called equations this result allows us to consider asymptotic tracking of periodic reference signals which only have absolutely summable fourier coefficients while in related existing work the reference signals are confined to be infinitely smooth we also discuss solution of the regulator equations and construct the actual feedback law to achieve output regulation in the single input single output siso case the output regulation problem is solvable if the transfer function of the stabilized plant does not have zeros at the frequencies i spl omega sub n of the periodic reference signals and if the sequence cr i spl omega sub n a bk b sup 1 spl times q spl phi sub n cr i spl omega sub n a bk p spl phi sub n sub n spl isin z spl isin l sup n2 a one dimensional heat equation is used as an illustrative example

what periodic signals can an exponentially stabilizable linear feedforward control system asymptotically track we study asymptotic tracking and rejection of continuous periodic signals in the context of exponentially stabilizable linear infinite dimensional systems our reference signals are in sobolev type spaces h omega n f n and they as well as the disturbance signals are generated by an infinite dimensional exogenous system we show that there exists a feedforward controller which achieves output regulation if and only if the so called regulator equations are satisfied and a decomposability condition holds for siso systems this result allows us to completely answer the question posed in the title we show that if the stabilized plant does not have transmission zeros at the frequencies i omega n of the reference signals then all reference signals in h omega n f n can be asymptotically tracked in the presence of disturbances if and only if bigl h k i omega n 1 1 h d n f n 1 bigr n in i in ell 2 here h k i omega n n in i is the transfer function of the stabilized plant evaluated at i omega n and h d n n in i is a sequence of disturbance coefficients for the stabilized plant moreover the sequence f n n in i consists of weights for the fourier coefficients of the reference signals we give four examples to illustrate the theory

on the realization of periodic functions abstract in this article canonical and spectrally minimal infinite dimensional state space realizations for periodic functions are considered it is shown that the periodic functions having l 1 fourier coefficients are precisely those realizable by a riesz spectral system rss in which the system operator generates a periodic strongly continuous semigroup and the observation operator is bounded this realization can easily be converted to a canonical and spectrally minimal form it is shown how the use of rss and cesaro sums of fourier series allows the construction of a state space realization for a given periodic function merely integrable over its period simple finite dimensional approximations with error bounds are derived for the rss realization regular well posed linear systems wpls are used to construct a fuhrmann type realization for a given periodic function integrable over its period it is shown that the rss realizations and wpls realizations are precisely equally good at coping with the possible ill behavior of a given bounded periodic function integrable over its period but the wpls realization is not always spectrally minimal or canonical

the hp mortar finite element method for the mixed elasticity and stokes problems abstract the motivation of this work is to apply the hp version of the mortar finite element method to the nearly incompressible elasticity model formulated as a mixed displacement pressure problem as well as to stokes equations in primal velocity pressure variables within each subdomain the local approximation is designed using div stable hp mixed finite elements the displacement is computed in a mortared space while the pressure is not subjected to any constraints across the interfaces by a boland nicolaides argument we prove that the discrete saddle point problem satisfies a babuska brezzi inf sup condition the inf sup constant is optimal in the sense that it depends only on the local to the subdomains characteristics of the mixed finite elements and in particular it does not increase with the total number of the subdomains the consequences that we are aware of of such an important result are twofold 1 the numerical analysis of the approximability properties of the hp mortar discretization for the mixed elasticity problem allows us to derive an asymptotic rate of convergence that is optimal up to log p in the displacement this is addressed in the present contribution 2 when the mortar discrete problem is inverted by substructured iterative methods based on krylov subspaces with block preconditioners in view of the results for conforming finite elements 1 the condition number of the solver should grow logarithmically on p h and not depend on the total number of the subdomains

on the streamfunction vorticity formulation in sliding bi period frames application to bulk behavior for polymer blends the lees edwards description of bi periodic boundary conditions has been extended to the streamfunction and streamfunction vorticity formulation in sliding bi periodic frames the required compatibility conditions are formulated and uniqueness of the solution is shown the model has been implemented in a spectral element method context to describe bulk shear behavior far away from walls where no simple periodic boundary conditions can be used in the numerical model a lagrangian multiplier is introduced to couple the shearing boundaries the proposed method has been validated for a mathematical test problem convergence is shown and the influence of the order of approximation of the lagrangian multiplier is studied finally results are presented for drop coalescence across the boundaries of the bi periodic frame

from h to p efficiently implementing finite and spectral hp element methods to achieve optimal performance for low and high order discretisations the spectral hp element method can be considered as bridging the gap between the traditionally low order finite element method on one side and spectral methods on the other side consequently a major challenge which arises in implementing the spectral hp element methods is to design algorithms that perform efficiently for both low and high order spectral hp discretisations as well as discretisations in the intermediate regime in this paper we explain how the judicious use of different implementation strategies can be employed to achieve high efficiency across a wide range of polynomial orders furthermore based upon this efficient implementation we analyse which spectral hp discretisation which specific combination of mesh size h and polynomial order p minimises the computational cost to solve an elliptic problem up to a predefined level of accuracy we investigate this question for a set of both smooth and non smooth problems

a non conforming computational methodology for modeling coupled problems a variety of engineering applications that involve coupling different physical phenomena often require detailed finite element analysis to be carried out over complex domains often such analysis may be accomplished by dividing the global domain into several local subdomains over each of which a local model can be analyzed independently the global solution can then be constructed by suitably piecing together local solutions from these individually modeled subdomains however during the assembly it is often too cumbersome or even infeasible to coordinate the meshes over separate subdomains one must therefore employ non conforming techniques to accomplish such modeling in this paper we develop a non conforming computational methodology via the mortar finite element method to solve a coupled problem where we are interested in determining the effects of temperature variations on a given flow or the transfer of heat within the flow using this method the solution over different subdomains with different multigrid levels is efficiently computed our numerical results clearly suggest that the proposed methodology is robust and stable 2005 elsevier ltd all rights reserved

on the finite size behaviour of systems with asymptotically large critical shift exact results of the finite size behaviour of the susceptibility in three dimensional mean spherical model films under dirichlet dirichlet dirichlet neumann and neumann neumann boundary conditions are presented the corresponding scaling functions are explicitly derived and their asymptotics close to above and below the bulk critical temperature tc are obtained the results can be incorporated in the framework of the finite size scaling theory where the exponent characterizing the shift of the finite size critical temperature with respect to tc is smaller than 1 with being the critical exponent of the bulk correlation length

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

on the concept of point value in the infinite dimensional realization theory in this article we study the effect of the chosen representation of a point value and point evaluation on the class of periodic signals realizable using a certain type of infinite dimensional linear system by suitably representing the point evaluation at the origin in a hilbert space we are able to give a complete characterization of its extensions these extensions involve a new concept called sequence the use of which as an observation operator of an infinite dimensional linear system is studied in this article in particular we consider their use in the realization of periodic signals we also investigate how the use of sequences affects the convergence properties of such realizations we consider the rate and character of convergence and the removal of the gibbs phenomenon as still a further demonstration of the significance of the chosen concept of a point value we discuss the use of distributional point values in the realization of periodic distributions the possible applications of this work lie in regulator problems of infinite dimensional control theory as is indicated by the well known internal model principle

the operator equationax xb c admissibility and asymptotic behavior of differential equations it is shown that there exists a natural relationship between the regular admissibility of a translation invariant subspace m ofbuc r e the space of uniformly continuous bounded functions onrwith values in a banach spacee w r t the differential equationu t au t f t and the unique solvability of a special operator equation of lyapunov s typeax xdm 0 where dmis the restriction of the operator d d dtonto m and 0 f f 0 this leads to some spectral conditions for the regular admissibility applications to questions of exponential dichotomy exponential stability the existence of periodic and almost periodic solutions of equation as well as analogous questions for some nonlinear equations and functional differential equations are presented

direct simulation of particle suspensions in sliding bi periodic frames we present a new finite element scheme for direct simulations of inertialess particle suspensions in simple shear flows of a newtonian fluid the sliding bi periodic domain concept of lees and edwards j phys c 5 1972 1921 has been combined with a standard velocity pressure formulation of a fictitious domain finite element method by introducing sliding bi periodic frame constraints and it has been implemented with mortar element methods force free torque free rigid body motions of particles are described through rigid ring constraints and implemented by lagrangian multipliers only on the particle boundary which allows easy treatment of boundary crossing particles in our formulation the bulk stress is obtained by simple boundary integrals of lagrangian multipliers concentrating on two dimensional circular disk particles we discuss numerical examples of single two and many particle problems in sliding bi periodic frames which can represent an infinite number of such systems because of the bi periodicity the accuracy and convergence have been verified via comparison with a boundary fitted mesh problem for velocities pressures and velocity gradients the present formulation is quite well suited for suspensions of micro nano particles in simple shear flows and can be easily extended to viscoelastic flow problems

function generators the operator equation πs aπ bq and inherited dynamics in inhomogenous cauchy problems abstract this article concerns the interrelation between the existence of a bounded solution to the operator equation s a bq in d s and the asymptotic behaviour of the mild solutions z t of the abstract cauchy problem z t az t bu t t 0 in a banach space z here b and q are bounded whereas a and s generate c 0 semigroups t a t and t s t on z and w w is a banach space respectively banach space valued inputs u t u are generated by linear dynamical systems we define asymptotically inherited dynamics of z t and show that for strongly stable semigroups t a t z t asymptotically inherits the dynamics of the inputs if there exists l w z such that s a bq in d s if t a t and t s t are bounded then z t is bounded and uniformly continuous provided that s a bq in d s for the converse we show that if z t asymptotically inherits the dynamics of the inputs and if t s t is a suitable c 0 group then t a t is strongly stable and there exists l w z such that s a bq in a subspace of d s we also discuss why inputs u t frequently completely determine the asymptotic properties of z t if t a t is exponentially stable as an application we consider almost periodic inputs u t in sobolev spaces h u f n n

the approximation of solutions of elliptic boundary value problems via the p version of the finite element method the approximation theory developed in 11 is used to determine the piecewise polynomial approximability of solutions of elliptic problems on polygonal domains in mathbb r 2 and polyhedra in mathbb r 3 from these estimates convergence orders for the p version of the finite element method applied to such problems are readily obtained the critical issue is the approximation of the singularities which occur at the nonsmooth parts of the domain boundaries it is seen that the estimates of 11 involving the weighted sobolev spaces z l s are well suited for treating such singular functions yielding directly the optimal approximation degree up to an arbitrarily small varepsilon numerical results for two problems from two dimensional linear elasticity are also presented the computations show that the predicted order of convergence is achieved even for low values of p moreover in contrast to the usual h version of the finite element method the point at which the p version enters the asym

on solenoidal high degree polynomial approximations to solutions of the stationary navier stokes equations the cell discretization algorithm a nonconforming extension of the finite element method is used to obtain approximations to the navier stokes equations for viscous steady state incompressible flow an implementation using polynomial bases is described that permits the use of approximations that exactly satisfy the solenoidal requirement a galerkin basis is constructed and starting with the solution of the associated stokes problem newton s method can be used to generate an approximate solution a unique solution exists if the viscosity is sufficiently large here an a posteriori computation is described that tests if uniqueness is likely to hold and gives an error estimate showing closeness of the approximation tests of the algorithm applied to problems in polygonal domains are described where approximations are 10th degree polynomials

stability and convergence of nonconforming hp finite element methods the stability and convergence of nonconforming hp finite element methods in par ticular the mortar finite element method and its variants are established based on a new stability measure for these methods using a generalized eigenvalue analysis estimates for this measure are computed numerically our numerical results demonstrate that these nonconforming methods prove to be good candidates for hp implementation and also behave ss well as conforming finite element methods the discussion here ls primarily in two dimensions but some extensions to three dimensions

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

output regulation for linear distributed parameter systems this work extends the geometric theory of output regulation to linear distributed parameter systems with bounded input and output operator in the case when the reference signal and disturbances are generated by a finite dimensional exogenous system in particular it is shown that the full state feedback and error feedback regulator problems are solvable under the standard assumptions of stabilizability and detectability if and only if a pair of regulator equations is solvable for linear distributed parameter systems this represents an extension of the geometric theory of output regulation developed in francis 1997 and isidori and byrnes 1990 we also provide simple criteria for solvability of the regulator equations based on the eigenvalues of the exosystem and the system transfer function examples are given of periodic tracking set point control and disturbance attenuation for parabolic systems and periodic tracking for a damped hyperbolic system

a nonconforming finite element method for fluid structure interaction problems in this paper we develop a nonconforming finite element methodology using a three field formulation to analyze a fluid structure interaction problem the methodology is used to couple a lagrangian model describing the structure with the arbitrary lagrangian eulerian strategy used to describe the fluid in order to simulate a full unsteady physical phenomenon consistency error estimates are obtained which show that the numerical scheme employed yields a first order approximation for the solution to the fluid structure interaction problem finally we present a discrete energy estimate to demonstrate the stablity of the proposed method 2005 elsevier b v all rights reserved

on the decoupling effects in the spherical model the decoupling effects in the ferromagnetic mean spherical model with a layer geometry of finite thickness l under dirichlet boundary conditions and in the presence of a step like external field are reconsidered the result of abraham and robert that in the bulk limit the magnetization profile near the dirichlet boundary is exactly the same as the one near the central layer of zero magnetization has a possible interpretation within the following decoupling hypothesis dirichlet respectively neumann boundary conditions can be thought of being physically realizable at least in the spherical model by coupling together two identical copies of the system placed in uniform fields of equal magnitude and opposite respectively the same sign we show that this is indeed the case as far as the magnetization profile is considered on the scale of a large bulk correlation length in the high temperature bulk limit close to the critical point the decoupling effects in the magnetization profile are studied also in the critical finite size scaling regime and in the low temperature moderate field regime in general it is found that the decoupling hypothesis breaks down since the mean square length of the spins at the dirichlet neumann boundary is different from the one at the central layers of a system in a step like uniform field

a new dual mortar method for curved interfaces 2d elasticity dual mortar method formulations have shown to be a very effective and efficient way for interfacing e g tying contacting dissimilar meshes on the other hand we have recently found that they can sometimes perform quite poorly when applied to curved surfaces in some solid mechanics applications a new modified two dimensional dual mortar method for piecewise linear finite elements is developed that overcomes this deficiency and is demonstrated on a model problem furthermore mathematical analysis is provided to demonstrate the optimal convergence and stability of the new method copyright 2005 john wiley sons ltd

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

further results on the critical behaviour of the mean spherical model layer and local susceptibilities abstract the critical behaviour of some properties of the ferromagnetic mean spherical model with a film geometry l 2 and the neumann dirichlet boundary conditions is investigated in the presence of three external fields a bulk field a step like field which changes sign at distance lx 0 x 1 from the neumann boundary and a surface field acting on the lth layer the behaviour of the mean spherical constraint is studied at three different temperatures and field regimes high temperature bulk limit critical finite size scaling regime and low temperature moderate field regime exact expressions for the layer and local susceptibilities are derived and studied in the three different regimes

new surface critical exponents in the spherical model the three dimensional mean spherical model with a l layer film geometry under neumann neumann and neumann dirichlet boundary conditions is considered surafce fields and are supposed to act at the surfaces bounding the system in the case of neumann boundary conditions a new surface critical exponent is found it is argued that this exponent corresponds to a special surface bulk phase transition in the model the privman fisher scaling hypothesis for the free energy is verified and the corresponding scaling functions for both the neumann neumann and neumann dirichlet boundary conditions are explicitly derived if the layer field is applied at some distance from the dirichlet boundary a family of critical exponents emerges their values depend on the exponent defining how the distance scales with the finite size of the system and interpolate continuously between the extreme cases and

stable lagrange multipliers for quadrilateral meshes of curved interfaces in 3d for the discretization of coupled problems by means of mortar finite elements the choice of the discrete lagrange multiplier space is of crucial importance for the performance of the resulting numerical scheme dual lagrange multipliers offer several advantages since they can be locally eliminated in this paper the lowest order dual lagrange multipliers are extended to arbitrary quadrilateral or triangular surface grids in a first step two alternatives are provided for the case of planar interfaces for the approximation of vector fields two more modifications are given for use on curvilinear interfaces a priori results are obtained and several numerical examples are shown

new effects in the magnetization profile of the spherical model in a step like field the ferromagnetic mean spherical model with a layer geometry of thickness l and neumann dirichlet boundary conditions is investigated in the presence of a step like external field which changes sign at distance from the neumann boundary the amplitude of the field can be taken to vanish in the thermodynamic limit as an inverse power of l exact expressions for the magnetization profile are derived and studied in three different temperature and field regimes high temperature bulk limit critical finite size scaling regime and low temperature moderate field regime it is found that in the critical finite size scaling regime there exist two special values of x denoted by which depend on the scaled temperature and field variables and have the property that the magnetization changes sign only when the magnetization is everywhere negative when and everywhere positive when in the low temperature moderate field regime we establish that the field induced critical point in the case of periodic boundary conditions and a step like field with appears at

the influence of three external fields on the mean spherical model magnetization profile abstract explicit expressions are derived for the free energy and the magnetization profile of the three dimensional mean spherical model with a layer geometry of finite thickness l under neumann dirichlet boundary conditions in the presence of three external fields a bulk field a step like field and a surface field acting on the l th layer the scaling functions that govern the critical behaviour of the system are derived and with the use of the asymptotic properties of these functions various predictions of the privman fisher scaling hypothesis are verified in the finite size scaling regime

a spectral element methodology tuned to parallel implementations abstract we present in this paper a modification of the conforming spectral element method for the approximation of the poisson equation this new procedure allows the implementation on a parallel machine in an easier and faster way the resulting method is nonconforming but the numerical analysis shows that the error between the exact solution and the discrete solution is of the same asymptotic order as the error of the original conforming method

circular spectrum and bounded solutions of periodic evolution equations abstract we consider the existence and uniqueness of bounded solutions of periodic evolution equations of the form u a t u h t u f t where a t is in general an unbounded operator depending 1 periodically on t h is 1 periodic in t is small and f is a bounded and continuous function that is not necessarily uniformly continuous we propose a new approach to the spectral theory of functions via the concept of circular spectrum and then apply it to study the linear equations u a t u f t with general conditions on f for small we show that the perturbed equation inherits some properties of the linear unperturbed one the main results extend recent results in the direction saying that if the unitary spectrum of the monodromy operator does not intersect the circular spectrum of f then the evolution equation has a unique mild solution with its circular spectrum contained in the circular spectrum of f

solution of wave propagation problems by the cell discretization method abstract the cell discretization algorithm cd is first applied to a fairly complex steady state wave scattering problem and the results compared with the same problem solved by the finite element method the p d e solved is the elliptic helmholtz equation for the components of the complex scattered amplitude the method is then directly applied to some hyperbolic problems in space time using a total discretization instead of semidiscretization the problem then becomes one of solving a discretized elliptic equation in successive time slabs as the process progresses through time the main difficulty is in choosing the right combination of collocation moments peculiar to the cd method intracell polynomials and the cfl ratio i e the ratio of the cell length in the time direction to its length s in the space direction s apart from this serious difficulty there is little problem in solving several problems involving first and second order wave equations in one and two space dimensions and one solution of a second order wave equation in two space dimensions copious figures are supplied showing surface plots of the solutions and plots of the spectrum in the complex plane of the propagation matrix associated with the problem are supplied

on the use of lagrange multipliers in domain decomposition for solving elliptic problems the primal hybrid method for solving second order elliptic equa tions is extended from finite element approximations to general bases varia tional techniques are used to show convergence of approximations to the so lution of the homogeneous dirichlet problem for selfadjoint equations error estimates are obtained and examples are given

a segment to segment mortar contact method for quadratic elements and large deformations abstract this paper describes a new extension of mortar based segment to segment algorithms for large deformation contact analysis permitting their use when quadratic interpolations are used in the underlying finite element method the work builds upon results previously described by puso and laursen m a puso t a laursen a mortar segment to segment contact method for large deformation solid mechanics comput methods appl mech engrg 193 2004 601 629 m a puso t a laursen a mortar segment to segment frictional contact method for large deformations comput methods appl mech engrg 193 2004 601 629 where methods were developed for quasistatic and implicit dynamic analysis in the context of linear element interpolations here we see that many algorithmic ideas from the linear case can be adopted for use with quadratic elements along with different alternative interpolations of the mortar contact multipliers the result is a class of methods appropriate for use for either mesh tying true large sliding simulation frictionless or frictional and readily admits mixing of element types several numerical examples are given to demonstrate the effectiveness of the approach

hp submeshing via non conforming finite element methods abstract non conformity in the hp version can involve incompatibility in both the degrees and the meshes between adjoining subdomains in this paper we show how the mortar finite element method m0 and two new variants m1 m2 can be used to join together such incompatible hp sub discretizations our results show optimality of the resulting non conforming method for various h p and hp discretizations including the case of exponential hp convergence over geometric meshes we also present numerical results for the lagrange multiplier when the method is implemented via a mixed method three dimensional considerations suggest that our methods m1 m2 are easier to generalize to arbitrary meshes than m0

surface critical exponents for a three dimensional modified spherical model a modified three dimensional mean spherical model with a l layer film geometry under neumann neumann boundary conditions is considered two spherical fields are present in the model a surface one fixes the mean square value of the spins at the boundaries at some 0 and a bulk one imposes the standard spherical constraint the mean square value of the spins in the bulk equals one the surface susceptibility 1 1 has been evaluated exactly for 1 we find that 1 1 is finite at the bulk critical temperature tc in contrast with the recently derived value 1 1 1 in the case of just one global spherical constraint the result 1 1 1 is recovered only if c 2 12kc 1 where kc is the dimensionless critical coupling when c 1 1 diverges exponentially as t t c an effective hamiltonian which leads to an exactly solvable model with 1 1 2 the value for the n limit of the corresponding o n model is proposed too

asymptotically almost periodic solutions of evolution equations in banach spaces abstract tile linear abstract evolution equation u t au t t t r is considered where a d a e e is the generator of a strongly continuous semigroup of operators in the banach space e starting from analogs of kadets and loomis theorems for vector valued almost periodic functions we show that if a i r is countable and r e is asymptotically almost periodic then every bounded and uniformly continuous solution u to is asymptotically almost periodic provided e tu t has uniformly convergent means for all a i r related results on eberlein weakly asymptotically almost periodic periodic asymptotically periodic and c0 solutions of as well as on the discrete case of solutions of difference equations are included

on using the cell discretization algorithm for mixed boundary value problems and domain decomposition the cell discretization algorithm is used to approximate solutions to self adjoint elliptic equations with general nonhomogeneous dirichlet or neumann or mixed boundary values error estimates are obtained showing general convergence this provides the framework for a nonoverlapping iterative algorithm for domain decomposition the domain of a dirichlet problem is partitioned into two subdomains solutions on the two subdomains can be patched together to form a solution to the original problem provided the solutions agree across the common interface of the subdomains and the normal derivatives there have equal absolute values and are opposite in sign we generate such a solution by alternating between imposing neumann and dirichlet conditions on the interface with boundary data adapted from the results of the previous approximation a posteriori error estimates show that we have global convergence provided computed interface errors are sufficiently small

stability and stabilizability of infinite dimensional systems in this paper we are concerned with stability problems for infinite dimensional systems first we review the theory for linear systems where the dynamics are governed by strongly continuous semigro

the h p and h p versions of the finite element method in 1 dimension this paper is the first one in the series of three which are addressing in detail the properties of the three basic versions of the finite element method in the one dimensional setting the main emphasis is placed on the analysis when the exact solution has singularity of x type the first part analyzes thep version the second theh version and generalh p version and the final third part addresses the problems of the adaptiveh p version

finite size effects in fluid interfaces abstract finite size effects in interfacial tensions of fluid interfaces are studied at the level of the gaussian model of capillary waves it had been suggested that such effects might play a significant role in surface tension measurements based on capillary rise between plates spaced a small distance d apart the finite size correction varying as 1 d a reconsideration of the thermodynamics of finite size effects followed by careful calculations for the gaussian model leads to a finite size correction varying as 1 d 2 with a universal coefficient the effect is too small to be noticeable in current experiments the calculations have been carried out for rectangular interfaces of arbitrary dimensionality and general shapes subject to many types of boundary conditions they also have implications for finite size effects in interfacial free energies in two and three dimensional ising models which are discussed in connection with recent exact and monte carlo calculations

finite size effects in the spherical model of finite thickness a detailed analysis of the finite size effects on the bulk critical behaviour of the d dimensional mean spherical model confined to a film geometry with finite thickness l is reported along the finite direction different kinds of boundary conditions are applied periodic p antiperiodic a and free surfaces with dirichlet d neumann n and a combination of neumann and dirichlet nd on both surfaces a systematic method for the evaluation of the finite size corrections to the free energy for the different types of boundary conditions is proposed the free energy density and the equation for the spherical field are computed for arbitrary d it is found for 2 d 4 that the singular part of the free energy has the required finite size scaling form at the bulk critical temperature only for p and a for the remaining boundary conditions the standard finite size scaling hypothesis is not valid at d 3 the critical amplitude of the singular part of the free energy related to the so called casimir amplitude is estimated we obtain p 2 3 5 0 153 051 a 0 274 543 and nd 0 019 22 implying a fluctuation induced attraction between the surfaces for p and repulsion in the other two cases for d and n we find a logarithmic dependence on l

error estimates using the cell discretization method for some parabolic problems the cell discretization algorithm is used to approximate solutions to parabolic problems with coefficients independent of time error estimates are obtained showing general convergence for homogeneous problems a polynomial implementation of the algorithm is described that can be viewed as a nonconforming extension of the finite element method that can also produce the continuous approximations of an h p finite element method numerical tests that confirm the theoretical estimates are discussed

on approximating the solution of the non stationary stokes equations using the cell discretization algorithm the cell discretization algorithm a nonconforming extension of the finite element method is used to obtain approximations to the velocity and pressure satisfying the nonstationary stokes equations error estimates show convergence of the approximations an implementation using polynomial bases is described that permits the use of the continuous approximations of the h p finite element method and exactly satisfies the solenoidal requirement we express the error estimates in terms of the diameter h of a cell and the degree p of the approximation on each cell results of an experiment with p 10 are presented that confirm the theoretical estimates

out of equilibrium properties of the semi infinite kinetic spherical model we study the ageing properties of the semi infinite kinetic spherical model at the critical point and in the ordered low temperature phase for both dirichlet and neumann boundary conditions the surface fluctuation dissipation ratio and the scaling functions of two time surface correlation and response functions are determined explicitly in the dynamical scaling regime in the low temperature phase our results show that for the case of dirichlet boundary conditions the value of the non equilibrium surface exponent b1 differs from the usual bulk value of systems undergoing phase ordering

finite size effects in film geometry with nonperiodic boundary conditions gaussian model and renormalization group theory at fixed dimension finite size effects are investigated in the gaussian model with isotropic and anisotropic short range interactions in film geometry with nonperiodic boundary conditions bc above at and below the bulk critical temperature tc we have obtained exact results for the free energy and the casimir force for antiperiodic neumann dirichlet and neumann dirichlet mixed bc in 1 d 4 dimensions for the casimir force finite size scaling is found to be valid for all bc for the free energy finite size scaling is valid in 1 d 3 and 3 d 4 dimensions for antiperiodic neumann and dirichlet bc but logarithmic deviations from finite size scaling exist in d 3 dimensions for neumann and dirichlet bc this is explained in terms of the borderline dimension d 3 where the critical exponent 1 d 3 2 of the gaussian surface energy density vanishes for neumann dirichlet bc finite size scaling is strongly violated above tc for 1 d 4 because of a cancelation of the leading scaling terms for antiperiodic dirichlet and neumann dirichlet bc a finite film critical temperature tc film l tc exists at finite film thickness l our results include an exact description of the dimensional crossover between the d dimensional finite size critical behavior near bulk tc and the d 1 dimensional critical behavior near tc film l this dimensional crossover is illustrated for the critical behavior of the specific heat particular attention is paid to an appropriate representation of the free energy in the region tc film l t tc for 2 d 4 the gaussian results are renormalized and reformulated as one loop contributions of the 4 field theory at fixed dimension d and are then compared with the e 4 d expansion results at e 1 as well as with d 3 monte carlo data for d 2 the gaussian results for the casimir force scaling function are compared with those for the ising model with periodic antiperiodic and free bc unexpected exact relations are found between the gaussian and ising scaling functions for both the d dimensional gaussian model and the two dimensional ising model it is shown that anisotropic couplings imply nonuniversal scaling functions of the casimir force that depend explicitly on microscopic couplings our gaussian results provide the basis for the investigation of finite size effects of the mean spherical model in film geometry with nonperiodic bc above at and below the bulk critical temperature

on the convergence rate of the cell discretization algorithm for solving elliptic problems error estimates for the cell discretization algorithm are obtained for polynomial bases used to approximate both h k and analytic solutions to selfadjoint elliptic problems the polynomial implementation of this algorithm can be viewed as a nonconforming version of the h p finite element method that also can produce the continuous approximations of the h p method the examples provided by our experiments provide discontinuous approximations that have errors similar to the finite element results

a non conforming finite element method for sub meshing in engineering applications there is a constant need for solving problems using finite elements over large and complicated domains such analysis is often accomplished by decomposing the global domain into several sub domains and performing the analysis individually on each local sub domain the global analysis can then be realized by piecing together the information that is available from each sub domain non conforming finite elements are particularly useful in this regard in this paper we discuss such a technique for a model problem we derive necessary and sufficient conditions in order for the mixed method formulation of such a non conforming method to have a unique solution error estimates for the finite element solution are obtained finally we present computational experiments to demonstrate that this non conforming technique is a good candidate for finite element implementation

volumetric coupling approaches for multiphysics simulations on non matching meshes summary in finite element analysis of volume coupled multiphysics different meshes for the involved physical fields are often highly desirable in terms of solution accuracy and computational costs we present a general methodology for volumetric coupling of different meshes within a monolithic solution scheme a straightforward collocation approach is compared to a mortar based method for nodal information transfer for the latter dual shape functions based on the biorthogonality concept are used to build the projection matrices thus further reducing the evaluation costs we give a detailed explanation of the integration scheme and the construction of dual shape functions for general first order and second order langrangian finite elements within the mortar method as well as an analysis of the conservation properties of the projection operators moreover possible incompatibilities due to different geometric approximations of curved boundaries are discussed numerical examples demonstrate the flexibility of the presented mortar approach for arbitrary finite element combinations in two and three dimensions and its applicability to different multiphysics coupling scenarios copyright 2016 john wiley sons ltd

the p and h p versions of the finite element method basic principles and properties in the classical form of the finite element method called the hversion piecewise polynomials of fixed degree p are used and the mesh size h is decreased for accuracy in this paper we discuss the fundamental theoretical ideas behind the relatively recent p version and h p version in the p version a fixed mesh is used and p is allowed to increase the h p version combines both approaches the authors describe and explain the basic properties and characteristics of these newer versions especially in areas where their behavior is significantly different from that of the h version simplified proofs of key concepts are included and computational illustrations of several results are provided a benchmark comparison between the various versions in included

uniform hp convergence results for the mortar finite element method the mortar finite element is an example of a non conforming method which can be used to decompose and re compose a domain into sub domains without requiring compatibility between the meshes on the separate components we obtain stability and convergence results for this method that are uniform in terms of both the degree and the mesh used without assuming quasiuniformity for the meshes our results establish that the method is optimal when non quasiuniform h or hp methods are used such methods are essential in practice for good rates of convergence when the interface passes through a corner of the domain we also give an error estimate for when the p version is used numerical results for hp and hp mortar fems show that these methods behave as well as conforming fems an hp extension theorem is also proved

the p version of the finite element method in the p version of the finite element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increased until some desired level of precision is reached in this paper we first establish the basic approximation properties of some spaces of piecewise polynomials defined on a finite element triangulation these properties lead to an a priori estimate of the asymptotic rate of convergence of the p version the estimate shows that the p version gives results which are not worse than those obtained by the conventional finite element method called the h version in which h represents the maximum diameter of the elements when quasi uniform triangulations are employed and the basis for comparison is the number of degrees of freedom furthermore in the case of a singularity problem we show under conditions which are usually satisfied in practice that the rate of convergence of the p version is twice that of the h version with quasi uniform mesh inve

almost periodic solutions of first and second order cauchy problems abstract almost periodicity of solutions of first and second order cauchy problems on the real line is proved under the assumption that the imaginary resp real spectrum of the underlying operator is countable related results have been obtained by ruess v and basit our proof uses a new idea it is based on a factorisation method which also gives a short proof of the vector valued version of loomis classical theorem saying that a bounded uniformly continuous function from r into a banach spacexwith countable spectrum is almost periodic ifc0 x our method can also be used for solutions on the half line this is done in a separate paper

a simple robust controller for the approximate regulation of almost periodic signals for linear systems by using a delay line as a signal generator we design a simple robust controller for the approximate regulation i e approximate asymptotic tracking and rejection of almost periodic signals for linear systems as opposed to the related existing results our controller design does not require online parameter tuning besides the usual assumptions about stabilizability detectability and nonexistence of transmission zeros for the plant the controller design algorithm of this paper only requires knowledge of the desired tracking accuracy based on this information alone we can only design a robust controller achieving in the presence of unknown trigonometric polynomial disturbances and additive perturbations to the plant and the controller here is the output of the plant and is an arbitrary almost periodic reference signal taken from an infinite dimensional generalized sobolev space of almost periodic functions in this paper we also study robust output regulation in the limiting case where it turns out that due to the general loss of exponential closed loop stability asymptotic tracking rejection can also be lost as unless the exogenous signals are smooth enough this last result extends some recent theorems on nonrobust open loop output regulation for infinite dimensional exosystems the results of this paper are new and potentially useful for finite dimensional plants but the main results are also true for infinite dimensional systems with bounded control and observation operators

the influence of external boundary conditions on the spherical model of a ferromagnet i magnetization profiles the spherical model of a ferromagnet is investigated for various external boundary conditions it is shown that besides the well known critical point a second one can be produced by the boundary conditions although the main asymptotic of the free energy is analytic at the new critical point theo n1 2 d asymptotic possesses a singularity here a natural order parameter of the model has singularities at both critical points the magnetization profile is studied for the whole range of the model s parameters and at different scales it is shown that in an appropriate regime below the second critical temperature the magnetization profile freezes that is becomes temperature independent distributions of the single spin variables and some macroscopic observables including normalized total spin are studied for the whole temperature range including the critical points

error estimates using the cell discretization method for steady state convection diffusion equations the cell discretization algorithm is applied to generate approximate solutions for some second order non self adjoint elliptic equations general convergence for homogeneous problems is shown by obtaining suitable error estimates the method is applied using polynomial bases this provides a nonconforming extension of the finite element method that can also produce the continuous approximations of an h p finite element method numerical tests on convection diffusion problems are made that confirm the theoretical estimates and methods for dealing with boundary layer problems are illustrated