a priori and a posteriori analysis of finite volume discretizations of darcy s equations this paper is devoted to the numerical analysis of some finite volume discretizations of darcy s equations we propose two finite volume schemes on unstructured meshes and prove their equivalence with either conforming or nonconforming finite element discrete problems this leads to optimal a priori error estimates in view of mesh adaptivity we exhibit residual type error indicators and prove estimates which allow to compare them with the error in a very accurate way

the value of a kurtosis metric in estimating the hazard to hearing of complex industrial noise exposures a series of gaussian and non gaussian equal energy noise exposures were designed with the objective of establishing the extent to which the kurtosis statistic could be used to grade the severity of noise trauma produced by the exposures here 225 chinchillas distributed in 29 groups with 6 to 8 animals per group were exposed at 97 db spl the equal energy exposures were presented either continuously for 5 d or on an interrupted schedule for 19 d the non gaussian noises all differed in the level of the kurtosis statistic or in the temporal structure of the noise where the latter was defined by different peak interval and duration histograms of the impact noise transients embedded in the noise signal noise induced trauma was estimated from auditory evoked potential hearing thresholds and surface preparation histology that quantified sensory cell loss results indicated that the equal energy hypothesis is a valid unifying principle for estimating the consequences of an exposure if and only if the equivalent energy exposures had the same kurtosis furthermore for the same level of kurtosis the detailed temporal structure of an exposure does not have a strong effect on trauma

on the role of the rank condition in cce estimation of factor augmented panel regressions a popular approach to factor augmented panel regressions is the common correlated effects cce estimator of pesaran 2006 this paper points to a problem with the cce approach that appears in the empirically relevant case when the number of factors is strictly less than the number of observables used in their estimation specifically the use of too many observables causes the second moment matrix of the estimated factors to become asymptotically singular an issue that has not yet been appropriately accounted for the purpose of the present paper is to fill this gap in the literature

noise levels and hearing thresholds in the drop forging industry a weighted equivalent continuous noise levels for hammer and press operations in a drop forging industry were determined using both tape recordings of the noise and personal noise dosimeters the results indicated average a weighted leq values of 108 db for hammer operators and 99 db for press operators comparison of hearing level statistics for 716 hammer and press operators and 293 control subjects indicated the severe hazard to hearing of impact noise exposures for mean exposure times of less than 10 years hearing levels for the press 99 db and hammer 108 db operator age groups are nearly identical and in the latter case are less than those predicted for exposure to equivalent continuous noise for long term exposures of 10 years or more the results of this study indicate that hearing losses resulting from impact noise in the drop forging industry are as great or greater than those resulting from continuous noise

hearing loss from interrupted intermittent and time varying gaussian noise exposures the applicability of the equal energy hypothesis eight groups of chinchillas n 74 were exposed to various equivalent energy 100 or 106 db a sound pressure level spl noise exposure paradigms six groups received an interrupted intermittent time varying iitv gaussian noise exposure that lasted 8 h d 5 d week for 3 weeks the exposures modeled an idealized workweek at each level three different temporal patterns of gaussian iitv noise were used the 100 db a iitv exposure had a db range of 90 108 db spl while the range of the 106 db a iitv exposure was 80 115 db spl two reference groups were exposed to a uniform 100 or 106 db a spl noise 24 h d for 5 days each reference group and the three corresponding iitv groups comprised a set of equivalent energy exposures evoked potentials were used to estimate hearing thresholds and surface preparation histology quantified sensory cell populations all six groups exposed to the iitv noise showed threshold toughening effects of up to 40 db all iitv exposures produced hearing and sensory cell loss that was similar to their respective equivalent energy reference group these results indicate that for gaussian noise the equal energy hypothesis for noise induced hearing loss is an acceptable unifying principle

a stopping criterion for the iterative solution of partial differential equations abstract a stopping criterion for iterative solution methods is presented that accurately estimates the solution error using low computational overhead the proposed criterion uses information from prior solution changes to estimate the error when the solution changes are noisy or stagnating it reverts to a less accurate but more robust low cost singular value estimate to approximate the error given the residual this estimator can also be applied to iterative linear matrix solvers such as krylov subspace or multigrid methods examples of the stopping criterion s ability to accurately estimate the non linear and linear solution error are provided for a number of different test cases in incompressible fluid dynamics

the convergence of the cascadic conjugate gradient method applied to elliptic problems in domains with re entrant corners we study the convergence properties of the cascadic conjugate gradient method ccg method which can be considered as a multilevel method without coarse grid correction nevertheless the ccg method converges with a rate that is independent of the number of unknowns and the number of grid levels we prove this property for two dimensional elliptic second order dirichlet problems in a polygonal domain with an interior angle greater than for plecewise linear finite elements we construct special nested triangulations that satisfy the conditions of a triangulation of type h l in the sense of i babuska r b kellogg and j pitkaranta in this way we can guarantee both the same order of accuracy in the energy norm of the discrete solution and the same convergence rate of the ccg method as in the case of quasiuniform triangulations of a convex polygonal domain

a generalized approach to random noise synthesis theory and computer simulation a generalized approach to the synthesis of gaussian and non gaussian random noises as well as purely impulsive waveforms having a preselected amplitude spectrum has been developed the basic idea behind the synthesis is to construct the amplitude time waveform from the frequency domain i e from the amplitude and phase spectra by maintaining a predetermined reference amplitude spectrum and performing certain specific manipulations of the phase spectrum within any selected band of frequencies and then applying the inverse discrete fourier transform idft peaks in the non gaussian random waveform can be constructed from the selected band of frequencies that have been phase manipulated entire families of signals can thus be produced having the same energy spectrum but statistical characteristics that vary along the continuum from gaussian skewness 0 and kurtosis 3 through non gaussian variable skewness kurtosis and crest factor to purely impulsive shock transient signals the theoretical background and the results of a series of numerical simulations will be presented which demonstrate the functional relation between various phase spectrum manipulations and the descriptors of the synthesized random noise the results show that the approach is viable and that the synthesized random waveforms can be easily tailored to simulate a variety of real world acoustic vibration signals e g high kurtosis impulsive industrial noises helicopter noises missile vibrational signals etc

applicability of the leq as a damage risk criterion an animal experiment within the european communities the leq8h is used as a damage risk criterion drc for hearing protection the use of such a drc supposes that sound exposures with equal energy imply equal risk for noise induced hearing loss nihl the aim of the present study carried out with guinea pigs was to test the applicability of the leq8h for estimating the hazard of different noises having the same spectrum and acoustic energy therefore only the temporal structure of noises was a variable continuous intermittent or impulsive and each noise had a leq8h of 92 db the results indicate the leq8h is not an accurate drc it overestimates the nihl for intermittent and short continuous noises whereas it seems to be useful for moderate intensity noises 95 db and for the impulse noise 101 db furthermore the data point out the notion of critical intensity which seems to play a determining role in the transition between metabolic and mechanical mechanisms involved in the acoustic trauma since the criti

robust error bounds for finite element approximation of reaction diffusion problems with non constant reaction coefficient in arbitrary space dimension abstract we present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary dimension the estimator provides a guaranteed upper bound on the energy norm of the error and it is robust for all values of the reaction coefficient including the singularly perturbed case the approach is based on robustly equilibrated boundary flux functions of ainsworth and oden 2000 and on subsequent robust and explicit flux reconstruction this paper simplifies and extends the applicability of the previous result of ainsworth and vejchodsk 2011 in three aspects i arbitrary dimension ii mixed boundary conditions and iii non constant reaction coefficient it is the first robust upper bound on the error with these properties an auxiliary result that is of independent interest is the derivation of new explicit constants for two types of trace inequalities on simplices

a posteriori error estimate for finite volume approximations to singularly perturbed nonlinear convection diffusion equations this paper is devoted to the study of a posteriori and a priori error estimates for the scalar nonlinear convection diffusion equation c t nabla cdot u f c varepsilon delta c 0 the estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the l 1 norm in the situation where the diffusion parameter varepsilon is smaller or comparable to the mesh size numerical experiments underline the theoretical results

a stopping criterion for the conjugate gradient algorithm in a finite element method framework the conjugate gradient method has always been successfully used in solving the symmetric and positive definite systems obtained by the finite element approximation of self adjoint elliptic partial differential equations taking into account recent results 13 19 20 22 which make it possible to approximate the energy norm of the error during the conjugate gradient iterative process we adapt the stopping criterion introduced in 3 moreover we show that the use of efficient preconditioners does not require to change the energy norm used by the stopping criterion finally we present the results of several numerical tests that experimentally validate the effectiveness of our stopping criterion

estimating and localizing the algebraic and total numerical errors using flux reconstructions this paper presents a methodology for computing upper and lower bounds for both the algebraic and total errors in the context of the conforming finite element discretization and an arbitrary iterative algebraic solver the derived bounds are based on the flux reconstruction techniques do not contain any unspecified constants and allow estimating the local distribution of both errors over the computational domain we also discuss bounds on the discretization error their application for constructing mathematically justified stopping criteria for iterative algebraic solvers global and local efficiency of the total error upper bound and the relationship to the previously published estimates on the algebraic error theoretical results are illustrated on numerical experiments for higher order finite element approximations and the preconditioned conjugate gradient method they in particular witness that the proposed methodology yields a tight estimate on the local distribution of the algebraic and total errors over thecomputational domain and illustrate the associate cost

a posteriori error estimations of some cell centered finite volume methods this paper presents the natural framework to residual based a posteriori error estimation of some cell centered finite volume methods for the laplace equation in r d d 2 or 3 for that purpose we associate with the finite volume solution a reconstructed approximation which is a kind of morley interpolant the error is then the difference between the exact solution and this morley interpolant the residual error estimator is based on the jump of normal and tangential derivatives of the morley interpolant we then prove the equivalence between the discrete h1 seminorm of the error and the residual error estimator numerical tests confirm our theoretical results

physics based preconditioners for flow in fractured porous media discrete fracture models are an attractive alternative to upscaled models for flow in fractured media as they provide a more accurate representation of the flow characteristics a major challenge in discrete fracture simulation is to overcome the large computational cost associated with resolving the individual fractures in large scale simulations in this work two characteristics of the fractured porous media are utilized to construct efficient preconditioners for the discretized flow equations first the preconditioners are tailored to the fracture geometry and presumed flow properties so that the dominant features are well represented there this assures good scalability of the preconditioners in terms of problem size and permeability contrast for fracture dominated problems numerical examples show that such geometric preconditioners are comparable or preferable when compared to state of the art algebraic multigrid preconditioners the robustness of the physics based preconditioner for less favorable fracture conditions is further demonstrated by a systematic degradation of the fracture hierarchy second the preconditioners are physics preserving in the sense that conservative fluxes can be computed even for an inexact pressure solutions this facilitates a scheme where accuracy in the linear solver can be traded for efficiency by terminating the iterative solvers based on error estimates and without sacrificing basic physical modeling principles with the combination of these two properties a novel preconditioner is obtained which bridges the gap between multiscale approximations and iterative linear solvers

trend function hypothesis testing in the presence of serial correlation in this paper test statistics are proposed that can be used to test hypotheses about the parameters of the deterministic trend function of a univariate time series the tests are valid in the presence of general forms of serial correlation in the errors and can be used without having to estimate the serial correlation parameters either parametrically or nonparametrically the tests are valid for i 0 and i 1 errors trend functions that are permitted include general linear polynomial trend functions that may have breaks at either known or unknown locations asymptotic distributions are derived and consistency of the tests is established the general results are applied to a model with a simple linear trend a local asymptotic analysis is used to compute asymptotic size and power of the tests for this example size is well controlled and is relatively unaffected by the variance of the initial condition asymptotic power curves are computed for the simple linear trend model and are compared to existing tests it is shown that the new tests have nontrivial asymptotic power a simulation study shows that the asymptotic approximations are adequate for sample sizes typically used in economics the tests are used to construct confidence intervals for average gnp growth rates for eight industrialized countries using post war data

residual flux based a posteriori error estimates for finite volume and related locally conservative methods we derive in this paper a posteriori error estimates for discretizations of convection diffusion reaction equations in two or three space dimensions our estimates are valid for any cell centered finite volume scheme and in a larger sense for any locally conservative method such as the mimetic finite difference covolume and other we consider meshes consisting of simplices or rectangular parallelepipeds and also provide extensions to nonconvex cells and nonmatching interfaces we allow for the cases of inhomogeneous and anisotropic diffusion dispersion tensors and of convection dominance the estimates are established in the energy semi norm for a locally postprocessed approximate solution preserving the conservative fluxes and are of residual type they are fully computable all occurring constants are evaluated explicitly and locally efficient give a local lower bound on the error times an efficiency constant so that they can serve both as indicators for adaptive refinement and for the actual control of the error they are semi robust in the sense that the local efficiency constant only depends on local variations in the coefficients and becomes optimal as the local peclet number gets sufficiently small numerical experiments confirm their accuracy

a posteriori error estimates for lowest order mixed finite element discretizations of convection diffusion reaction equations we establish residual a posteriori error estimates for lowest order raviart thomas mixed finite element discretizations of convection diffusion reaction equations on simplicial meshes in two or three space dimensions the upwind mixed scheme is considered as well and the emphasis is put on the presence of an inhomogeneous and anisotropic diffusion dispersion tensor and on a possible convection dominance global upper bounds for the approximation error in the energy norm are derived where in particular all constants are evaluated explicitly so that the estimators are fully computable our estimators give local lower bounds for the error as well and they hold from the cases where convection or reaction are not present to convection or reaction dominated problems we prove that their local efficiency depends only on local variations in the coefficients and on the local peclet number moreover the developed general framework allows for asymptotic exactness and full robustness with respect to inhomogeneities and anisotropies the main idea of the proof is a construction of a locally postprocessed approximate solution using the mean value and the flux in each element known in the mixed finite element method and a subsequent use of the abstract framework arising from the primal weak formulation of the continuous problem numerical experiments confirm the guaranteed upper bound and excellent efficiency and robustness of the derived estimators

estimation and inference in large heterogeneous panels with a multifactor error structure this paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure the unobserved factors and the individual specific errors are allowed to follow arbitrary stationary processes and the number of unobserved factors need not be estimated the basic idea is to filter the individual specific regressors by means of cross section averages such that asymptotically as the cross section dimension n tends to infinity the differential effects of unobserved common factors are eliminated the estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross sectional averages of the dependent variable and the individual specific regressors a number of estimators referred to as common correlated effects cce estimators are proposed and their asymptotic distributions are derived the small sample properties of mean group and pooled cce estimators are investigated by monte carlo experiments showing that the cce estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics and for relatively small values of n and t

fully adaptive multigrid methods adaptivity is a key concept for the effective numerical solution of differential equations the multilevel solution of elliptic partial differential equations can be combined with adaptive mesh refinement and an adaptive choice of the discretization order additionally adaptivity may be built into the relaxation and the multilevel cycling strategy the goal of these fully adaptive methods is to spend work only where it is most effective in the solution process this approach includes concepts like local relaxation and not only leads to particularly fast convergence but also to additional robustness and generality the efficient implementation of fully adaptive multilevel methods in a finite element framework will be discussed

an instrumental variable approach for panel unit root tests under cross sectional dependence for dynamic panel models with cross sectional dependence several unit root tests are constructed using a huber type instrument whose null asymptotics are standard gaussian and do not depend on nuisance parameters a monte carlo simulation shows that the proposed tests have better sizes and comparable powers relative to other two existing tests developed for cross sectionally dependent dynamic panel models

a posteriori error analysis for locally conservative mixed methods in this work we present a theoretical analysis for a residual type error estimator for locally conservative mixed methods this estimator was first introduced by braess and verfurth for the raviart thomas mixed finite element method working in mesh dependent norms we improve and extend their results to cover any locally conservative mixed method under minimal assumptions in particular avoiding the saturation assumption made by braess and verfurth our analysis also takes into account discontinuous coefficients with possibly large jumps across interelement boundaries the main results are applied to the p1 nonconforming finite element method and the interior penalty discontinuous galerkin method as well as the mixed finite element method

linear regression limit theory for nonstationary panel data this paper develops a regression limit theory for nonstationary panel data with large numbers of cross section n and time series t observations the limit theory allows for both sequential limits wherein t followed by n and joint limits where t n simultaneously and the relationship between these multidimensional limits is explored the panel structures considered allow for no time series cointegration heterogeneous cointegration homogeneous cointegration and near homogeneous cointegration the paper explores the existence of long run average relations between integrated panel vectors when there is no individual time series cointegration and when there is heterogeneous cointegration these relations are parameterized in terms of the matrix regression coefficient of the long run average covariance matrix in the case of homogeneous and near homogeneous cointegrating panels a panel fully modified regression estimator is developed and studied the limit theory enables us to test hypotheses about the long run average parameters both within and between subgroups of the full population

stopping criteria for adaptive finite element solvers we consider a family of practical stopping criteria for linear solvers for adaptive finite element methods for symmetric elliptic problems a contraction property between two consecutive levels of refinement of the adaptive algorithm is shown when a family of smallness criteria for the corresponding linear solver residuals are assumed on each level or refinement more importantly based on known and new results for the estimation of the residuals of the conjugate gradient method we show that the smallness criteria give rise to practical stopping criteria for the iterations of the linear solver which guarantees that the inexact adaptive algorithm converges a series of numerical experiments highlights the practicality of the theoretical developments

a posteriori error estimates including algebraic error and stopping criteria for iterative solvers for the finite volume discretization of a second order elliptic model problem we derive a posteriori error estimates which take into account an inexact solution of the associated linear algebraic system we show that the algebraic error can be bounded by constructing an equilibrated raviart thomas nedelec discrete vector field whose divergence is given by a proper weighting of the residual vector next claiming that the discretization error and the algebraic one should be in balance we construct stopping criteria for iterative algebraic solvers an attention is paid in particular to the conjugate gradient method which minimizes the energy norm of the algebraic error using this convenient balance we also prove the efficiency of our a posteriori estimates i e we show that they also represent a lower bound up to a generic constant for the overall energy error a local version of this result is also stated this makes our approach suitable for adaptive mesh refinement which also takes into account the algebraic error numerical experiments illustrate the proposed estimates and construction of efficient stopping criteria for algebraic iterative solvers

on the multilevel adaptive iterative method the multilevel adaptive iterative method is a technique for solving the sparse matrix equations that typically arise from partial differential systems its core consists of a relaxation scheme and an active set strategy the active set is used to monitor where the iteration efficiently reduces the error it is incrementally updated by exploiting the current solution and the matrix structure and most arithmetic operations are restricted to it the algorithm can be extended to a multilevel structure by additionally tracing the dependencies between unknowns on different levels it improves the robustness and efficiency of classical multilevel methods in particular it is an almost ideal supplement to adaptive refinement techniques

stopping criteria for iterations in finite element methods this work extends the results of arioli 1 2 on stopping criteria for iterative solution methods for linear finite element problems to the case of nonsymmetric positive definite problems we show that the residual measured in the norm induced by the symmetric part of the inverse of the system matrix is relevant to convergence in a finite element context we then use krylov solvers to provide alternative ways of calculating or estimating this quantity and present numerical experiments which validate our criteria

testing for a unit root in a random coefficient panel data model this paper proposes new unit root tests in the context of a random autoregressive coefficient panel data model in which the null of a unit root corresponds to the joint restriction that the autoregressive coefficient has unit mean and zero variance the asymptotic distributions of the test statistics are derived and simulation results are provided to suggest that they perform very well in small samples

hearing loss in the chinchilla from impact and continuous noise exposure the relative hazard posed to the peripheral auditory system by impact impulse and continuous noise of the same power spectrum was determined impact noise was generated by striking a nail with a hammer and was digitally recorded the acoustical power spectrum of the impact was determined and pink noise was filtered to produce a continuous noise stimulus with the same acoustic power spectrum pre exposure auditory evoked response aer thresholds were obtained at 1 2 4 and 8 khz on 16 adult chinchillas the pool of animals was divided into two equal groups based upon pre exposure aer thresholds one group was exposed to impact noise and the other group to the filtered pink noise exposures were 4 h day for 5 days thirty days following the exposure auditory evoked response thresholds were remeasured changes in auditory sensitivity were determined by subtracting the pre exposure thresholds from the post exposure thresholds hearing threshold shifts of the impact noise group were significantly greater

fast iterative solution of elliptic control problems in wavelet discretization we investigate wavelet methods for the efficient numerical solution of a class of control problems constrained by a linear elliptic boundary value problem where the cost functional may contain fractional sobolev norms of the control and the state starting point is the formulation of the infinite dimensional control problem in terms of boundary adapted biorthogonal spline wavelets involving only l2 norms of wavelet expansion coefficients where different norms are realized by a diagonal scaling together with a riesz map and constraints in form of an l2 isomorphism the coupled system of equations resulting from optimization is solved by an inexact conjugate gradient cg method for the control which involves the approximate inversion of the primal and the adjoint operator using again cg iterations starting from a coarse discretization level we use nested iteration to solve the coupled system on successively finer uniform discretizations up to discretization error accuracy on each level the resulting inexact cg scheme is a fast solver it is of asymptotic optimal complexity in the sense that the overall computational effort to compute the solution up to discretization error on the finest grid is proportional to the number of unknowns on that grid a consequence of grid independent condition numbers of the linear operators in wavelet coordinates in the numerical examples we study the choice of different norms and the regularization parameter in the cost functional and their effect on the solution moreover for different situations the performance of the fully iterative inexact cg scheme is investigated confirming the theoretical results

unit root tests in the presence of uncertainty about the non stochastic trend abstract a sequential procedure for determination of trend degree and testing for a unit root is introduced its properties are investigated by monte carlo experiment we implement the pseudo gls unit root tests of elliott et al 1996 econometrica 64 4 813 836 with lag length selected by the bic criterion our procedure allows for quadratic trend and we introduce a gls type test for this case we compare the sequential procedure in which trend degree is tested after a unit root pre test with a robust trend test recently developed by vogelsang 1998 econometrica 66 1 123 149 the sequential procedure is advocated in preference both to informal use of the usual family of unit root tests and to alternative formal sequential methods that have been advanced in the literature it is illustrated by application to the inventory data analysed in hall 1994 journal of business and economic statistics 12 4 461 470

the kurtosis metric as an adjunct to energy in the prediction of trauma from continuous nongaussian noise exposures data from an earlier study hamernik et al 2003 j acoust soc am 114 386 395 were consistent in showing that for equivalent energy leq 100 db a and spectra exposure to a continuous nongaussian nong noise could produce substantially greater hearing and sensory cell loss in the chinchilla model than a gaussian g noise exposure and that the statistical metric kurtosis computed on the amplitude distribution of the noise could order the extent of the trauma this paper extends these results to leq 90 and 110 db a and to nong noises that are generated using broadband noise bursts and band limited impacts within a continuous g background noise data from nine new experimental groups with 11 or 12 chinchillas group is presented evoked response audiometry established hearing thresholds and surface preparation histology quantified sensory cell loss at the lowest level leq 90 db a there were no differences in the trauma produced by g and nong exposures for leq 90 db a nong exposures produced increased trauma relative to equivalent g exposures removing energy from the impacts by limiting their bandwidth reduced trauma the use of noise bursts to produce the nong noise instead of impacts also reduced the amount of trauma

unified primal formulation based a priori and a posteriori error analysis of mixed finite element methods we derive in this paper a unified framework for a priori and a posteriori error analysis of mixed finite element discretizations of second order elliptic problems it is based on the classical primal weak formulation the postprocessing of the potential proposed in t arbogast and z chen on the implementation of mixed methods as nonconforming methods for second order elliptic problems math comp 64 1995 943 972 and the discrete friedrichs inequality our analysis in particular avoids any explicit use of the uniform discrete inf sup condition and in a straightforward manner and under minimal necessary assumptions known convergence and superconvergence results are recovered the same framework then turns out to lead to optimal a posteriori energy error bounds in particular estimators for all families and orders of mixed finite element methods on grids consisting of simplices or rectangular parallelepipeds are derived they give a guaranteed and fully computable upper bound on the energy error represent error local lower bounds and are robust under some conditions on the diffusion dispersion tensor they are thus suitable for both overall error control and adaptive mesh refinement moreover the developed abstract framework and a posteriori error estimates are quite general and apply to any locally conservative method we finally prove that in parallel and simultaneously in converse to galerkin finite element methods under some circumstances the weak solution is the orthogonal projection of the postprocessed mixed finite element approximation onto the h 1 0 space and also establish several links between mixed finite element approximations and some generalized weak solutions

a comparison of a posteriori error estimators for mixed finite element discretizations by raviart thomas elements we consider mixed finite element discretizations of linear second order elliptic boundary value problems with respect to an adaptively generated hierarchy of possibly highly nonuniform simplicial triangulations in particular we present and analyze four different kinds of error estimators a residual based estimator a hierarchical one error estimators relying on the solution of local subproblems and on a superconvergence result respectively finally we examine the relationship between the presented error estimators and compare their local components

the effect of recursive detrending on panel unit root tests this paper analyzes the properties of panel unit root tests based on recursively detrended data the analysis is conducted while allowing for a potentially non linear trend function which represents a more general consideration than the current state of affairs with at most a linear trend a new test statistic is proposed whose asymptotic behavior under the unit root null hypothesis and the simplifying assumptions of a polynomial trend and iid errors are shown to be surprisingly simple indeed the test statistic is not only asymptotically independent of the true trend polynomial but also is in fact unique in that it is independent also of the degree of the fitted polynomial however this invariance property does not carry over to the local alternative under which it is shown that local power is a decreasing function of the trend degree but while power does decrease the rate of shrinking of the local alternative is generally constant in the trend degree which goes against the common belief that the rate of shrinking should be decreasing in the trend degree the above results are based on simplifying assumptions to compensate for this lack of generality a second robust test statistic is proposed whose validity does not require that the trend function is a polynomial or that the errors are iid