a robust goodness of fit test statistic with application to ordinal regression models we propose a goodness of fit test statistic for linear regression with heterogeneous variance which is asymptotically chi square if the given model is correct the test statistic is computed as a quadratic form of observed minus predicted responses we apply the method to a linear regression for an ordinal categorical response the wheezing status of a child no wheeze wheeze with cold wheeze apart from cold as a function of maternal smoking and city of residence

implementation of a maximin power clustering criterion to select near replicates for regression lack of fit tests abstract in earlier work we presented a maximin power clustering criterion to partition observations into groups of near replicates specifically the criterion selects near replicate clusters for use with christensen s tests for orthogonal between and within cluster lack of fit this article further explores implementation of this clustering criterion in particular a methodology is developed to determine a collection of candidate groupings to which the maximin power criterion can be applied

discontinuous galerkin error estimation for linear symmetrizable hyperbolic systems we present an a posteriori error analysis for the discontinuous galerkin discretization error of first order linear symmetrizable hyperbolic systems of partial differential equations with smooth solutions we perform a local error analysis by writing the local error as a series and showing that its leading term can be expressed as a linear combination of legendre polynomials of degree and we apply these asymptotic results to show that projections of the error are pointwise superconvergent we solve relatively small local problems to compute efficient and asymptotically exact estimates of the finite element error we present computational results for several linear hyperbolic systems in acoustics and electromagnetism

alternative goodness of fit tests for linear models fan and huang 2001 presented a goodness of fit test for linear models based on fourier transformations of the residuals of the fitted model we present two more theoretically appealing tests in which the fourier transforms are incorporated into a fitted model we show that when suitably normalized the new test statistics have the same asymptotic distribution as fan and huang s test we propose modifications to the asymptotic normalization constants to improve the small sample sizes of our tests while retaining their asymptotic distributions small sample sizes and powers are examined via simulations an illustration is given

error estimates for finite element methods for scalar conservation laws in this paper new a posteriors error estimates for the shock capturing streamline diffusion scsd method and the shock capturing discontinuous galerkin scdg method for scalar conservation laws are obtained these estimates are then used to prove that the scsd method and the scdg method converge to the entropy solution with a rate of at least h 1 8 and h 1 8 respectively in the l infty l 1 norm the triangulations are made of general acute simplices and the approximate solution is taken to be piecewise a polynomial of degree k the result is independent of the dimension of the space

an exact test of fit for the gaussian linear model using optimal nonbipartite matching abstractfisher tested the fit of gaussian linear models using replicated observations we refine this method by 1 constructing near replicates using an optimal nonbipartite matching and 2 defining a distance that focuses on predictors important to the model s predictions near replicates may not exist unless the predictor set is low dimensional the test addresses dimensionality by betting that model failures involve a subset of predictors important in the old fit despite using the old fit to pair observations the test has exactly its stated level under the null hypothesis simulations show the test has reasonable power even when many spurious predictors are present

superconvergence and a posteriori error estimates of the dg method for scalar hyperbolic problems on cartesian grids in this paper we analyze the discontinuous galerkin dg finite element method for the steady two dimensional transport reaction equation on cartesian grids we prove the l2 stability and optimal l2 error estimates for the dg scheme we identify a special numerical flux for which the l2 norm of the solution is of order p 1 when tensor product polynomials of degree at most p are used we further prove superconvergence towards a particular projection of the directional derivative the order of superconvergence is proved to be p 1 2 we also provide a very simple derivative recovery formula which is o h p 1 superconvergent approximation to the directional derivative moreover we establish an o h 2 p 1 global superconvergence for the solution flux at the outflow boundary of the domain these results are used to construct asymptotically exact a posteriori error estimates for the directional derivative approximation by solving a local problem on each element finally we prove that the proposed a posteriori dg error estimates converge to the true errors in the l2 norm at o h p 1 rate and that the global effectivity index converges to unity at o h rate our results are valid without the flow condition restrictions we perform numerical experiments to demonstrate that theoretical rates proved in this paper are optimal

testing the independence assumption in linear models abstract we propose using an existing set of statistical tools in a new way that allows one to test the independence assumption in standard normal theory linear models the set of tools is near replicate lack of fit tests the classical lack of fit test requires a linear model in which some rows of the model matrix are repeated near replicate lack of fit tests were developed to mimic the behavior of the classical test by identifying clusters of rows in the design matrix that are similar though not necessarily exact replications we argue that meaningful clusters can be formed more generally by constructing rational subgroups of data collected under similar circumstances as such observations in the same subgroup may be more highly correlated than observations in different subgroups we investigate the behavior of these tests when used to identify lack of independence

algebraic and topological results on lifting properties in residuated lattices we define lifting properties for universal algebras which we study in this general context and then particularize to various such properties in certain classes of algebras next we focus on residuated lattices in which we investigate lifting properties for boolean and idempotent elements modulo arbitrary as well as specific kinds of filters we give topological characterizations to the lifting property for boolean elements and several properties related to it many of which we obtain by means of the reticulation

discontinuous galerkin error estimation for hyperbolic problems on unstructured triangular meshes we extend the error analysis of adjerid and baccouch 1 2 for the discontinuous galerkin discretization error to variable coefficient linear hyperbolic problems as well as nonlinear hyperbolic problems on unstructured meshes we further extend this analysis to transient hyperbolic problems and prove that the local superconvergence results presented in 1 still hold for both steady and transient variable coefficient linear and nonlinear problems this local error analysis allows us to construct asymptotically correct a posteriori error estimates by solving local hyperbolic problems with no boundary conditions on each element of general unstructured meshes we illustrate the superconvergence and the efficiency of our a posteriori error estimates by showing computational results for several linear and nonlinear numerical examples

testing linear regression function adequacy without replication the well known pure error lack of fit test which can be used to assess the adequacy of a linear regression model is generalized to accommodate the case of nonreplication the asymptotic null distribution of the proposed test statistic is derived also the proposed test statistic is shown to be asymptotically comparable under general alternatives to the test statistic obtained in the case of replication consistency properties associated with pseudo lack of fit and pure error mean squares are given which parallel those obtained in the case of replication in addition the test statistic is invariant with respect to location and scale changes made to the regression variables

maximin clusters for near replicate regression lack of fit tests to assess the adequacy of a nonreplicated linear regression model christensen introduced the concepts of orthogonal between and within cluster lack of fit with corresponding optimal tests however the properties of these tests depend on the choice of near replicate clusters in this paper a graph theoretic framework is presented to represent candidate clusterings a clustering is then selected according to a proposed maximin power criterion from among the clusterings consistent with a specified graph on the predictor settings examples are given to illustrate the methodology

asymptotically exact a posteriori ldg error estimates for one dimensional transient convection diffusion problems in this paper new a posteriori error estimates for the local discontinuous galerkin ldg formulation applied to transient convection diffusion problems in one space dimension are presented and analyzed these error estimates are computationally simple and are computed by solving a local steady problem with no boundary conditions on each element we first show that the leading error term on each element for the solution is proportional to a p 1 degree right radau polynomial while the leading error term for the solution s derivative is proportional to a p 1 degree left radau polynomial when polynomials of degree at most p are used these results are used to prove that for smooth solutions these error estimates at a fixed time converge to the true spatial errors in the l 2 norm under mesh refinement more precisely we prove that our ldg error estimates converge to the true spatial errors at o h p 5 4 rate finally we prove that the global effectivity indices in the l 2 norm converge to unity at o h 1 2 rate our computational results indicate that the observed numerical convergence rates are higher than the theoretical rates

some weaker versions of topological residuated lattices abstract the aim of this paper is to investigate some weaker versions of topological residuated lattices which are para topological residuated lattices continuous para topological residuated lattices continuous para topological residuated lattices continuous and para topological residuated lattices continuous respectively this paper mainly focuses on the latter two para topological residuated lattices we prove the independence of these para topological residuated lattices by using their algebraic properties moreover we establish the correspondence between algebraic properties and topologies in a residuated lattice l i e there is an injective mapping from m e q l i e q l a e q l c o n l resp to m t r l l i t r l l a t r l l t r l l resp finally some interactions between the topologies and algebraic properties in para semi topological residuated lattices are studied

a posteriori error estimation for discontinuous galerkin solutions of hyperbolic problems abstract we analyze the spatial discretization errors associated with solutions of one dimensional hyperbolic conservation laws by discontinuous galerkin methods dgms in space we show that the leading term of the spatial discretization error with piecewise polynomial approximations of degree p is proportional to a radau polynomial of degree p 1 on each element we also prove that the local and global discretization errors are o x2 p 1 and o x2p 1 at the downwind point of each element this strong superconvergence enables us to show that local and global discretization errors converge as o xp 2 at the remaining roots of radau polynomial of degree p 1 on each element convergence of local and global discretization errors to the radau polynomial of degree p 1 also holds for smooth solutions as p these results are used to construct asymptotically correct a posteriori estimates of spatial discretization errors that are effective for linear and nonlinear conservation laws in regions where solutions are smooth

a discontinuous galerkin method for the wave equation abstract we present a new discontinuous galerkin method for solving the second order wave equation using the standard continuous finite element method in space and a discontinuous method in time directly applied to second order ode systems we prove several optimal a priori error estimates in space time norms for this new method and show that it can be more efficient than existing methods we also write the leading term of the local discretization error in terms of lobatto polynomials in space and jacobi polynomials in time which leads to superconvergence points on each space time cell we discuss how to apply our results to construct efficient and asymptotically exact a posteriori estimates for space time discretization errors numerical results are in agreement with theory

a lack of fit test for the mean function in a generalized linear model abstract a supremum type statistic based on partial sums of residuals is proposed to test the validity of the mean function of the response variable in a generalized linear model the proposed test does not need a partition of the space of covariates to handle the case of nonreplication the new test is consistent against the alternative under which the deterministic part of the model is not the one specified in the null hypothesis the asymptotic null distribution of the test statistic can be approximated through simulations this approximation is valid even if the variance of the response variable is misspecified in the model for practical sample sizes the adequacy of this large sample approximation to the null distribution of the test statistic is carefully examined power comparisons with other lack of fit tests are also performed to show the advantage of the test in particular we find that the new procedure is rather sensitive to detect a misspecified mean function if the assumed mean functio

topology on bl algebras in this paper by using a special family of filters on a bl algebra l we construct a topology on l show that l is a topological bl algebra find the closure of any subsets of l and obtain some conditions under which that l is a hausdorff space also we prove some theorems about connected components of this topological space and use them to construct a quotient semitopological bl algebras finally we introduce the concept of complete bl algebra and attempt to construct a complete bl algebra from l

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

checking for lack of fit in linear models with parametric variance functions i adapt near replicate lack of fit tests for checking the adequacy of a linear model for means to check for lack of fit in a standard log linear model for variances a graphical method for checking lack of fit in the variance model is also proposed in addition an overall test of lack of fit in means or variances is presented three examples are used to illustrate the techniques

superconvergence and a posteriori error estimates for the ldg method for convection diffusion problems in one space dimension in this paper we investigate the superconvergence properties of the local discontinuous galerkin ldg method applied to transient convection diffusion problems in one space dimension we show that the leading terms of the local discretization errors for the p degree ldg solution and its spatial derivative are proportional to p 1 degree right and left radau polynomials respectively thus the discretization errors for the p degree ldg solution and its spatial derivative are o h p 2 superconvergent at the roots of p 1 degree right and left radau polynomials respectively the superconvergence results are used to construct asymptotically correct a posteriori error estimates these error estimates are computationally simple and are obtained by solving a local steady problem with no boundary conditions on each element numerical computations suggest that these a posteriori ldg error estimates for the solution and its spatial derivative at a fixed time t converge to the true errors at o h p 3 and o h p 2 rates respectively we also show that the global effectivity indices for the solution and its derivative in the l 2 norm converge to unity at o h 2 and o h rates respectively finally we show that the ldg method combined with the a posteriori error estimation procedure yields both accurate error estimates and o h p 2 superconvergent solutions our proofs are valid for arbitrary regular meshes and for p p polynomials with p 1 and for periodic dirichlet and mixed dirichlet neumann boundary conditions several numerical simulations are performed to validate the theory

discontinuous galerkin error estimation for linear symmetric hyperbolic systems in this manuscript we present an error analysis for the discontinuous galerkin discretization error of multi dimensional first order linear symmetric hyperbolic systems of partial differential equations we perform a local error analysis by writing the local error as a series and showing that its leading term can be expressed as a linear combination of legendre polynomials of degree p and p 1p 1 we apply these asymptotic results and solve relatively small local problems to compute efficient and asymptotically exact estimates of the finite element error we present computational results for several linear hyperbolic systems in one two and three dimensions

small sample characterizations of near replicate lack of fit tests abstract several ad hoc tests based on near replicates have been proposed for testing lack of fit in regression analysis christensen characterized lack of fit as existing between clusters of near replicates within clusters or as a combination of these pure types of these the between cluster variety is the type commonly associated with the idea of lack of fit christensen examined a test that was new to the normal theory regression literature and established uniformly most powerful invariant umpi properties of the test in particular the test is umpi for orthogonal lack of fit within clusters in this article a new test is proposed that is umpi for orthogonal lack of fit between clusters the relationship of this optimal test to other proposed tests is examined giving the first small sample theoretical justification for these tests the power of the new test is compared to that of others in the literature and consistency results are discussed

development of an adaptive discontinuous galerkin finite element method for advection reaction equations abstract this paper presents an adaptive discontinuous galerkin finite element method to solve linear advection reaction equations the method was developed for the prediction of hemolysis in prosthetic devices where the flow may include recirculation zones to ensure the well posedness of the problem we solve the transient form of the pde time discretization is achieved with an implicit euler scheme in order to obtain the steady state solution rapidly linear interpolation functions are used to approximate the hemolysis field the a posteriori estimation of the error is obtained by solving an advection reaction equation for the error which is approximated with quadratic interpolation functions then elementary estimations of the error are computed using a semi norm developed to achieve the best possible results even in the presence of recirculation code verification to assess the convergence and conservation properties of the method is performed with the method of manufactured solutions and with a conservation test using a sharp gaussian function as a reaction term excellent results are obtained in both cases predictions of hemolysis in a dialysis cannula are presented as an engineering application of our method

a superconvergent local discontinuous galerkin method for the second order wave equation on cartesian grids abstract in this paper we propose and analyze a new superconvergent local discontinuous galerkin ldg method equipped with an element residual error estimator for the spatial discretization of the second order wave equation on cartesian grids we prove the l 2 stability the energy conserving property and optimal l 2 error estimates for the semi discrete formulation in particular we identify special numerical fluxes for which the l 2 norm of the solution and its gradient are of order p 1 when tensor product polynomials of degree at most p are used we further perform a local error analysis and show that the leading term of the ldg error is spanned by two p 1 degree right radau polynomials in the x and y directions thus the ldg solution is o h p 2 superconvergent at radau points obtained as a tensor product of the roots of p 1 degree right radau polynomial furthermore numerical computations show that the first component of the solution s gradient is o h p 2 superconvergent at tensor product of the roots of left radau polynomial in x and right radau polynomial in y while the second component is o h p 2 superconvergent at the tensor product of the roots of the right radau polynomial in x and left radau polynomial in y computational results indicate that global superconvergence holds for ldg solutions we use the superconvergence results to construct a posteriori ldg error estimates these error estimates are computationally simple and are obtained by solving local steady problems with no boundary condition on each element finally we present several numerical examples to validate the superconvergence results and the asymptotic exactness of our a posteriori error estimates under mesh refinement

superconvergence of discontinuous galerkin solutions for a nonlinear scalar hyperbolic problem in this paper we study the superconvergence of the discontinuous galerkin solutions for nonlinear hyperbolic partial differential equations on the first inflow element we prove that the p degree discontinuous finite element solution converges at radau points with an o h p 2 rate we further show that the solution flux converges on average at o h 2p 2 o n element outflow boundary when no reaction terms are present for reaction convection problems we establish an o h min 2p 2 p 4 superconvergence rate of the flux on element outflow boundary globally we prove that the flux converges at o h 2p 1 on average at the outflow of smooth solution regions for nonlinear conservation laws numerical computations indicate that our results extend to nonrectangular meshes and nonuniform polynomial degrees we further include a numerical example which shows that discontinuous solutions are superconvergent to the unique entropy solution away from shock discontinuities 2005 elsevier b v all rights reserved msc 65m60 65m25 65m15

a posteriori error analysis of the discontinuous finite element methods for first order hyperbolic problems abstract in this paper we consider the a posteriori error analysis of discontinuous galerkin finite element methods for the steady and nonsteady first order hyperbolic problems with inflow boundary conditions we establish several residual based a posteriori error estimators which provide global upper bounds and a local lower bound on the error further for nonsteady problem we construct a fully discrete discontinuous finite element scheme and derive the a posteriori error estimators which yield global upper bound on the error in time and space our a posteriori error analysis is based on the mesh dependent a priori estimates for the first order hyperbolic problems these a posteriori error analysis results can be applied to develop the adaptive discontinuous finite element methods

optimal convergence of the original dg method for the transport reaction equation on special meshes we show that the approximation given by the original discontinuous galerkin method for the transport reaction equation in d space dimensions is optimal provided the meshes are suitably chosen the l 2 norm of the error is of order k 1 when the method uses polynomials of degree k these meshes are not necessarily conforming and do not satisfy any uniformity condition they are required only to be made of simplexes each of which has a unique outflow face we also find a new element by element postprocessing of the derivative in the direction of the flow which superconverges with order k 1

hp version discontinuous galerkin methods for hyperbolic conservation laws a parallel adaptive strategy this paper describes a parallel algorithm based on discontinuous hp finite element approximations of linear scalar hyperbolic conservation laws the paper focuses on the development of an effective parallel adaptive strategy for such problems numerical experiments suggest that these techniques are highly parallelizable and exponentially convergent thereby yielding efficiency many times superior to conventional schemes for hyperbolic problems

on equivalent forms of fuzzy logic systems nm and imtl the nilpotent minima are important t norms in fuzzy logic and fuzzy reasoning two interesting formal systems nilpotent minimum logic nm and l based on nilpotent minima have been proposed and have been intensively studied in this paper their equivalence is pointed out moreover coincidence of two related algebraic structures nm and r0 algebras is also proved in addition we give an equivalent form of involutive monoidal t norm based logic imtl

adaptive finite element methods for parabolic problems ii optimal error estimates in l l 2 and l l optimal error estimates are derived for a complete discretization of linear parabolic problems using space time finite elements the discretization is done first in time using the discontinuous galerkin method and then in space using the standard galerkin method the underlying partitions in time and space need not be quasi uniform and the partition in space may be changed from time step to time step the error bounds show in particular that the error may be controlled globally in time on a given tolerance level by controlling the discretization error on each individual time step on the same given level i e without error accumulation effects the derivation of the estimates is based on the orthogonality of the galerkin procedure and the use of strong stability estimates the particular and precise form of these error estimates makes it possible to design efficient adaptive methods with reliable automatic error control for parabolic problems in the norms under consideration

some alternatives to wald s confidence interval and test abstract the problem considered is that of inference for the variance ratio 2 s 2 e in mixed linear models of the form y x zs e where is a column vector of unknown parameters and s and e are statistically independent multivariate normal random vectors with e s 0 var s 2 s i e e 0 and var e 2 e i the case where there is a known upper bound on is emphasized the 100 1 confidence sets corresponding to the following two sided tests of the null hypothesis h 0 0 are discussed and compared 1 a size wald s test and 2 the test that rejects h 0 whenever h 0 is rejected by the most powerful size 1 invariant test of h 0 versus the alternative u or by the most powerful size 2 invariant test of h 0 versus the alternative l l 2 l 0 u if u and l are close to 0 the latter test is essentially equivalent to a two sided version of the locally most powerful invariant test

exact and optimum tests in unbalanced split plot designs under mixed and random models abstract unbalanced split plot designs are considered where the whole plot treatments could be replicated an unequal number of times in the design but each split plot treatment occurs exactly once in every whole plot analysis of such designs is provided when the various effects could be fixed or random in each case valid exact tests and optimum invariant tests whenever they exist are derived for testing the significance of the various effects in some cases optimum tests exist only under additional conditions on the design and these conditions are specified for the various setups

plane answers to complex questions the theory of linear models providing a wide ranging introduction to the use of linear models in analyzing data this text presents a vector space and projections approach to the subject the topics covered include anova estimation hypothesis testing multiple comparison regression analysis and experimental design also covered are testing for lack of fit models with singular covariance matrices variance component estimation best linear prediction colinearity and variable selection

numerical resolution of discontinuous galerkin methods for time dependent wave equations abstract the discontinuous galerkin dg method is known to provide good wave resolution properties especially for long time simulation in this paper using fourier analysis we provide a quantitative error analysis for the semi discrete dg method applied to time dependent linear convection equations with periodic boundary conditions we apply the same technique to show that the error is of order k 2 superconvergent at radau points on each element and of order 2 k 1 superconvergent at the downwind point of each element when using piecewise polynomials of degree k an analysis of the fully discretized approximation is also provided we compute the number of points per wavelength required to obtain a fixed error for several fully discrete schemes numerical results are provided to verify our error analysis

exact tests for variance components ofversten 1993 presented methods for obtaining exact f tests of variance components in three unbalanced mixed linear models he developed methods for models with one random factor models with nested classifications and models with interaction between two random factors in section 2 we review and extend wald s test which is a generalization of one of ofversten s methods ofversten s other method is a generalization of khuri 1987 1990 and khuri and littell 1987 it does not apply to the one random factor model in section 3 we present a unified treatment of ofversten s second method this treats all of ofversten s examples and gives a formal justification to ofversten s claim that the method extends quite generally section 3 also gives a formal condition for when the method does not require resampling from the residuals the unified treatment is conceptually simpler than ofversten s treatment in that it uses a single orthonormal basis rather than a series of matrix decompositions that change slightly from example to example there do not seem to be any particular computational advantages to the unified treatment the unified treatment also appears to generalize ofversten s method in that it applies in some cases where wald s test also applies section 4 compares the two tests when both apply all of the arguments are given in terms of vector space ideas cf christensen 1987

superconvergence of discontinuous galerkin methods for two dimensional hyperbolic equations this paper is concerned with superconvergence properties of discontinuous galerkin dg methods for two dimensional linear hyperbolic conservation laws over rectangular meshes when upwind fluxes are used we prove under some suitable initial and boundary discretizations the 2k 1 th order superconvergence rate of the dg approximation at the downwind points and for the cell averages when piecewise tensor product polynomials of degree k are used moreover we prove that the gradient of the dg solution is superconvergent with a rate of k 1 th order at all interior left radau points and the function value approximation is superconvergent at all right radau points with a rate of k 2 th order numerical experiments indicate that the aforementioned superconvergence rates are sharp

a posteriori finite element error estimation for second order hyperbolic problems abstract we develop a posteriori finite element discretization error estimates for the wave equation in one dimension we show that the significant part of the spatial finite element error is proportional to a lobatto polynomial and an error estimate is obtained by solving a set of either local elliptic or hyperbolic problems in two dimensions we show that the dichotomy principle of babuska and yu holds for even degree approximations error estimates are computed by solving a set of local elliptic or hyperbolic problems and for odd degree approximations an error estimate is computed using jumps of solution gradients across element boundaries this study also extends known superconvergence results for elliptic and parabolic problems superconvergence in galerkin finite element methods springer verlag new york 1995 to second order hyperbolic problems

graphical methods for assessing logistic regression models abstract in ordinary linear regression graphical diagnostic displays can be very useful for detecting and examining anomalous features in the fit of a model to data for logistic regression models the discreteness of binary data makes it difficult to interpret such displays modifications and extensions of linear model displays lead to three methods for diagnostic checking of logistic regression models local mean deviance plots are useful for detecting overall lack of fit empirical probability plots help point out isolated departures from the fitted model partial residual plots when smoothed to show underlying structure help identify specific causes of lack of fit these methods are illustrated through the analyses of simulated and real data

a posteriori discontinuous finite element error estimation for two dimensional hyperbolic problems abstract we analyze the discontinuous finite element errors associated with p degree solutions for two dimensional first order hyperbolic problems we show that the error on each element can be split into a dominant and less dominant component and that the leading part is o hp 1 and is spanned by two p 1 degree radau polynomials in the x and y directions respectively we show that the p degree discontinuous finite element solution is superconvergent at radau points obtained as a tensor product of the roots of p 1 degree radau polynomial for a linear model problem the p degree discontinuous galerkin solution flux exhibits a strong o h2p 2 local superconvergence on average at the element outflow boundary we further establish an o h2p 1 global superconvergence for the solution flux at the outflow boundary of the domain these results are used to construct simple efficient and asymptotically correct a posteriori finite element error estimates for multi dimensional first order hyperbolic problems in regions where solutions are smooth

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

on para quasi topological mv algebras abstract in this paper the notions of para quasi semi topological mv algebras are defined and their related properties are studied also topologies with which an mv algebra can be a para semi topological mv algebra are obtained clearly a topological mv algebra is a para quasi semi topological mv algebra but the converse is not true as shown by an example in addition we study ideals and filters in para quasi topological mv algebras and we show that a quasitopological mv algebra is a topological mv algebra if the ideal 0 or equivalently the filter 1 is open

stone like representation theorems and three valued filters in r0 algebras nilpotent minimum algebras nilpotent minimum algebras nm algebras are algebraic counterpart of a formal deductive system where conjunction is modeled by the nilpotent minimum t norm a logic also independently introduced by guo jun wang in the mid 1990s such algebras are to this logic just what boolean algebras are to the classical propositional logic in this paper by introducing respectively the stone topology and a three valued fuzzy stone topology on the set of all maximal filters in an nm algebra we first establish two analogues for an nm algebra of the well known stone representation theorem for a boolean algebra which state that the boolean skeleton of an nm algebra is isomorphic to the algebra of all clopen subsets of its stone space and the three valued skeleton is isomorphic to the algebra of all clopen fuzzy subsets of its three valued fuzzy stone space respectively then we introduce the notions of boolean filter and of three valued filter in an nm algebra and finally we prove that three valued filters and closed subsets of the stone space of an nm algebra are in one to one correspondence and boolean filters uniquely correspond to closed subsets of the subspace consisting of all ultrafilters

a discontinuous galerkin method for higher order ordinary differential equations in this paper we propose a new discontinuous finite element method to solve initial value problems for ordinary differential equations and prove that the finite element solution exhibits an optimal o tp 1 convergence rate in the l2 norm we further show that the p degree discontinuous solution of differential equation of order m and its first m 1 derivatives are o t2p 2 m superconvergent at the end of each step we also establish that the p degree discontinuous solution is o tp 2 superconvergent at the roots of p 1 m degree jacobi polynomial on each step finally we present several computational examples to validate our theory and construct asymptotically correct a posteriori error estimates

discontinuous galerkin discretization and hp refinement for the resolution of the neutron transport equation this paper presents an hp refinement method for a first order scalar transport reaction equation discretized by a discontinuous galerkin method first the theoretical rates of convergence of h and p refinement are recalled and numerically tested then in order to design some meshes we propose two different estimators of the local error on the spatial domain these quantities are analyzed and compared depending on the regularity of the solution so as to find the best way to lead the refinement process and the best strategy to choose between h and p refinement finally the different possible refinement strategies are compared first on analytical examples and then on realistic applications for neutron transport in a nuclear reactor core

hp version discontinuous galerkin methods for hyperbolic conservation laws abstract the development of hp version discontinuous galerkin methods for hyperbolic conservation laws is presented in this work a priori error estimates are derived for a model class of linear hyperbolic conservation laws these estimates are obtained using a new mesh dependent norm that reflects the dependence of the approximate solution on the local element size and the local order of approximation the results generalize and extend previous results on mesh dependent norms to hp version discontinuous galerkin methods a posteriori error estimates which provide bounds on the actual error are also developed in this work numerical experiments verify the a priori estimates and demonstrate the effectiveness of the a posteriori estimates in providing reliable estimates of the actual error in the numerical solution

a posteriori error estimation for the method of lumped masses applied to second order hyperbolic problems we develop a posteriori finite element discretization error estimates for the method of lumped masses applied to the wave equation in one dimension we show that the significant part of the spatial finite element error is proportional to a lobatto polynomial and an error estimate is obtained by solving a set of local elliptic problems in two dimensions we show that the dichotomy principle of babuska and yu still holds for even degree approximations error estimates are computed by solving a set of local elliptic problems and for odd degree approximations an error estimate is computed using jumps of solution gradients across element boundaries this study also extends known superconvergence results for elliptic and parabolic problems l b whalbin superconvergence in galerkin finite element methods springer verlag new york 1995 26 to the method of lumped masses for second order hyperbolic problems

a posteriori discontinuous galerkin error estimation on tetrahedral meshes abstract in this manuscript we present a simple and efficient a posteriori error estimation procedure for a discontinuous finite element method applied to scalar first order hyperbolic problems on structured and unstructured tetrahedral meshes we present a local error analysis to derive a discontinuous galerkin orthogonality condition for the leading term of the discretization error and find basis functions spanning the error we describe an implicit error estimation procedure for the leading term of the discretization error by solving a local problem on each tetrahedron numerical computations show that the implicit a posteriori error estimation procedure yields accurate estimates for linear and nonlinear problems with smooth solutions furthermore we show the performance of our error estimates on problems with discontinuous solutions