a new code for electrostatic simulation by numerical integration of the vlasov and ampere equations using maccormack s method abstract we present a new simulation code for electrostatic waves in one dimension which uses the vlasov equation to integrate the distribution function and ampere s equation to integrate the electric field forward in time previous vlasov codes used the vlasov and poisson equations using ampere s equation has two advantages first boundary conditions do not have to be set on the electric field second it forms a logical basis for an electromagnetic code since the time integration of the electric and magnetic fields is treated in a similar way maccormack s method is used to integrate the vlasov equation which was found to be easy to implement and reliable a stability analysis is presented for the maccormack scheme applied to the vlasov equation conditions for stability are more stringent than the simple courant friedrich s lewy cfl conditions for the spatial and velocity grids we provide a simple linear function which when combined with the cfl conditions should ensure stability simulation results for landau damping are in excellent agreement with numerical solutions of the linear dispersion relation for a wide range of wavelengths the code is also able to retain phase memory as demonstrated by the recurrence effect and reproduce the effects of particle trapping the use of ampere s equation enables standing and traveling waves to be produced depending on whether the current is zero or non zero respectively in simulations where the initial current is non zero and maxwell s equations are satisfied initially additional standing waves may be set up which could be important when the coupling of wave fields from a transmitter to a plasma is considered

on the efficient use of the informational content of estimating equations implied probabilities and euclidean empirical likelihood abstract a number of information theoretic alternatives to gmm have recently been proposed in the literature for practical use and general interpretation the main drawback of these alternatives particularly in the case of conditional moment restrictions is that they give up the computational and interpretational simplicity of quadratic optimization the main contribution of this paper is to analyze the informational content of estimating equations within the unified framework of chi square distance improved inference by control variables closed form formulae for implied probabilities and information theoretic interpretations of continuously updated gmm are discussed in the two cases of unconditional and conditional moment restrictions

higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

semi lagrangian schemes for the vlasov equation on an unstructured mesh of phase space a new scheme for solving the vlasov equation using an unstructured mesh for the phase space is proposed the algorithm is based on the semi lagrangian method which exploits the fact that the distribution function is constant along the characteristic curves we use different local interpolation operators to reconstruct the distribution function f some of which need the knowledge of the gradient of f we can use limiter coefficients to maintain the positivity and the l bound of f and optimize these coefficients to ensure the conservation of the l1 norm that is to say the mass by solving a linear programming problem several numerical results are presented in two and three axisymmetric case dimensional phase space the local interpolation technique is well suited for parallel computation

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

solute transport in highly heterogeneous aquifers the paper deals with the transport of nonreactive solute in heterogeneous formations with prescribed statistical properties of the hydraulic log conductivity y ln k available solutions obtained from perturbation methods are limited to first and second order solutions valid only for small values of the log conductivity variance 2y published numerical investigations give comparative results with finite values of 2y but some discrepancies among the results generate doubts about the capability of numerical methods to capture high order effects for media with large variance values when these large 2y values are encountered in natural formations the related nonlinear effects could be significant in the velocity statistics and in the overall dispersion process the nonlinearity consequences are here investigated in two dimensional isotropic porous media by the monte carlo technique coupled with a finite element analysis the analysis includes 2y values from 0 05 to 4 enhancing the relevance of the nonlinear effects in the dispersion tensor solution to dissipate the doubts related to the numerical approach the accuracy of the solutions was defined by checking the influence of the factors which can affect the solution and by giving an estimation of the related errors the numerical results confirm the validity of the first order and second order analyses when 2y 0 the second order solution captures the nonlinear effects in a small range of log conductivity variance close to zero the nonlinear terms neglected in the first order formulation for higher 2y values give 1 late travel time longitudinal dispersion values greater than the linear solution 2 notably non gaussian distribution of the lagrangian velocity and particle displacements and 3 travel times to approach the asymptotic fickian regime longer than those obtained using the linear solution

conservative numerical schemes for the vlasov equation abstract a new scheme for solving the vlasov equation using a phase space grid is proposed the algorithm is based on the conservation of the flux of particles and the distribution function is reconstructed using various techniques that allow control of spurious oscillations or preservation of the positivity several numerical results are presented in two and four dimensional phase space and the scheme is compared with the semilagrangian method this method is almost as accurate as the semilagrangian one and the local reconstruction technique is well suited for parallel computation

accurate calculation of specific discharge in heterogeneous porous media existing continuous schemes for computing the specific discharge in heterogeneous porous media result in inaccuracy in simulating the local specific discharge field at and in the vicinity of an interface between subdomains of different material properties the domain decomposition method used in multilayered systems and a consistent scheme in a randomly heterogeneous domain are applicable only to some particular cases such as when the material interfaces are parallel to an axis along a material interface the law of refraction of streamlines related to both the tangential and the normal specific discharge components should be satisfied by incorporating these interface conditions into the weak formulation of darcy s law two consistent numerical schemes have been developed these schemes can be applied to accurately and efficiently simulate the specific discharge field in a heterogeneous domain with different values of the ratio of hydraulic conductivities between adjacent elements in particular they provide an easy way for treating aquifers with semipervious layers as a single system numerical simulations have been used to demonstrate the capability and accuracy of the proposed schemes comparison between the specific discharge fields computed by the proposed schemes and by other techniques shows that the new schemes are superior to the traditional ones

simulation of groundwater age distributions the objective of our work is to examine how to simulate the age of groundwater in such a way that it can be compared to actual measurements we start by showing that computation of kinematic age the one obtained by tracking water along streamlines is ill posed in heterogeneous aquifers this together with its inability to account for mixing processes makes it inadequate for comparison with age measurements which are the result of some averaging of the age distribution in the water sample the type of averaging depends on the measurement procedure therefore we go on to write the equations for the cumulative distribution function of residence time under transient flow conditions this allows us to derive transient equations for the mean age as well as for the higher order moments of its distribution which generalize previous results by others these moments can be used for approximating age measurements which need not be equal to the mean age of the water sample using both a synthetic and a real example we show that mean age is an acceptable estimate of radiometric age measurements in many cases including a second order correction variance of residence time distribution always improves results on the other hand higher order approximations converge slowly for old compared to half life waters to the point that third order approximations often worsen the results

an explicit unconditionally stable numerical solution of the advection problem in irrotational flow fields 1 a new methodology for the eulerian numerical solution of the advection problem is proposed the methodology is based on the conservation of both the zero and the first order spatial moments inside each element of the computational domain and leads to the solution of several small systems of ordinary differential equations since the systems are solved sequentially one element after the other the method can be classified as explicit the proposed methodology has the following properties 1 it guarantees local and global mass conservation 2 it is unconditionally stable and 3 it applies second order approximation of the concentration and its fluxes inside each element limitation of the procedure to irrotational flow fields for the 2 d and 3 d cases is discussed the results of three 1 d and 2 d literature tests are compared with those obtained using other techniques a new 2 d test with radially symmetric flow is also carried out

empirical likelihood based inference in conditional moment restriction models this paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions our estimator generalizes the maximum empirical likelihood estimator mele of qin and lawless 1994 using a kernel smoothing method we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood based procedure this yields a one step estimator which avoids estimating optimal instruments our likelihood ratio type statistic for parametric restrictions does not require the estimation of variance and achieves asymptotic pivotalness implicitly the estimation and testing procedures we propose are normalization invariant simulation results suggest that our new estimator works remarkably well in finite samples

a new specification test for the validity of instrumental variables we develop a new specification test for iv estimators adopting a particular second order approximation of bekker the new specification test compares the difference of the forward conventional 2sls estimator of the coefficient of the right hand side endogenous variable with the reverse 2sls estimator of the same unknown parameter when the normalization is changed under the null hypothesis that conventional first order asymptotics provide a reliable guide to inference the two estimates should be very similar our test sees whether the resulting difference in the two estimates satisfies the results of second order asymptotic theory essentially the same idea is applied to develop another new specification test using second order unbiased estimators of the type first proposed by nagar if the forward and reverse nagar type estimators are not significantly different we recommend estimation by liml which we demonstrate is the optimal linear combination of the nagar type estimators to second order we also demonstrate the high degree of similarity for k class estimators between the approach of bekker and the edgeworth expansion approach of rothenberg an empirical example and monte carlo evidence demonstrate the operation of the new specification test

a semianalytical method of path line computation for transient finite difference groundwater flow models this paper presents a new method of semianalytical particle tracking analysis under transient conditions to permit accurate particle tracking in transient flows the particle velocity is interpolated linearly in both space and time coordinates within each finite difference cell and time step by using the total derivative and this interpolation scheme the particle velocity is derived and integrated analytically to obtain the particle s trajectory within each cell and time step errors are much smaller than in numerical integration schemes numerical experiments show that the transient semianalytical solutions are efficient and accurate

arbitrarily high order convected scheme solution of the vlasov poisson system abstract the convected scheme cs is a forward trajectory semi lagrangian method for solution of transport equations which has been most often applied to the kinetic description of plasmas and rarefied neutral gases in its simplest form the cs propagates the solution forward in time by advecting the so called moving cells along their characteristic trajectories and by remapping them on the mesh at the end of the time step the cs is conservative positivity preserving simple to implement and it is not subject to time step restriction to maintain stability recently guclu and hitchon 2012 1 a new methodology was introduced for reducing numerical diffusion based on a modified equation analysis the remapping error was compensated by applying small corrections to the final position of the moving cells prior to remapping while the spatial accuracy was increased from 2nd to 4th order the new scheme retained the important properties of the original method and was shown to be extremely simple and efficient for constant advection problems here the cs is applied to the solution of the vlasov poisson system which describes the evolution of the velocity distribution function of a collection of charged particles subject to reciprocal coulomb interactions the vlasov equation is split into two constant advection equations one in configuration space and one in velocity space and high order time accuracy is achieved by proper composition of the operators the splitting procedure enables us to use the constant advection solver which we extend to arbitrarily high order of accuracy in time and space a new improved procedure is given which makes the calculation of the corrections straightforward focusing on periodic domains we describe a spectrally accurate scheme based on the fast fourier transform the proposed implementation is strictly conservative and positivity preserving the ability to correctly reproduce the system dynamics as well as resolving small scale features in the solution is shown in classical 1d 1v test cases both in the linear and the non linear regimes

unconditionally stable mixed finite element methods for darcy flow unconditionally stable finite element methods for darcy flow are derived by adding least squares residual forms of the governing equations to the classical mixed formulations the proposed methods are free of mesh dependent stabilization parameters and allow the use of the classical continuous lagrangian finite element spaces of any order for the velocity and the potential stability convergence and error estimates are derived and numerical experiments are presented to demonstrate the flexibility of the proposed finite element formulations and to confirm the predicted rates of convergence

continuous groundwater velocity fields and path lines in linear bilinear and trilinear finite elements darcy velocity fields obtained from finite element solutions of heads in groundwater flow exhibit discontinuities at element boundaries thus giving rise to inaccuracies in path line construction several methods have been developed to resolve those inaccuracies including global postprocessing of velocity fields mixed hybrid finite element formulations and stream function formulations all of these techniques either lead to a considerable increase in the computational effort or are not general enough for all purposes the point of view taken here is that standard finite element flow models yield exact water balances which in the usual approach to path line computation are not fully used by starting out from patches with flux conserving boundaries a new postprocessing procedure is derived that allows construction of a continuous flux distribution over the whole model domain in this procedure only the head gradients of adjacent elements are used thus avoiding the solution of another global system of equations furthermore application of a stream function interpolation inside each patch allows the fast computation of path lines without any time stepping the path lines computed with the proposed procedure are compared to path lines computed by usual particle tracking and examples are presented showing that the new method is vastly superior to traditional particle tracking

comment on application of the mixed hybrid finite element approximation in a groundwater flow model luxury or necessity by r mose p siegel p ackerer and g chavent

on finite element methods for heterogeneous elliptic problems dealing with variational formulations of second order elliptic problems with discontinuous coefficients we recall a single field minimization problem of an extended functional presented by bevilacqua et al bevilacqua l feijoo r a rojas l f 1974 a variational principle for the laplace operator with application in the torsion of composite rods international journal of solids structuring 10 1091 1102 which we associate with the basic idea supporting discontinuous galerkin finite element methods we review residual based stabilized mixed methods applied to darcy flow in homogeneous porous media and extend them to heterogeneous media with an interface of discontinuity for smooth interfaces the proposed formulations preserve the continuity of the flux and exactly imposes the constraint between the tangent components of darcy velocity on the interface convergence studies for a heterogeneous and anisotropic porous medium confirm the same rates of convergence predicted for homogeneous problem with smooth solutions

accuracy of mixed and control volume finite element approximations to darcy velocity and related quantities the accuracy of the darcy velocity flux and stream function computed from lowest order triangle based control volume and mixed finite element approximations to the two dimensional pressure equation is considered the control volume finite element method similar to integrated finite difference methods and analogous to the interpolation of galerkin finite element results over control volumes is shown to yield a conservative velocity field and smooth streamlines the streamlines and fluxes through the system computed with the control volume finite element approach are compared to those computed from the mixed finite element method which approximates the pressure and velocity variables separately it is shown that for systems with only moderate degrees of heterogeneity the control volume finite element method is the more computationally efficient alternative i e it provides more accurate flow results for a given number of unknowns for more variable or discontinuous permeability fields by contrast such as sand shale systems the mixed finite element method is shown to approximate flow variables more accurately and more realistically than the control volume method with the same number of unknowns

efficient information theoretic inference for conditional moment restrictions abstract the generalised method of moments estimator may be substantially biased in finite samples especially so when there are large numbers of unconditional moment conditions this paper develops a class of first order equivalent semi parametric efficient estimators and tests for conditional moment restrictions models based on a local or kernel weighted version of the cressie read power divergence family of discrepancies this approach is similar in spirit to the empirical likelihood methods of kitamura et al 2004 empirical likelihood based inference in conditional moment restrictions models econometrica 72 1667 1714 and tripathi and kitamura 2003 testing conditional moment restrictions annals of statistics 31 2059 2095 these efficient local methods avoid the necessity of explicit estimation of the conditional jacobian and variance matrices of the conditional moment restrictions and provide empirical conditional probabilities for the observations

mixed finite elements and newton type linearizations for the solution of richards equation we present the development of a two dimensional mixed hybrid finite element mhfe model for the solution of the non linear equation of variably saturated flow in groundwater on unstructured triangular meshes by this approach the darcy velocity is approximated using lowest order raviart thomas rt0 elements and is exactly mass conserving hybridization is used to overcome the ill conditioning of the mixed system the scheme is globally first order in space nevertheless numerical results employing non uniform meshes show second order accuracy of the pressure head and normal fluxes on specific grid points the non linear systems of algebraic equations resulting from the mhfe discretization are solved using picard or newton iterations realistic sample tests show that the mhfe newton approach achieves fast convergence in many situations in particular when a good initial guess is provided by either the picard scheme or relaxation techniques copyright 1999 john wiley sons ltd

maximization by parts in likelihood inference this article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest the method circumvents the need to compute second order derivatives of the full likelihood function it exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function in this decomposition the first part is a log likelihood from a simply analyzed model and the second part is used to update estimates from the first part convergence properties of this iterative fixed point algorithm are examined and asymptotics are derived for estimators obtained using only a finite number of iterations illustrative examples considered in the article include multivariate gaussian copula models nonnormal random effects models generalized linear mixed models and state space models properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal

flow and travel time statistics in highly heterogeneous porous media 1 in this paper we present flow and travel time ensemble statistics based on a new simulation methodology the adaptive fup monte carlo method afmcm as a benchmark case we considered two dimensional steady flow in a rectangular domain characterized by multi gaussian heterogeneity structure with an isotropic exponential correlation and lnk variance y2 up to 8 advective transport is investigated using the travel time framework where lagrangian variables e g velocity transverse displacement or travel time depend on space rather than on time we find that eulerian and lagrangian velocity distributions diverge for increasing lnk variance due to enhanced channeling transverse displacement is a nonnormal for all y2 and control planes close to the injection area but after xiy 20 was found to be nearly normal even for high y2 travel time distribution deviates from the fickian model for large lnk variance and exhibits increasing skewness and a power law tail for large lnk variance the slope of which decreases for increasing distance from the source no anomalous features are found second moment of advective transport is analyzed with respect to the covariance of two lagrangian velocity variables slowness and slope which are directly related to the travel time and transverse displacement variance which are subsequently related to the longitudinal and transverse dispersion we provide simple estimators for the eulerian velocity variance travel time variance slowness and longitudinal dispersivity as a practical contribution of this analysis both two parameter models considered the advection dispersion equation and the lognormal model provide relatively poor representations of the initial part of the travel time probability density function in highly heterogeneous porous media we identify the need for further theoretical and experimental scrutiny of early arrival times and the need for computing higher order moments for a more accurate characterization of the travel time probability density function a brief discussion is presented on the challenges and extensions for which afmcm is suggested as a suitable approach

probability density functions of hydraulic head and velocity in three dimensional heterogeneous porous media 1 in this study we assess probability density functions of hydraulic heads and specific discharges in three dimensional bounded heterogeneous porous media by monte carlo mc simulation we discuss their empirical shapes and demonstrate that the intuitive use of obvious information on boundedness leads to parametric distribution functions which fit surprisingly well on the basis of statistical moments of hydraulic heads and velocities up to fourth order we discuss the spatial dependence of the empirical distributions and their dependence on the variance of log conductivity comparison of the first and second central moment to the results from classical numerical first order second moment fosm analysis reveals that fosm predicts these moments surprisingly close for hydraulic heads on the basis of this fact we demonstrate that fitting the chosen parametric distributions for hydraulic heads to fosm moments is promising for the sake of estimating exceedance probabilities our mc scenarios vary in variance of log conductivity 0 125 to 5 0 in the type of multivariate dependence in correlation scale and types of boundary conditions our study illustrates that in contrast to the common assumption fosm is a reasonable choice for evaluating multivariate and univariate moments for heads if used in conjunction with additional information on distribution shapes in the absence of utilizable additional information we demonstrate that second moment methods are mostly inadequate for assessing distributions accurately significant deviations from gaussian distributions occurred for discharge components even at a variance of log conductivity as low as 0 125 and we found that the distributions of transverse discharge components are extremely fat tailed the observed non gaussianity questions the results of approximate approaches in solute flux and dispersion studies where velocity fields are assumed to be multi gaussian and then directly represented by or generated from their covariances the main implication is to apply more accurate schemes such as exact non local methods extensive mc or higher order stochastic galerkin approaches and to include higher order moments at least if no additional assumptions on the shape of distributions are available or justifiable

construction of locally conservative fluxes for high order continuous galerkin finite element methods abstract despite their robustness it is known that standard continuous galerkin finite element methods cgfems do not produce a locally conservative flux field as a result their application to solving model problems that are derived from conservation laws can be limited to remedy this issue some form of post processing must be performed on the cgfem solution in this work a simple post processing technique is proposed to obtain a locally conservative flux field from a cgfem solution one distinct advantage of the proposed method is that it produces continuous normal flux at the element s boundary the post processing is implemented on nodal centered control volumes that are constructed from the original finite element mesh the post processing method is performed by solving an independent set of low dimensional problems posed on each element the associated linear algebra systems are of dimension 1 2 k 1 k 2 where k is the polynomial degree of cgfem basis on a triangular mesh a theoretical investigation is conducted to confirm that the post processed solution converges in an optimal fashion to the true solution in the h 1 semi norm various numerical examples that demonstrate the performance of technique are given specifically a simulation of a model for single phase flow in a heterogeneous system is presented to show the necessity of the local conservation as well as the effective performance of the post processing technique

an information theoretic alternative to generalized method of moments estimation while optimally weighted gmm estimation has desirable large sample properties its small sample performance is poor in some applications we propose a computationally simple alternative for weakly dependent data generating mechanisms based on minimization of the kullback leibler information criterion conditions are derived under which the large sample properties of this estimator are similar to gmm i e the estimator will be consistent and asymptotically normal with the same asymptotic covariance matrix as gmm in addition we propose overidentifying and parametric restrictions tests as alternatives to analogous gmm procedures

robust streamline tracing using inter cell fluxes in locally refined and unstructured grids 1 we present a comprehensive study of velocity interpolation methods in polygons these methods are often used as postprocessing procedures for numerical schemes that do not directly calculate the velocity field but only provide cell boundary flux conditions such as the finite volume schemes these methods extend the widely used velocity interpolation algorithms such as the pollock s algorithm to more complex geometries such as perpendicular bisection pebi grids unstructured triangular grids and grids with local refinement once the velocity field is interpolated streamline trajectories and time of flight along the streamlines can be calculated for reservoir simulation model calibration and waterflood management for instance these velocity interpolation methods assume known lower order or higher order cell boundary fluxes which satisfy global mass conservation and normal flux continuity however they differ in the interpolation of velocities within the interior of the cells the interpolating velocity may be locally conservative or nonconservative continuous or discontinuous lower order or higher order results show that the interpolated velocity field has to be locally conservative in order to guarantee the correct volumetric transformation for the calculated streamlines and the time of flight velocity continuity is not as important as local conservation for the purpose of streamline applications compared to higher order interpolation for the streamline trajectories lower order interpolation has the advantage of an analytic solution and an efficient implementation based on our analysis we recommend a lower order locally conservative method for the most robust and numerically efficient calculation of streamline trajectories on unstructured grids

locally conservative stabilized finite element methods for variably saturated flow standard galerkin finite element methods for variably saturated groundwater flow have several deficiencies for instance local oscillations can appear around sharp infiltration fronts without the use of mass lumping and velocity fields obtained from differentiation of pressure fields are discontinuous at element boundaries here we consider conforming finite element discretizations based on a multiscale formulation along with recently developed local postprocessing schemes the resulting approach maintains the basic flexibility and appeal of traditional finite element methods while controlling nonphysical oscillations and producing element wise mass conservative velocity fields accuracy and efficiency of the proposed schemes are evaluated through a series of steady state and transient variably saturated groundwater flow problems in homogeneous as well as heterogeneous domains the schemes are formulated for a generic nonlinear advection diffusion equation and are thus applicable to many other flow models

a particle in cell method for the simulation of plasmas based on an unconditionally stable field solver abstract we propose a new particle in cell pic method for the simulation of plasmas based on a recently developed unconditionally stable solver for the wave equation this method is not subject to a cfl restriction limiting the ratio of the time step size to the spatial step size typical of explicit methods while maintaining computational cost and code complexity comparable to such explicit schemes we describe the implementation in one and two dimensions for both electrostatic and electromagnetic cases and present the results of several standard test problems showing good agreement with theory with time step sizes much larger than allowed by typical cfl restrictions

the stochastic difference between econometric statistics dans un contexte general et dans divers cas particuliers on calcule l ordre en probabilite de la difference entre des racines consistantes d equations d estimation rivales

efficient instrumental variables estimation of nonlinear models this paper considers asymptotically efficient instrumental variables estimation of nonlinear models in an i i d environment the class of models includes nonlinear simultaneous equations models and other models of interest a problem in constructing efficient instrumental variables estimators for such models is that the optimal instruments involve a conditional expectation calculation of which can require functional form assumptions for the conditional distribution of endogenous variables as well as integration nonparametric methods provide a way of avoiding this difficulty here it is shown that nonparametric estimates of the optimal instruments can give asymptotically efficient instrumental variables estimators also ways of choosing the nonparametric estimate in applications are discussed two types of nonparametric estimates of the optimal instruments are considered each involves nonparametric regression one by nearest neighbor and the other by series approximation the finite sample properties of the estimators are considered in a small sampling experiment involving an endogenous dummy variable model

goal oriented a posteriori error estimation for the travel time functional in porous media flows in this article we consider the a posteriori error estimation and adaptive mesh refinement for the numerical approximation of the travel time functional arising in porous media flows the key application of this work is in the safety assessment of radioactive waste facilities in this setting the travel time functional measures the time taken for a nonsorbing radioactive solute transported by groundwater to travel from a potential site deep underground to the biosphere to ensure the computability of the travel time functional we employ a mixed formulation of darcy s law and conservation of mass together with raviart thomas h mathrm div omega conforming finite elements the proposed a posteriori error bound is derived based on a variant of the standard dual weighted residual approximation which takes into account the lack of smoothness of the underlying functional of interest the proposed adaptive refinement strategy is tested on both a simple academic test case and a problem based on the

information theoretic approaches to inference in moment condition models one step efficient gmm estimation has been developed in the recent papers of back and brown 1990 imbens 1993 and qin and lawless 1994 these papers emphasized methods that correspond to using owen s 1988 method of empirical likelihood to reweight the data so that the reweighted sample obeys all the moment restrictions at the parameter estimates in this paper we consider an alternative klic motivated weighting and show how it and similar discrete reweightings define a class of unconstrained optimization problems which includes gmm as a special case such klic motivated reweightings introduce m auxiliary tilting parameters where m is the number of moments parameter and overidentification hypotheses can be recast in terms of these tilting parameters such tests when appropriately conditioned on the estimates of the original parameters are often startlingly more effective than their conventional counterparts this is apparently due to the local ancillarity of the original parameters for the tilting parameters

origins of anomalous transport in heterogeneous media structural and dynamic controls anomalous or non fickian transport is ubiquitous in the context of tracer migration in geological formations we quantitatively identify the origin of anomalous transport in a representative model of a heterogeneous porous medium under uniform in the mean flow conditions we focus on anomalous transport which arises in the complex flow patterns of lognormally distributed hydraulic conductivity k fields with several decades of k values transport in the domains is determined by a particle tracking technique and characterized by breakthrough curves btcs the btc averaged over multiple realizations demonstrates anomalous transport in all cases which is accounted for entirely by a power law distribution t 1 of local transition times the latter is contained in the probability density function t of transition times embedded in the framework of a continuous time random walk ctrw a unique feature of our analysis is the derivation of t as a function of parameters quantifying the heterogeneity of the domain in this context we first establish the dominance of preferential pathways across each domain and characterize the statistics of these pathways by forming a particle visitation weighted histogram hw k of the hydraulic conductivity by converting the ln k dependence of hw k into time we demonstrate the equivalence of hw k and t and delineate the region of hw k that forms the power law of t this thus defines the origin of anomalous transport analysis of the preferential pathways clearly demonstrates the limitations of critical path analysis and percolation theory as a basis for determining the origin of anomalous transport furthermore we derive an expression defining the power law exponent in terms of the hw k parameters the equivalence between hw k and t is a remarkable result particularly given the nature of the k heterogeneity the complexity of the flow field within each realization and the statistics of the particle transitions

robustness infinitesimal neighborhoods and moment restrictions this paper is concerned with robust estimation under moment restrictions a moment restriction model is semiparametric and distribution free therefore it imposes mild assumptions yet it is reasonable to expect that the probability law of observations may have some deviations from the ideal distribution being modeled due to various factors such as measurement errors it is then sensible to seek an estimation procedure that is robust against slight perturbation in the probability measure that generates observations this paper considers local deviations within shrinking topological neighborhoods to develop its large sample theory so that both bias and variance matter asymptotically the main result shows that there exists a computationally convenient estimator that achieves optimal minimax robust properties it is semiparametrically efficient when the model assumption holds and at the same time it enjoys desirable robust properties when it does not

reply to comment on application of the mixed hybrid finite element approximation in a groundwater flow model luxury or necessity by r mose p siegel p ackerer and g chavent

a critical comparison of eulerian grid based vlasov solvers a common problem with direct vlasov solvers is ensuring that the distribution function remains positive a related problem is to guarantee that the numerical scheme does not introduce false oscillations in velocity space in this paper we use a variety of schemes to assess the importance of these issues and to determine an optimal strategy for eulerian split approaches to vlasov solvers from these tests we conclude that maintaining positivity is less important than correctly dissipating the fine scale structure which arises naturally in the solution to many vlasov problems furthermore we show that there are distinct advantages to using high order schemes i e third order rather than second a natural choice which satisfies all of these requirements is the piecewise parabolic method ppm which is applied here to vlasov s equation for the first time

a new class of asymptotically efficient estimators for moment condition models in this paper we propose a new class of asymptotically efficient estimators for moment condition models these estimators share the same higher order bias properties as the generalized empirical likelihood estimators and once bias corrected have the same higher order efficiency properties as the bias corrected generalized empirical likelihood estimators unlike the generalized empirical likelihood estimators our new estimators are much easier to compute a simulation study finds that our estimators have better finite sample performance than the two step gmm and compare well to several potential alternatives in terms of both computational stability and overall performance

hierarchical high order finite element spaces in h div ω h1 ω for a stabilized mixed formulation of darcy problem abstract the classical dual mixed finite element method for flow simulations is based on h div conforming approximation spaces for the flux which guarantees continuous normal components on element interfaces and discontinuous approximations in l 2 for the pressure however stability and convergence can only be obtained for compatible approximation spaces stabilized finite element methods may provide an alternative stable procedure to avoid this kind of delicate balance the main purpose of this paper is to present a high order finite element methodology to solve the darcy problem based on the combination of an unconditionally stable mixed finite element method with a hierarchical methodology for the construction of finite dimensional subspaces of h div and h 1 the chosen stabilized method is free of mesh dependent stabilization parameters and allows for the use of different high order finite element approximations for the flux and the pressure variables without requiring any compatibility constraint as required in mixed methods for these problems convergence studies are presented comparing the numerical solutions obtained for different approximation orders on quadrilateral elements with the ones given by classical mixed formulation with raviart thomas elements

random walk simulation of transport in heterogeneous porous media local mass conservation problem and implementation methods the random walk method for simulating solute transport in porous media is typically based on the assumption that the velocity and velocity dependent dispersion tensor vary smoothly in space however in cases where sharp interfaces separate materials with contrasting hydraulic properties these quantities may be discontinuous normally velocities are interpolated to arbitrary particle locations when finite difference or finite element methods are used to solve the flow equation the use of interpolation schemes that preserve discontinuities in velocity at material contacts can result in a random walk model that does not locally conserve mass unless a correction is applied at these contacts test simulations of random walk particle tracking with and without special treatment of material contacts demonstrate the problem techniques for resolving the problem including interpolation schemes and a reflection principle are reviewed and tested results from simulations of transport in porous media with discontinuities in the dispersion tensor show which methods satisfy continuity simulations of transport in two dimensional heterogeneous porous media demonstrate the potentially significant effect of using a nonconservative model to compute spatial moments and breakthrough of a solute plume

application of the mixed hybrid finite element approximation in a groundwater flow model luxury or necessity selected groundwater flow scenarios are used in a two way comparison between the mixed hybrid finite element method and the standard finite element method also called the conforming finite element method the simulations presented are performed in the bidimensional case with a triangular space discretization because of its practical interest for hydrogeologists the basic idea of the mixed procedure is to approximate both the hydraulic potential and the velocity simultaneously and to satisfy an exact water balance for each element by contrast the conforming finite element method calculates the potential field everywhere and then calculates the velocity by differentiation of the potential the conventional approach results in an elementwise constant velocity which can be subject to significant problems because of the normal component discontinuity of the velocity the mixed hybrid finite element method provides velocities everywhere in the field as well as potentials at the center of each element and each edge moreover the normal component of the velocity field is continuous between adjacent elements the results of the simulations are presented in the form of streamlines to avoid the problem of velocity discontinuity the method of cordes and kinzelbach 1992 is used it allows the construction of a continuous velocity field from potentials obtained by the conforming finite element method the comparison studies show that the mixed hybrid finite element is superior to the conforming method in terms of accuracy it is also superior to the conforming method in terms of computational effort the potential fields obtained by the mixed hybrid and the conforming finite element methods are the same

testing parameters in gmm without assuming that they are identified we propose a generalized method of moments gmm lagrange multiplier statistic i e the k statistic that uses the jacobian at the evaluated parameter value instead of the expected jacobian to obtain its limit behavior we use a novel assumption that brings gmm closer to maximum likelihood and which is easily satisfied the usual asymptotic x2 distribution of the k statistic then holds under a wider set of circumstances like weak and many instrument asymptotics and combinations thereof than the standard full rank case for the jacobian the behavior of the k statistic can be spurious around inflexion points and the maximum of the objective function since the moment conditions are then not satisfied combinations of the k statistic with statistics that test the validity of the moment equations overcome the spurious behavior we conduct a power comparison to test for the risk aversion parameter in a stochastic discount factor model and construct its confidence set for observed consumption growth and asset return series

robust streamline tracing for the simulation of porous media flow on general triangular and quadrilateral grids streamline methods for subsurface flow simulation have received renewed attention as fast alternatives to traditional finite volume or finite element methods key aspects of streamline simulation are the accurate tracing of streamlines and the computation of travel time along individual streamlines in this paper we propose a new streamline tracing framework that enables the extension of streamline methods to unstructured grids composed of triangular or quadrilateral elements and populated with heterogeneous full tensor coefficients the proposed method is based on the mathematical framework of mixed finite element methods which provides approximations of the velocity field that are especially suitable for streamline tracing we identify and implement two classes of velocity spaces the lowest order raviart thomas space low order tracing and the brezzi douglas marini space of order one high order tracing both on triangles and quadrilaterals we discuss the implementation of the streamline tracing method in detail and we investigate the performance of the proposed tracing strategy by means of carefully designed test cases we conclude that for the same computational cost high order tracing is more accurate smaller error in the time of flight and robust less sensitive to grid distortion than low order tracing