superconvergent patch recovery with equilibrium and conjoint interpolant enhancements the superconvergent patch derivative recovery method of zienkiewicz and zhu is enhanced by adding the squares of the residuals of the equilibrium equation and natural boundary conditions in addition a new conjoint polynomial for interpolating the local patch stresses over the element which significantly improves the local projection scheme is presented results show that in the 4 node quadrilateral the equilibrium and boundary condition residuals usually improve accuracy but not the rate of convergence whereas in the 9 node quadrilateral results are mixed the conjoint polynomial always improves the accuracy of the derivative field within the element as compared to the standard nodal interpolation particularly in 4 node quadrilaterals

assessment of discretized errors and adaptive refinement with quadrilateral finite elements this paper studies discretized errors and their estimation in conjunction with quadrilateral finite element meshes which are generated by the intelligent mesh generator xformq 1 the exact energy error is used to evaluate the distortion effect of the quadrilateral mesh the zienkiewicz zhu2 error estimate and actaptive procedure are applied to the short cantilever and the square plate problems using the quadrilateral mesh generator xformq it is shown that the multistage quadrilateral element refinement produces results superior to the triangular element refinement in the test cases

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

a nonparametric trend test for seasonal data with serial dependence statistical tests for monotonic trend in seasonal e g monthly hydrologic time series are commonly confounded by some of the following problems nonnormal data missing values seasonality censoring detection limits and serial dependence an extension of the mann kendall test for trend designed for such data is presented here because the test is based entirely on ranks it is robust against nonnormality and censoring seasonality and missing values present no theoretical or computational obstacles to its application monte carlo experiments show that in terms of type i error it is robust against serial correlation except when the data have strong long term persistence e g arma 1 1 monthly processes with 0 6 or short records 5 years when there is no serial correlation it is less powerful than a related simpler test which is not robust against serial correlation

water quality modeling a review of the analysis of uncertainty this paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction more specifically four problem areas are examined in detail uncertainty about model structure uncertainty in the estimated model parameter values the propagation of prediction errors and the design of experiments in order to reduce the critical uncertainties associated with a model the review is rather lengthy and it has therefore been prepared in effect as two papers there is a shorter largely nontechnical version which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling enclosed by this shorter discussion is the main body of the review dealing in turn with 1 identifiability and experimental design 2 the generation of preliminary model hypotheses under conditions of sparse grossly uncertain field data 3 the selection and evaluation of model structure 4 parameter estimation model calibration 5 checks and balances on the identified model i e model verification and model discrimination and 6 prediction error propagation much time is spent in discussing the algorithms of system identification in particular the methods of recursive estimation and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first order error analysis there are two obvious omissions from the review it is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty although clearly some reference must be made to these topics in brief the review concludes not surprisingly that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality and much remains to be done a lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior and there is ample evidence to show that the larger more comprehensive models are easily capable of generating highly uncertain predictions of future behavior for the future of the subject it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification a need for new questions to be posed in the problem of prediction and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence

the problem of plate modeling theoretical and computational results abstract the paper analyzes in detail the problem of various plate models properties of their solution and the question how well these models approximate the three dimensional formulation the boundary layer and corner singularities of the solution are analyzed a hierarchy of the models converging to the three dimensional solution is constructed the detailed numerical computations show various basic aspects of plate modeling in a concrete setting

on the rates of convergence of the finite element method abstract the rate of convergence of the finite element method is a function of the strategy by which the number of degrees of freedom are increased alternative strategies are examined in the light of recent theoretical results and computational experience author

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

an adaptive h refinement using transition element for plate bending problems an adaptive h refinement procedure utilizing compatible 5 to 7 node quadrilateral transition elements together with 4 node elements is presented for reissner mindlin plate bending problems by introducing the transition elements which have physical midside nodes some difficulties associated with imposing displacement constraints on irregular nodes to enforce interelement compatibility in common adaptive h refinement on quadrilateral mesh are easily overcome numerical examples are presented to show the effectiveness of using the transition elements for the adaptive h refinement

techniques of trend analysis for monthly water quality data some of the characteristics that complicate the analysis of water quality time series are non normal distributions seasonality flow relatedness missing values values below the limit of detection and serial correlation presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonie trends the first procedure described is a nonparametric test for trend applicable to data sets with seasonality missing values or values reported as less than the seasonal kendall test under realistic stochastic processes exhibiting seasonality skewness and serial correlation it is robust in comparison to parametric alternatives although neither the seasonal kendall test nor the alternatives can be considered an exact test in the presence of serial correlation the second procedure the seasonal kendall slope estimator is an estimator of trend magnitude it is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal the third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed e g drought effects in this method a flow adjusted concentration is defined as the residual actual minus conditional expectation based on a regression of concentration on some function of discharge these flow adjusted concentrations which may also be seasonal and non normal can then be tested for trend by using the seasonal kendall test

the hp mitc finite element method for the reissner mindlin plate problem the popular mitc finite elements used for the approximation of the reissner mindlin plate are extended to the case where elements of non uniform degree p distribution are used on locally refined meshes such an extension is of particular interest to the hp version and hp adaptive finite element methods a priori error bounds are provided showing that the method is locking free the analysis is based on new approximation theoretic results for non uniform brezzi douglas fortin marini spaces and extends the results obtained in the case of uniform order approximation on globally quasi uniform meshes presented by stenberg and suri siam j numer anal 34 1997 544 numerical examples illustrating the theoretical results and comparing the performance with alternative standard galerkin approaches are presented for two new benchmark problems with known analytic solution including the case where the shear stress exhibits a boundary layer the new method is observed to be locking free and able to provide exponential rates of convergence even in the presence of boundary layers

on constructing accurate recovered stress fields for the finite element solution of reissner mindlin plate bending problems the effectiveness and reliability of three local least squares fit procedures for the construction of smoothed moments and shear forces for the solution of the reissner mindlin rm thick plate model are reviewed the three procedures considered are namely the superconvergent patch recovery technique spr the recovery by equilibrium in patches rep and the recovery procedure suggested by lee park and lee lp numerical studies are carried out by applying these three recovery procedures for the construction of smoothed stress fields for various rm plate bending problems the results obtained indicate that if the order of polynomial used in the stress recovery is the same as that for the finite element analysis all three procedures produce recovered stress fields with very similar accuracy and convergence rate however when the order of polynomial is raised if the exact solution is smooth without any strong boundary layers or singularities both the rep and lp procedures can produce more accurate stress fields than the spr in case that singularities or boundary layers are present the lp procedure often outperforms the rep procedure and results in more stable recovery matrices and more accurate recovered stress fields

effects of element distortions on the performance of isoparametric elements we discuss the effects of element distortions on the performance of displacement based isoparametric quadrilateral finite elements suitable example problems for both the lagrangian and the serendipity types of elements are used to show numerically the effects of element distortions the effects of angular and curved edge distortions are evaluated analytically in terms of the abilities of the elements to represent exactly various polynomial displacement fields we then solve a plane stress problem adaptively to demonstrate the effect of element distortions on the accuracy of the stress distribution the conclusion is that the lagrangian elements are not affected by angular distortions and are therefore the more reliable elements for general use

nonparametric tests for trend in water quality recently several nonparametric tests for trends in water quality have been proposed these tests have been developed because the assumptions of classical parametric methods i e normality linearity independence are usually not met by typical water quality data additional idiosyncrasies of the data such as missing values censored data and seasonality compound the analysis problem the nonparametric methods are more flexible and can handle these problems more easily however information on relative power of the various nonparametric procedures has not been reported in the hydrologic literature for this reason two classes of procedures intrablock methods procedures that compute a statistic such as kendall s tau for each block or season and then sum these to produce a single overall statistic and aligned rank methods procedures that remove the block effect from each datum sum the data over blocks and then create a statistic from these sums are examined in detail results from the statistical literature show that aligned rank methods are asymptotically more powerful than intrablock methods in contrast intrablock methods are more adaptable procedures to analyze more general models including multistation designs and models which include a trend season or trend site interaction are developed by using kendall s tau and intrablock methods finally some recommendations on the analysis of data sets with missing values and multiple values per season values are presented

statistical estimation and interpretation of trends in water quality time series three approaches to trend analysis of water quality time series are discussed 1 seasonal model with a test for trend based on ranks of observations with observations assumed to be m dependent 2 transfer function noise model in which covariate series may be included by means of transfer functions with the remaining noise modeled as a seasonal autoregressive moving average process and 3 component model with the noise decomposed into series which describe trends and irregular and seasonal variation models are studied with regards to their ability to include covariate series possibility of interpretation of trends treatment of seasonal variation and serial dependence and robustness for outliers we regard the component model being the most realistic and the most informative of the three approaches models are applied to series of monthly phosphorus concentration in the ljungbyan river in southern sweden

error estimates and adaptive refinement for plate bending problems the zienkiewicz zhu error estimator is shown to be effective in problems of plate flexure when used in conjunction with triangular elements and an adaptive mesh generator allowing a prescribed size of elements to be developed very fast adaptive convergence for results of specified accuracy is achieved

a study of boundary layers in plates using mindlin reissner and 3 d elements finite elements based on mindlin reissner theory and three dimensional theory are used to study the distribution of shear forces and twisting moments in plates with various simple support conditions differences between the results obtained using these two theories are highlighted a crude adaptive mesh refinement procedure is applied to improve the accuracy of the finite element analysis

adaptive error control in multi physical thin structure mems fe simulation simulating the physical behavior of thin multi layered structures accurately is central to micro electro mechanical systems mems cad we have produced an automatic method with which to simulate the structural response of multi layer plate and beam micro structures accurately and reliably the method also covers thermo mechanical and piezoelectric effects we use a kirchhoff love thin structure model implemented as a conforming argyris finite element suited for the calculation of thermo mechanical membrane and bending behavior and which is extended to simulate piezoelectric effects in thin structures for the first time a posteriori estimation is presented for such multi layered multiphysically active thin structures different sources of errors are identified and specified for several usecases the error analysis covers locally prestressed regions plate composition inhomogeneities geometrical singularities and singularities conditional upon the presence of source functions of various types together with a refinement strategy and a geometrical split pattern the efficiency of the method is demonstrated local mesh refinement guarantees the computation of the most accurate solution at a minimum of computational costs

on using degenerated solid shell elements in adaptive refinement analysis three different degenerated shell elements are studied in an adaptive refinement procedure for the solution of shell problems the stress recovery procedure expressed in a convective patch co ordinate system is used for the construction of continuous smoothed stress fields for the a posteriori error estimation the performance of the stress recovery procedure the error estimator and the adaptive refinement strategy are tested by solving three benchmark shell problems it is found that when adaptive refinement is used the adverse effects of boundary layers and stress singularities are eliminated and all the elements tested are able to achieve their optimal convergence rates it is also found that the accuracy of the shell elements increases with the number of polynomial terms included in the stress and strain approximations in addition if complete lagrangian polynomial terms are used the element will be less sensitive to shape distortion than the one in which only complete polynomial terms are employed copyright 1999 john wiley sons ltd