postprocessing the galerkin method the finite element case a postprocessing technique developed earlier for spectral methods is extended here to galerkin finite element methods for dissipative evolution partial differential equations the postprocessing amounts to solving a linear elliptic problem on a finer grid or higher order space once the time integration on the coarser mesh is completed this technique increases the convergence rate of the finite element method to which it is applied and this is done at almost no additional computational cost the numerical experiments presented here show that the resulting postprocessed method is computationally more efficient than the method to which it is applied say quadratic finite elements as well as standard methods of similar order of convergence as the postprocessed one say cubic finite elements the error analysis of the new method is performed in l2 and in l infty norms

degree complexity of birational maps related to matrix inversion for a q q matrix x x i j we let j x x i j 1 be the hadamard inverse which takes the reciprocal of the elements of x we let i x x i j 1 denote the matrix inverse and we define k i circ j to be the birational map obtained from the composition of these two involutions we consider the iterates k n k circ cdots circ k and determine the degree complexity of k which is the exponential rate of degree growth delta k lim n to infty left deg k n right 1 n of the degrees of the iterates earlier studies of this map were restricted to cyclic matrices in which case k may be represented by a simpler map here we show that for general matrices the value of k is equal to the value conjectured by angles d auriac maillard and viallet

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

two level method based on finite element and crank nicolson extrapolation for the time dependent navier stokes equations a fully discrete two level finite element method the two level method is presented for solving the two dimensional time dependent navier stokes problem the method requires a crank nicolson extrapolation solution u h tau 0 p h tau 0 on a spatial time coarse grid j h tau 0 and a backward euler solution u h tau p h tau on a space time fine grid j h tau the error estimates of optimal order of the discrete solution for the two level method are derived compared with the standard crank nicolson extrapolation method the one level method based on a space time fine grid j h tau the two level method is of the error estimates of the same order as the one level method in the h1 norm for velocity and the l2 norm for pressure however the two level method involves much less work than the one level method

a two grid finite difference scheme for nonlinear parabolic equations we present a two level finite difference scheme for the approximation of nonlinear parabolic equations discrete inner products and the lowest order raviart thomas approximating space are used in the expanded mixed method in order to develop the finite difference scheme analysis of the scheme is given assuming an implicit time discretization in this two level scheme the full nonlinear problem is solved on a coarse grid of size h the nonlinearities are expanded about the coarse grid solution and an appropriate interpolation operator is used to provide values of the coarse grid solution on the fine grid in terms of superconvergent node points the resulting linear but nonsymmetric system is solved on a fine grid of size h some a priori error estimates are derived which show that the discrete l infty l2 and l2 h1 errors are o h 2 h 4 d 2 delta t where d geq 1 is the spatial dimension

dynamics of bimeromorphic maps of surfaces we classify bimeromorphic self maps f x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of compact kahler surfaces x in terms of their actions f h 1 1 x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i on cohomology we observe that the growth rate of f n is invariant under bimeromorphic conjugacy and that by conjugating one can always arrange that f n f n we show that the sequence f n can be bounded grow linearly grow quadratically or grow exponentially in the first three cases we show that after conjugating f is an automorphism virtually isotopic to the identity f preserves a rational fibration or f preserves an elliptic fibration respectively in the last case we show that there is a unique up to scaling expanding eigenvector for f that is nef and that f is bimeromorphically conjugate to an automorphism if and only if 2 0 we go on in this case to construct a dynamically natural positive current representing and we study the growth rate of periodic orbits of f we conclude by illustrating our results with a particular family of examples

degree complexity of birational maps related to matrix inversion symmetric case for q 3 we let mathcal s q denote the projectivization of the set of symmetric q q matrices with coefficients in mathbb c we let i x x i j 1 denote the matrix inverse and we let j x x i j 1 be the matrix whose entries are the reciprocals of the entries of x we let k mathcal s q i circ j mathcal s q rightarrow mathcal s q denote the restriction of the composition i j to mathcal s q this is a birational map whose properties have attracted some attention in statistical mechanics in this paper we compute the degree complexity of k mathcal s q thus confirming a conjecture of angles d auriac et al j phys a math gen 39 3641 3654 2006

iterative two grid methods for semilinear elliptic equations abstract we design and analyze a new finite element discretization technique based on iterative two grid methods for semilinear elliptic partial differential equations pdes we first present an iterative two grid method that just applies the classical two grid for semilinear elliptic pdes in a successive fashion namely to solve a semilinear problem on the coarse space and then to solve a symmetric positive definite problem on the fine space thus we only need to deal with semilinear problems in the coarse space in the first algorithm secondly we replace the semilinear term by using the corresponding first order taylor expansion in the second iterative two grid we provide the error estimates for the second iterative algorithm and present numerical experiments to show the efficiency of our methods

stabilized finite element method based on the crank nicolson extrapolation scheme for the time dependent navier stokes equations this paper provides an error analysis for the crank nicolson extrapolation scheme of time discretization applied to the spatially discrete stabilized finite element approximation of the two dimensional time dependent navier stokes problem where the finite element space pair x h m h for the approximation u n h p n h of the velocity u and the pressure p is constructed by the low order finite element the q 1 p 0 quadrilateral element or the p 1 p 0 triangle element with mesh size h error estimates of the numerical solution u n h p n h to the exact solution u t n p t n with t n 0 t are derived

nonlinear galerkin methods the finite elements case with the increase in the computing power and the advent of supercomputers the approximation of evolution equations on large intervals of time is emerging as a new type of numerical problem in this article we consider the approximation of evolution equations on large intervals of time when the space discretization is accomplished by finite elements the algorithm that we propose called the nonlinear galerkin method stems from the theory of dynamical systems and amounts to some approximation of the attractor in the discrete finite elements space essential here is the utilization of incremental unknown which is accomplished in finite elements by using hierarchical bases beside a detailed description of the algorithm the article includes some technical results on finite elements spaces and a full study of the stability and convergence of the method

finite element approximation for the viscoelastic fluid motion problem in this article the variational formulation of the two dimensional viscoelastic fluid motion problem and its finite element approximation are considered an local error estimate for the velocity with h1 norm and the pressure with l2 norm is obtained and a uniform error estimate for the velocity and pressure with the above norms is provided if the given data satisfies the uniqueness condition

error estimates for spatially discrete approximations of semilinear parabolic equations with initial data of low regularity etude des methodes d elements finis semi discretes appliquees aux equations paraboliques semi lineaires en r d avec d 3 certains resultats concernant le taux de convergence sont ameliores

on the complexity of some birational transformations using three different approaches we analyse the complexity of various birational maps constructed from simple operations inversions on square matrices of arbitrary size the first approach comprises the study of the images of lines and relies mainly on univariate polynomial algebra the second approach is a singularity analysis and the third method is more numerical using integer arithmetics these three methods have their own domain of application but they give corroborating results and lead us to a conjecture on the algebraic entropy of a class of maps constructed from matrix inversions

stability of galerkin and inertial algorithms with variable time step size this paper provides galerkin and inertial algorithms for solving a class of nonlinear evolution equations spatial discretization can be performed by either spectral or finite element methods time discretization is done by euler explicit or euler semi implicit difference schemes with variable time step size moreover the boundedness and stability of these algorithms are studied by comparison we find that the boundedness and stability of inertial algorithm are superior to the ones of galerkin algorithm in the case of explicit scheme and the boundedness and stability of two algorithms are same in the case of semi implicit scheme

two grid nonconforming finite element method for second order elliptic problems in this paper we present and analyze two grid p1 nonconforming finite element method for second order elliptic problems the two grid method involves solving one small origin problem on coarse grid with grid size h and some correction problems on local fined grids with grid size h if h o h2 is chosen we show that the convergence rate of this two grid method is optimal in broken h1 norm numerical results conforming the theory are also provided

a classification of four state spin edge potts models we classify four state spin models with interactions along the edges according to their behaviour under a specific group of symmetry transformations this analysis uses the measure of complexity of the action of the symmetries in the spirit of the study of discrete dynamical systems on the space of parameters of the models and aims at uncovering solvable ones we find that the action of these symmetries has low complexity polynomial growth zero entropy we obtain natural parametrizations of various models among which an unexpected elliptic parametrization of the four state chiral potts model which we use to localize possible integrability conditions associated with high genus curves

a two grid method of the non conforming crouzeix raviart element for the steklov eigenvalue problem abstract this paper discusses a high efficient scheme for the steklov eigenvalue problem a two grid discretization scheme of nonconforming crouzeix raviart element is established with this scheme the solution of a steklov eigenvalue problem on a fine grid h is reduced to the solution of the eigenvalue problem on a much coarser grid h and the solution of a linear algebraic system on the fine grid h by using spectral approximation theory and nitsche lascaux lesaint technique in space h 1 2 we prove that the resulting solution obtained by our scheme can maintain an asymptotically optimal accuracy by taking h h and the numerical experiments indicate that when the eigenvalues k h of nonconforming crouzeix raviart element approximate the exact eigenvalues from below the approximate eigenvalues k h obtained by the two grid discretization scheme also approximate the exact ones from below and the accuracy of k h is higher than that of k h

error estimates on a new nonlinear galerkin method based on two grid finite elements a new nonlinear galerkin method based on finite element discretization is presented in this paper for semilinear parabolic equations the new scheme is based on two different finite element spaces defined respectively on one coarse grid with grid size h and one fine grid with grid size h ll h nonlinearity and time dependence are both treated on the coarse space and only a fixed stationary equation needs to be solved on the fine space at each time with linear finite element discretizations it is proved that the difference between the new nonlinear galerkin solution and the standard galerkin solution in h 1 omega norm is of the order of h 3

a two grid discretization scheme for eigenvalue problems a two grid discretization scheme is proposed for solving eigenvalue problems including both partial differential equations and integral equations with this new scheme the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid and the resulting solution still maintains an asymptotically optimal accuracy

error estimates for spatially discrete approximations of semilinear parabolic equations with nonsmooth initial data on considere les approximations spatialement discretes continues par rapport au temps des problemes mixtes par la methode des elements finis de galerkin pour les equations paraboliques semi lineaires avec des donnees initiales irregulieres ou incompatibles on etablit des estimations d erreur

local and parallel algorithms for fourth order problems discretized by the morley wang xu element method this paper systematically studies numerical solution of fourth order problems in any dimensions by use of the morley wang xu mwx element discretization combined with two grid methods xu and zhou math comp 69 881 909 1999 since the coarse and fine finite element spaces are nonnested two intergrid transfer operators are first constructed in any dimensions technically based on which two classes of local and parallel algorithms are then devised for solving such problems following some ideas in xu and zhou math comp 69 881 909 1999 the intrinsic derivation of error analysis for nonconforming finite element methods of fourth order problems huang et al appl numer math 37 519 533 2001 huang et al sci china ser a 49 109 120 2006 and the error estimates for the intergrid transfer operators we prove that the discrete energy errors of the two classes of methods are of the sizes o h h 2 and o h h 2 h h d 1 2 respectively here h and h denote respectively the mesh sizes of the coarse and fine finite element triangulations and d indicates the space dimension of the solution region numerical results are performed to support the theory obtained and to compare the numerical performance of several local and parallel algorithms using different intergrid transfer operators

a monte carlo investigation of the sampling behavior of conditional moment tests in tobit and probit models this paper provides a monte carlo examination of conditional moment tests for several forms of misspecification in tobit and probit models the experimental design is based on actual data taken from a study of labor supply our results indicate that the tests work well in terms of size and power for the tobit model whereas they perform poorly for the probit model the major conclusion is that although there is little to choose between the various forms of the tests the degree of censoring of the latent dependent variable is crucial

factorization properties of birational mappings abstract we analyse birational mappings generated by transformations on q q matrices which correspond respectively to two kinds of transformations the matrix inversion and a permutation of the entries of the q q matrix remarkable factorization properties emerge for quite general involutive permutations it is shown that factorization properties do exist even for birational transformations associated with noninvolutive permutations of entries of q q matrices and even for more general transformation which are rational transformations but no longer birational the existence of factorization relations independent of q the size of the matrices is underlined the relations between the polynomial growth of the complexity of the iterations the existence of recursions in a single variable and the integrability of the mappings are sketched for the permutations yielding these properties all these results show that permutations of the entries of the matrix yielding factorization properties are not so rare in contrast the occurrence of recursions in a single variable or of the polynomial growth of the complexity are of course less frequent but not completely exceptional

non parametric maximum likelihood estimation of censored regression models abstract this paper presents a consistent estimator of a censored linear regression model which does not require knowledge of the distribution of the error term the estimator considered here applies duncan s 1982 suggestion that the likelihood function for the censored regression model be treated as a functional of both the unknown regression vector and the unknown error distribution our estimator is the majorizing regression vector for this non parametric likelihood functional we find conditions which ensure the consistency of the npmle the paper concludes with the results of monte carlo experiments which show the npmle to be more efficient than powell s least absolute deviations lad estimator particularly when the fraction of censored observations is large and the sample size is small

birational mappings and matrix subalgebra from the chiral potts model we study birational transformations of the projective space originating from lattice statistical mechanics specifically from various chiral potts models associating these models with stable patterns and signed patterns we give general results which allow us to find all chiral q state spin edge potts models when the number of states q is a prime or the square of a prime as well as several q dependent family of models we also prove the absence of monocolor stable signed pattern with more than four states this demonstrates a conjecture about cyclic hadamard matrices in a particular case the birational transformations associated with these lattice spin edge models show complexity reduction in particular we recover a one parameter family of integrable transformations for which we give a matrix representation when the parameter has a suitable value

two level penalty finite element methods for the stationary incompressible magnetohydrodynamics problem in the paper we consider the penalty finite element method for the stationary incompressible magnetohydrodynamics mhd problem with a factor of penalty parameter stability and convergence of numerical solutions are established furthermore two level penalty methods are also developed for the mhd problem our methods consist of solving a nonlinear mhd problem by the usual penalty method on a coarse mesh with mesh size h and then a linearized mhd problem based on the stokes newton and oseen iterations on a fine mesh is solved by the penalty method with mesh size h h h respectively stability and error estimates of numerical solutions in two level penalty methods are presented finally some numerical tests are provided to demonstrate the effectiveness of the developed algorithms

local and parallel finite element algorithms based on two grid discretizations a number of new local and parallel discretization and adaptive nite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems these algorithms are motivated by the observation that for a solution to some elliptic problems low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a ne grid by some local and parallel procedure the theoretical tools for analyzing these methods are some local a priori and a posteriori estimates that are also obtained in this paper for nite element solutions on general shape regular grids some numerical experiments are also presented to support the theory in this paper we will propose some new parallel techniques for nite element computation these techniques are based on our understanding of the local and global properties of a nite element solution to some elliptic problems simply speaking the global behavior of a solution is mostly governed by low frequency components while the local behavior is mostly governed by high frequency compo nents the main idea of our new algorithms is to use a coarse grid to approximate the low frequencies and then to use a ne grid to correct the resulted residue which contains mostly high frequencies by some local parallel procedures let us now give a somewhat more detailed but informal and hopefully infor mative description of the main ideas and results in this paper we consider the following very simple model problem posed on a convex polygonal domain r 2 u bru f in

bounded influence estimators for the tobit model abstract this paper introduces a class of bounded influence estimators for the gaussian censored regression or tobit model these estimators can be interpreted as weighted ml estimators with weights chosen to attain the best trade off between efficiency and robustness an empirical example illustrates the feasibility and usefulness of these estimators as well as their performance vis a vis the tobit ml clad and scls estimators

long time behavior of the two grid finite element method for fully discrete semilinear evolution equations with positive memory abstract based on two grid discretizations two fully discrete finite element algorithms for semilinear parabolic integro differential equations with positive memory are proposed with the backward euler scheme for the temporal discretization the basic idea of the space two grid finite element algorithms is to approximate the semilinear equations on a coarse space grid and to solve the linearized equations on a finer space grid at each time step to further decreases the amount of computational work a space time two grid algorithm based on a coarse space grid with large time stepsize t and a finer space grid with small time stepsize t for the evolutional equations is proposed in this paper the sharp long time stability and error estimates for the standard finite element method the space two grid finite element method and the space time two grid finite element method are derived it is showed that the two grid algorithms long time stability and error estimates are similar to those of the direct resolution of the semilinear problem on a fine grid

nonlinear galerkin methods this article presents a new method of integrating evolution differential equations the non linear galerkin method that is well adapted to the long term integration of such equations while the usual galerkin method can be interpreted as a projection of the considered equation on a linear space the methods considered here are related to the projection of the equation on a nonlinear manifold from the practical point of view some terms have been identified as small and sometimes but not always disregarded

the relationship among the specification tests of hausman ramsey and chow abstract this article describes a relationship between the tests for specification error in regression models introduced by ramsey 1969 and hausman 1978 it also shows that the chow 1960 test for structural shift can be viewed as a special case of specification error tests this article shows the common structure of these tests the common basis is the comparison of alternative estimators of regression coefficients under the null hypothesis one estimator is efficient and consistent and the other is consistent the probability limits of the two estimators are different under the alternative hypothesis