on the p and hp extension of nedelec s curl conforming elements abstract we establish interpolation error estimates for the hp extension of nedelec s curl and divergence conforming three dimensional finite elements using these interpolation estimates we investigate the use of higher order edge finite elements for the linear three dimensional magnetostatic problem our estimates show that the standard mixed method for the magnetostatic problem can be approximated to optimal order in both h and p

on the stabilization of a flexible beam with a tip mass we study the stability of a flexible beam that is clamped at one end and free at the other a mass is also attached to the free end of the beam to stabilize this system we apply a boundary control force at the free end of the beam we prove that the closed loop system is well posed and is exponentially stable we then analyze the spectrum of the system for a special case and prove that the spectrum determines the exponential decay rate for the considered case

fully automatic hp adaptivity for maxwell s equations i report on the development of a fully automatic hp adaptive strategy for the solution of time harmonic maxwell equations the strategy produces a sequence of grids that deliver exponential convergence for both regular and singular solutions given a coarse mesh we refine it first globally in both h and p and solve the problem on the resulting fine mesh we consider then the projection based interpolants of the fine mesh solution with respect to both current and next to be determined coarse grid and introduce the interpolation error decrease rate equal to the difference of the old and new coarse mesh interpolation errors vs number of degrees of freedom added the optimal hp refinements leading to the next coarse grid are then determined by maximizing the interpolation error decrease rate

solving homogeneous linear equations over gf 2 via block wiedemann algorithm we propose a method of solving large sparse systems of homogeneous linear equations over g f 2 the field with two elements we modify an algorithm due to wiedemann a block version of the algorithm allows us to perform 32 matrix vector operations for the cost of one the resulting algorithm is competitive with structured gaussian elimination in terms of time and has much lower space requirements it may be useful in the last stage of integer factorization we address here the problem of solving a large sparse system of homogeneous linear equations over gf 2 the field with two elements one important application which motivates the present work arises in integer factorization during the last stage of most integer factorization algorithms we are presented with a large sparse integer matrix and are asked to find linear combinations of the columns of this matrix which vanish modulo 2 for example 7 the matrix may have 100 000 columns with an average of 15 nonzero entries per column for this application we would like to obtain several solutions because a given solution will lead to a nontrivial factorization with probability 112 with n independent solutions our probability of finding a factorization rises to 1 2 structured gaussian elimination can be used 7 but as problems get larger it may become infeasible to store the matrices obtained in the intermediate stages of gaussian elimination the wiedemann algorithm 9 71 has smaller storage requirements one need only store a few vectors and an encoding of a sparse matrix not a dense matrix as occurs in gaussian elimination after fillin and it may have fewer computational steps since one takes advantage of the sparseness of the matrix but its efficiency is hampered by the fact that the algorithm acts on only one bit at a time in the present paper we work with blocks of vectors at a single time by treating 32 vectors at a time on a machine with 32 bit words we can perform 32 matrix vector products at once thus considerably decreasing the cost of indexing this can be viewed as a block wiedemann algorithm the main technical difficulty is in obtaining the correct generalization of the berlekamp massey algorithm to a block version namely a multidimensional version of the extended euclidean algorithm received by the editor november 20 1991 and in revised form july 24 1992 1991 mathematics subject classijication primary 15a33 11y05 11 04 15 04 1994 amencan mathernat cal soc ety 0025 571 8 94 1 oo 25 per page

on the wave equation with hyperbolic dynamical boundary conditions interior and boundary damping and supercritical sources abstract the aim of this paper is to study the problem u t t u p x u t f x u in 0 u 0 on 0 0 u t t u u q x u t g x u on 0 1 u 0 x u 0 x u t 0 x u 1 x in where is a bounded open subset of r n with c 1 boundary n 2 1 is relatively open on denotes the laplace beltrami operator on is the outward normal to and the terms p and q represent nonlinear damping terms while f and g are nonlinear perturbations in the paper we establish local and global existence uniqueness and hadamard well posedness results when source terms can be supercritical or super supercritical

uniform stabilization of a hybrid system of elasticity the problem of boundary feedback stabilization of a euler bernoulli beam with an endmass is considered using a method of compact perturbation the lack of uniform stabilization is proved in the case of a clamped beam with the usual boundary feedbacks applied to the end with the mass next the uniform stabilization when the usual boundary feedbacks are applied to the end without the mass is proved also the uniform decay of energy by means of higher order feedbacks applied to the end with the mass is established

on the exponential decay of the euler bernoulli beam with boundary energy dissipation abstract we study the asymptotic behavior of the euler bernoulli beam which is clamped at one end and free at the other end we apply a boundary control with memory at the free end of the beam and prove that the exponential decay of the memory kernel is a necessary and sufficient condition for the exponential decay of the energy

toward hp adaptive solution of 3d electromagnetic scattering from cavities an effective hp adaptive finite element fe approach is presented for a reliable and accurate solution of 3d electromagnetic scattering problems the far field is approximated with the infinite element method this allows one to reduce the external domain discretised with finite elements to a minimum preserving the possibility of arbitrary reduction of the error as the method does not introduce modelling error the work is focused on scattering from cavity backed apertures recessed in a ground plane near optimal discretisations that can effectively resolve local rapid variations in the scattered field can be obtained adaptively by local mesh refinements so called h type refinements blended with graded polynomial enrichments p enrichments the discretisation error can be controlled by a self adaptive process which is driven by a posteriori error estimates in terms of the energy norm or in a quantity of interest the radar cross section rcs is an example of the latter h and p adaptively constructed solutions are compared to pure uniform p approximations numerical highly accurate and fairly converged solutions for generic cavities are given and compared to previously published results

efficient preconditioning for the p version finite element method in two dimensions parallel preconditioners are formulated and analyzed for systems of equations arising from the p version finite element method applied to second order self adjoint elliptic boundary value problems in two dimensions by using new theoretical results for polynomial spaces it is proved that the condition number of the preconditioned system grows as log 2 p where p is the degree of the polynomial space numerical results are presented showing that the condition number indeed grows very slowly with p

the space complexity analysis in the general number field sieve integer factorization the general number sieve is the most efficient algorithm for integer factorization it consists of polynomial selection sieving solving equations and finding square roots root lifting of polynomial is discussed in this paper the p adic evaluation provided by each root and the expected p value are also given then we gain the space complexity of sieving and building equations over the ring z 2 z

an hp error analysis of mitc plate elements we give an hp error analysis of several rectangular families of finite elements for the reissner mindlin plate bending equations we consider both the original mitc families k j bathe f brezzi and m fortin internat j numer methods engrg 28 1989 pp 1787 1801 and some new ones introduced in this paper for the deflection and rotation we give error estimates which are optimal with respect to the mesh size h and optimal up to ordo p varepsilon varepsilon 0 arbitrary with respect to the polynomial degree p we also obtain estimates for the error in the shear force calculated via two different methods our analysis utilizes some recent results of ours for the mixed method for the stokes problem as well as hp interpolation estimates for mixed methods for second order elliptic equations in this regard we derive new hp results in this paper for the brezzi douglas fortin marini spaces and improve upon previous estimates for the brezzi douglas marini spaces

compensator design for stability enhancement with collocated controllers a continuum model rather than a finite element model is used the optimal compensator design is formulated as a stochastic regulator problem and is shown to be solvable by the general infinite dimensional theory developed by the author despite the lack of exponential stabilizability infinite dimensional steady state riccati equations characterizing the feedback control gain and the kalman filter gain operators can be solved explicitly the associated performance indexes including the mean square control effort are calculated in closed form as a first approximation the compensator transfer function can be realized as a bank of bandpass filters in parallel centered at the undamped mode frequencies numerical calculations for the gain and bandwidths for a typical configuration are presented the performance of the compensator is evaluated when in fact in the true model there is no actuator noise the theoretical problem involved is to show that the infinite dimensional stochastic process is asymptotically stationary it is possible to calculate the steady state covariance in closed form and thereby calculate performance indexes of interest explicitly facilitating the choice of optimal design parameters

goal oriented adaptivity using unconventional error representations for the multidimensional helmholtz equation in goal oriented adaptivity goa the error in the quantity of interest qoi is represented using the error functions of the direct and adjoint problems this error representation is subsequently bounded above by element wise error indicators that are used to drive optimal refinements in this work we propose to replace in the error representation the adjoint problem by an alternative operator the main advantage of the proposed approach is that when judiciously selecting such alternative operator the corresponding upper bound of the error representation becomes sharper leading to a more efficient goa while the method can be applied to a variety of problems we focus here on two and threedimensional 2d and 3d helmholtz problems we show via extensive numerical experimentation that the upper bounds provided by the alternative error representations are sharper than the classical ones and lead to a more robust p adaptive process we also provide guidelines for finding operators delivering sharp error representation upper bounds we further extend the results to a convectiondominated diffusion problem as well as to problems with discontinuous material coefficients finally we consider a sonic logging while drilling lwd problem to illustrate the applicability of the proposed method

solving sparse linear equations over finite fields a coordinate recurrence method for solving sparse systems of linear equations over finite fields is described the algorithms discussed all require o n 1 omega n 1 log k n 1 field operations where n 1 is the maximum dimension of the coefficient matrix omega is approximately the number of field operations required to apply the matrix to a test vector and the value of k depends on the algorithm a probabilistic algorithm is shown to exist for finding the determinant of a square matrix also probabilistic algorithms are shown to exist for finding the minimum polynomial and rank with some arbitrarily small possibility of error

de rham diagram for hp finite element spaces abstract we prove that the hp finite elements for h curl spaces introduced in 1 fit into a general de rham diagram involving hp approximations the corresponding interpolation operators generalize the notion of hp interpolation introduced in 2 and are different from the classical operators of nedelec and raviart thomas

singularities of electromagnetic fields in polyhedral domains in this paper we investigate the singular solutions of time harmonic maxwell equations in a domain which has edges and polyhedral corners it is now well known that in the presence of non convex edges the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the laplace operator 4 5 we show how this type of result can be derived from the classical mellin analysis and how this analysis leads to sharper results concerning the singular parts which belong to h 1 for the singular functions we exhibit simple and explicit formulas based on generalized dirichlet and neumann singularities for the laplace operator these formulas are more explicit than the results announced in our note 10

the optimal convergence rate of the p version of the finite element method optimal error estimates for the p version of the finite element method in two dimensions are proven for the case when u in h k omega or u has singularities induced by the corners of the domain the case of nonhomogenous essential boundary conditions is also analyzed

on polynomial selection for the general number field sieve the general number field sieve gnfs is the asymptotically fastest algorithm for factoring large integers its runtime depends on a good choice of a polynomial pair in this article we present an improvement of the polynomial selection method of montgomery and murphy which has been used in recent gnfs records

local bounded cochain projections we construct projections from h k the space of differential k forms on which belong to l2 and whose exterior derivative also belongs to l2 to finite dimensional subspaces of h k consisting of piecewise polynomial differential forms defined on a simplicial mesh of thus their definition requires less smoothness than assumed for the definition of the canonical interpolants based on the degrees of freedom moreover these projections have the properties that they commute with the exterior derivative and are bounded in the h k norm independent of the mesh size h unlike some other recent work in this direction the projections are also locally defined in the sense that they are defined by local operators on overlapping macroelements in the spirit of the clement interpolant a double complex structure is introduced as a key tool to carry out the construction

integration of hp adaptivity and a two grid solver for elliptic problems we present implementation details and analyze convergence of a two grid solver forming the core of the fully automatic hp adaptive strategy for elliptic problems the solver delivers a solution for a fine grid obtained from an arbitrary coarse hp grid by a global hp refinement the classical v cycle algorithm combines an overlapping block jacobi smoother with optimal relaxation and a direct solve on the coarse grid a simple theoretical analysis is illustrated with extensive numerical experimentation

hp vector finite element method for eigenmode analysis of waveguides a new stable variational formulation for full wave analysis of waveguides is presented numerical experiments show that the method remains stable at very low frequencies theoretical results apply to a wide class of vector finite elements including two families of nedelec numer math 35 1980 315 numer math 50 1986 57 and their generalization hp edge elements comput methods appl mech engrg 152 1998 103 comput methods appl mech engrg 169 1999 331

maxwell eigenvalues and discrete compactness in two dimensions abstract we present an elementary proof of the discrete compactness result for a general class of hp finite elements introduced in 1 2 we discuss h convergence of 2d elements only and in this context the results are not new as the analysis of h curl conforming elements for maxwell s equations can be reduced to the long known results for raviart thomas elements 3 the work is based on the result of kikuchi 4 5 for nedelec s edge triangular elements of the lowest order and presents an alternative to techniques presented in 3 6 in particular the present version does not use an inverse inequality argument and therefore is valid for h adaptive meshes we conclude the presentation with a number of 2d computational experiments including nonconvex domains

toward a universal h p adaptive finite element strategy part 2 a posteriori error estimation abstract in this second paper of the series on h p adaptive finite element methods we present five different techniques for a posteriori error estimation of h p methods for linear elliptic boundary value problems the techniques are referred to as the residual estimation method the duality method the subdomain residual method a method based on interpolation theory and a post processing method the present study examines the theory and behavior of such techniques applied specifically to h p adaptive finite element methods several numerical examples illustrate the efficiency of the methods

fully automatic hp adaptivity in three dimensions the paper presents a three dimensional implementation of the fully automatic hp adaptive mesh refinement strategy proposed in l demkowicz w rachowicz ph devloo a fully automatic hp adaptivity j sci comput 17 1 3 2002 127 155 the methodology is based on a minimization of the projection based interpolation error with a fixed number of degrees of freedom a coarse grid is first uniformly refined in both h and p to yield a corresponding fine grid a two grid solver is used to solve the problem on the fine grid or iterate towards the fine grid solution the fine grid solution possibly partially converged serves then as a reference solution to be interpolated on the original coarse mesh and the next optimal coarse grid to be determined the difference between the coarse and fine grid solutions provides an excellent error estimate for the coarse grid error the procedure is repeated with the coarse and fine meshes generated during the adaptive process simultaneously until a prescribed error tolerance for the coarse grid error is met the solution obtained on the last fine grid is considered to be the final product delivered by the adaptive procedure

kirchhoff systems with dynamic boundary conditions abstract we are interested in the study of the global non existence of solutions of hyperbolic nonlinear problems governed by the p kirchhoff operator under dynamic boundary conditions when p p n with p n 2 the systems involve nonlinear external forces and may be affected by a perturbation of the type u p 2 u several models already treated in the literature are covered in special subcases and concrete examples are provided for the source term f and the external nonlinear boundary damping q

a two dimensional self adaptive hp finite element method for the characterization of waveguide discontinuities part i energy norm based automatic hp adaptivity abstract the accurate analysis and characterization of waveguide discontinuities is an important issue in microwave engineering in some cases the discontinuities are an unavoidable result of mechanical or electric transitions which effects have to be minimized in other cases the discontinuities are deliberately introduced into the waveguide to perform a certain electric function this is the first of two papers analyzing different types of rectangular waveguide discontinuities by using a fully automatic hp adaptive finite element method in this paper a fully automatic energy norm based hp adaptive finite element fe strategy applied to a number of relevant waveguide structures is presented the methodology produces exponential convergence rates in terms of the energy norm error of the solution against the problem size number of degrees of freedom extensive numerical results demonstrate the suitability of the hp method for solving different rectangular waveguide discontinuities these results illustrate the flexibility reliability and high accuracy of the method the self adaptive hp fem provides similar sometimes more accurate results than those obtained with semi analytical techniques such as the mode matching method for problems where semi analytical methods can be applied at the same time the hp fem provides the flexibility of modeling more complex waveguide structures and including the effects of dielectrics metallic screws round corners etc which cannot be easily considered when using semi analytical techniques in the second part the work is extended by presenting a fully automatic goal oriented hp adaptive fe in terms of the scattering or s parameters which are widely used in microwave engineering for the characterization of microwave devices

stabilization of beams by pointwise feedback control a flexible structure consisting of serially connected euler bernoulli beams with co located sensors and actuators is considered controls are point forces and point bending moments applied at the nodes it is known that uniform exponential stability can be achieved with linear velocity feedback a sensitivity analysis of the system s spectrum with respect to feedback coefficients is set up it is also proved that in a particular case exponential decay rate can be obtained from the spectrum of the system

a three dimensional self adaptive hp finite element method for the characterization of waveguide discontinuities abstract we propose the use of a highly accurate three dimensional 3d fully automatic hp adaptive finite element method fem for the characterization of rectangular waveguide discontinuities these discontinuities are either the unavoidable result of mechanical electrical transitions or deliberately introduced in order to perform certain electrical functions in modern communication systems the proposed numerical method combines the geometrical flexibility of finite elements with an accuracy that is often superior to that provided by semi analytical methods it supports anisotropic refinements on irregular meshes with hanging nodes and isoparametric elements it makes use of hexahedral elements compatible with high order h curl discretizations the 3d hp adaptive fem is applied for the first time to solve a wide range of 3d waveguide discontinuity problems of microwave communication systems in which exponential convergence of the error is observed

polynomial extension operators part ii consider the tangential trace of a vector polynomial on the surface of a tetrahedron we construct an extension operator that extends such a trace function into a polynomial on the tetrahedron this operator can be continuously extended to the trace space of h mathbf curl furthermore it satisfies a commutativity property with an extension operator we constructed in part i of this series such extensions are a fundamental ingredient of high order finite element analysis

the concept of a minimal state in viscoelasticity new free energies and applications to pdes we show here the impact on the initial boundary value problem and on the evolution of viscoelastic systems of the use of a new definition of state based on the stress response see e g 48 16 41 comparisons are made between this new approach and the traditional one which is based on the identification of histories and states we shall refer to a stress response definition of state as the minimal state 29 materials with memory and with relaxation are discussed the energetics of linear viscoelastic materials is revisited and new free energies expressed in terms of the minimal state descriptor are derived together with the related dissipations furthermore both the minimum and the maximum free energy are recast in terms of the minimal state variable and the current strain the initial boundary value problem governing the motion of a linear viscoelastic body is re stated in terms of the minimal state and the velocity field through the principle of virtual power the advantages are i the elimination of the need to know the past strain history at each point of the body and ii the fact that initial and boundary data can now be prescribed on a broader space than resulting from the classical approach based on histories these advantages are shown to lead to natural results about well posedness and stability of the motion finally we show how the evolution of a linear viscoelastic system can be described through a strongly continuous semigroup of linear contraction operators on an appropriate hilbert space the family of all solutions of the evolutionary system obtained by varying the initial data in such a space is shown to have exponentially decaying energy

quasioptimality of some spectral mixed methods in this paper we construct a sequence of projectors into certain polynomial spaces satisfying a commuting diagram property with norm bounds independent of the polynomial degree using the projectors we obtain quasioptimality of some spectral mixed methods including the raviart thomas method and mixed formulations of maxwell equations we also prove some discrete friedrichs type inequalities involving curl

an hp adaptive finite element method for electromagnetics part 1 data structure and constrained approximation abstract this is the first of papers describing an implementation of the hp adaptive mixed finite element fe method for the solution of steady state maxwell s equations proposed in l demkowicz and l vardapetyan modeling of electromagnetic absoption scattering problems using hp adaptive finite elements computer methods in applied mechanics and engineering 152 1998 103 124 the discretization is defined on a hybrid grid consisting of both triangles and quads and allows for both h and p refinements of the mesh the paper focuses on the data structure and constrained approximation issues and provides a number of illustrative examples

stabilization of vibrating beam with a tip mass controlled by combined feedback forces abstract a flexible structure consisting of a euler bernoulli beam with a tip mass is considered to stabilize this system we use a boundary control laws uxxx 1 t mutt 1 t ut 1 t uxxxt 1 t and uxx 1 t uxt 1 t a sensitivity asymptotic analysis of the system s eigenvalues and eigenfunctions is set up we prove that all of the generalized eigenfunctions of 2 9 form a riesz basis of h by a new method we prove that the operator a generates a c0 contraction semigroup t t t 0 furthermore t t t 0 is uniformly exponentially stable and the optimal exponential decay rate can be obtained from the spectrum of the system

asymptotic stability of the euler bernoulli beam with boundary control abstract we show that under appropriate conditions a euler bernoulli beam clamped at one end with boundary controls at the other end can be made uniformly exponentially stable the method can also be applied to multibeam structures with controls either at the end or somewhere along the structure

on the c0 semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam in this paper we show that a linear unbounded operator associated with an euler bernoulli beam equation under shear boundary feedback generates a c0 semig roup in the underlyingstate hilbert space this provides an answer to a longtime unsolved problem due to the lack of dissipativity for the operator the main steps are a careful estimation of the green s function and the verification of the riesz basis property for the generalized eigenfunctions as a consequence we show that this semigroup is differentiable and exponentially stable which is in sharp contrast to the properties possessed by most feedback controlled beams based on a passive design principle 2005 elsevier b v all rights reserved

simple boundary cooperative control of two one link flexible arms for grasping this paper considers a grasping task by means of two one link flexible arms to accomplish this task we propose a simple boundary cooperative control based on a dynamic model which consists of partial differential equations pdes and ordinary differential equations odes subject to geometric constraints since the data which is needed for the implementation of the controller can be obtained by a strain gauge and a rotary encoder it is easy to implement it the asymptotic stability of a closed loop system and the exponential stability of the system under some conditions are studied

an improved parallel block lanczos algorithm over gf 2 for integer factorization abstract rsa algorithm is one of the most popular and secure public key cryptographic algorithms and has been widely used in many real life applications the security of the rsa algorithm lies in the difficulty of factoring large integers efficiently and the general number field sieve gnfs algorithm is the most efficient algorithm for factoring integers greater than 110 digits at present in this paper targeted to speed up the factorization process of rsa we discuss the current research about solving large and sparse linear systems over gf 2 which is one of the most time consuming steps of the gnfs algorithm with that we propose an improved parallel block lanczos ibl algorithm to reduce the communication cost of solving large and sparse linear systems over gf 2 more specifically we firstly re implement the parallel block lanczos algorithm from the bsp paradigm to open mpi to further improve the performance we then reorganize and redesign the algorithm to reduce the synchronization and communication costs during the outer product step after this we integrate the improved parallel block lanczos algorithm with the gnfs algorithm finally theoretical and experimental results demonstrate that the ibl algorithm greatly enhances the performance of gnfs compared with previous parallel block lanczos pbl algorithm in terms of both execution time and speedup

guaranteed a posteriori error estimator for mixed finite element methods of elliptic problems abstract in this work we analyze a posteriori error estimator for a general class of mixed finite element methods of elliptic problems which guarantees an upper bound on the vector error thus extending the recent result obtained for the lowest order triangular raviart thomas mixed finite element method in m ainsworth a posteriori error estimation for lowest order raviart thomas mixed finite elements siam j sci comput 30 2007 08 189 204 the error estimator is constructed through a variant of stenberg s postprocessing procedure and the guaranteed upper bound is readily established by making use of the argument similar to the hypercircle method however the proof of the lower bound given in the above reference does not seem to apply to other kinds of mixed elements so we employ a different technique using the discrete friedrichs inequality to establish the lower bound of the error estimator

generalized finite element systems for smooth differential forms and stokes problem we provide both a general framework for discretizing de rham sequences of differential forms of high regularity and some examples of finite element spaces that fit in the framework the general framework is an extension of the previously introduced notion of finite element systems and the examples include conforming mixed finite elements for stokes equation in dimension 2 we detail four low order finite element complexes and one infinite family of highorder finite element complexes in dimension 3 we define one low order complex which may be branched into whitney forms at a chosen index stokes pairs with continuous or discontinuous pressure are provided in arbitrary dimension the finite element spaces all consist of composite polynomials the framework guarantees some nice properties of the spaces in particular the existence of commuting interpolators it also shows that some of the examples are minimal spaces

a priori error analysis of stochastic galerkin mixed approximations of elliptic pdes with random data we construct stochastic galerkin approximations to the solution of a first order system of pdes with random coefficients under the standard finite dimensional noise assumption we transform the variational saddle point problem to a parametric deterministic one approximations are constructed by combining mixed finite elements on the computational domain with m variate tensor product polynomials we study the inf sup stability and well posedness of the continuous and finite dimensional problems the regularity of solutions with respect to the m parameters describing the random coefficients and establish a priori error estimates for stochastic galerkin finite element approximations

finite elements with mesh refinement for wave equations in polygons error estimates for the space semi discrete approximation of solutions of the wave equation in polygons g r 2 are presented based on corner asymptotics of the solution it is shown that for continuous simplicial lagrangian finite elements of polynomial degree p 1 with either suitably graded mesh refinement or with bisection tree mesh refinement towards the corners of g the maximal rate of convergence o n p 2 which is afforded by the lagrangian finite element approximations on quasiuniform meshes for smooth solutions is restored dirichlet neumann and mixed boundary conditions are considered numerical experiments which confirm the theoretical results are presented generalizations to nonhomogeneous coefficients and elasticity and electromagnetics are indicated

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

existence and exponential stability of a damped wave equation with dynamic boundary conditions and a delay term abstract in this paper we consider a multi dimensional wave equation with dynamic boundary conditions related to the kelvin voigt damping and a delay term acting on the boundary if the weight of the delay term in the feedback is less than the weight of the term without delay or if it is greater under an assumption between the damping factor and the difference of the two weights we prove the global existence of the solutions under the same assumptions the exponential stability of the system is proved using an appropriate lyapunov functional more precisely we show that even when the weight of the delay is greater than the weight of the damping in the boundary conditions the strong damping term still provides exponential stability for the system

integration of hp adaptivity and a two grid solver for electromagnetic problems we present implementation details and analyze convergence of a two grid solver forming the core of a fully automatic hp adaptive strategy for electromagnetic problems the solver delivers a solution for a fine grid obtained from an arbitrary coarse hp grid by a global hp refinement the classical v cycle algorithm combines an overlapping block jacobi smoother with optimal relaxation and a direct solve on the coarse grid a theoretical analysis of the two grid solver is illustrated with numerical experiments several electromagnetic applications show the efficiency of combining the fully automatic hp adaptive strategy with the two grid solver

on the stability and convergence of higher order mixed finite element methods for second order elliptic problems we investigate the use of higher order mixed methods for second order elliptic problems by establishing refined stability and convergence estimates which take into account both the mesh size h and polynomial degree p our estimates yield asymptotic convergence rates for the p and h p versions of the finite element method they also describe more accurately than previously proved estimates the increased rate of convergence expected when the h version is used with higher order polynomials

optimal error estimation for bfh rmcurl conforming p interpolation in two dimensions in this paper we prove an optimal error estimate for the bf h rm curl conforming projection based p interpolation operator introduced in l demkowicz and i babuska siam j numer anal 41 2003 pp 1195 1208 this result is proved on the reference element either triangle or square k for regular vector fields in bf h r rm curl k with arbitrary r 0 the formulation of the result in the bf h rm div conforming setting which is relevant for the analysis of high order boundary element approximations for maxwell s equations is provided as well