projected score methods for approximating conditional scores summary this paper extends the projected score methods of small mcleish 1989 it is shown that the conditional score function may be approximated with arbitrarily small stochastic error in terms of a natural basis for the space of centred likelihood ratios the utility of using this basis is established by identifying a u statistic representation theorem and a class of expectation identities for the basis elements making higher order asymptotics more tractable the results are applied to a canonical exponential family model where it is shown that the projected scores with estimated nuisance parameters can provide an accurate approximation to the conditional score function

a simple and accurate method for approximate conditional inference applied to exponential family models summary a simple method for approximate conditional inference is described the methodology is applied to natural exponential family models where it is shown to provide accurate approximations to fully conditional estimates the approximation technique can be applied much more generally than in this particular class of models the technique depends only on the construction of certain projected scores derived from higher order likelihood derivatives and their covariances and so can be used in many problems where it is relevant to control for the estimation of nuisance parameters

the hp local discontinuous galerkin method for low frequency time harmonic maxwell equations the local discontinuous galerkin method for the numerical approximation of the time harmonic maxwell equations in a low frequency regime is introduced and analyzed topologically nontrivial domains and heterogeneous media are considered containing both conducting and insulating materials the presented method involves discontinuous galerkin discretizations of the curl curl and grad div operators derived by introducing suitable auxiliary variables and so called numerical fluxes an hp analysis is carried out and error estimates that are optimal in the meshsize h and slightly suboptimal in the approximation degree p are obtained

simple relaxed conditional likelihood when the data are sparse but not exceedingly so we face a trade off between bias and precision that makes the usual choice between conducting either a fully unconditional inference or a fully conditional inference unduly restrictive we propose a method to relax the conditional inference that relies upon commonly available computer outputs in the rectangular array asymptotic setting the relaxed conditional maximum likelihood estimator has smaller bias than the unconditional estimator and smaller mean square error than the conditional estimator

secret sharing schemes from three classes of linear codes secret sharing has been a subject of study for over 20 years and has had a number of real world applications there are several approaches to the construction of secret sharing schemes one of them is based on coding theory in principle every linear code can be used to construct secret sharing schemes but determining the access structure is very hard as this requires the complete characterization of the minimal codewords of the underlying linear code which is a difficult problem in general in this paper a sufficient condition for all nonzero codewords of a linear code to be minimal is derived from exponential sums some linear codes whose covering structure can be determined are constructed and then used to construct secret sharing schemes with nice access structures

a priori and posteriori error analysis for time dependent maxwell s equations abstract we consider time dependent maxwell s equations discretized by variable time steps in time domain and edge elements in spatial domain first the stability and optimal a priori error estimate are proved for both semi and fully discrete schemes then a posteriori error analysis is carried out for both schemes

on secret sharing systems a secret sharing system permits a secret to be shared among n trustees in such a way that any k of them can recover the secret but any k 1 have complete uncertainty about it a linear coding scheme for secret sharing is exhibited which subsumes the polynomial interpolation method proposed by shamir and can also be viewed as a deterministic version of blakley s probabilistic method bounds on the maximum value of n for a given k and secret size are derived for any system linear or nonlinear the proposed scheme achieves the lower bound which for practical purposes differs insignificantly from the upper bound the scheme may be extended to protect several secrets methods to protect against deliberate tampering by any of the trustees are also presented

analysis of variable degree hdg methods for convection diffusion equations part ii semimatching nonconforming meshes in this paper we provide a projection based analysis of the hversion of the hybridizable discontinuous galerkin methods for convectiondiffusion equations on semimatching nonconforming meshes made of simplexes the degrees of the piecewise polynomials are allowed to vary from element to element we show that for approximations of degree k on all elements the order of convergence of the error in the diffusive flux is k 1 and that that of a projection of the error in the scalar unknown is 1 for k 0 and k 2 for k 0 we also show that for the variable degree case the projection of the error in the scalar variable is h times the projection of the error in the vector variable provided a simple condition is satisfied for the choice of the degree of the approximation on the elements with hanging nodes these results hold for any bounded irregularity index of the nonconformity of the mesh moreover our analysis can be extended to hypercubes

estimating dynamic panel data discrete choice models with fixed effects abstract this paper considers the estimation of dynamic binary choice panel data models with fixed effects it is shown that the modified maximum likelihood estimator mmle used in this paper reduces the order of the bias in the maximum likelihood estimator from o t 1 to o t 2 without increasing the asymptotic variance no orthogonal reparametrization is needed monte carlo simulations are used to evaluate its performance in finite samples where t is not large in probit and logit models containing lags of the endogenous variable and exogenous variables the estimator is found to have a small bias in a panel with eight periods a distinctive advantage of the mmle is its general applicability estimation and relevance of different policy parameters of interest in this kind of models are also addressed

a projection based error analysis of hdg methods we introduce a new technique for the error analysis of hybridizable discontinuous galerkin hdg methods the technique relies on the use of a new projection whose design is inspired by the form of the numerical traces of the methods this renders the analysis of the projections of the discretization errors simple and concise by showing that these projections of the errors are bounded in terms of the distance between the solution and its projection our studies of influence of the stabilization parameter are reduced to local analyses of approximation by the projection we illustrate the technique on a specific hdg method applied to a model second order elliptic problem

a priori and computable a posteriori error estimates for an hdg method for the coercive maxwell equations abstract in this paper we present and analyze a hybridizable discontinuous galerkin hdg method for a mixed curl curl formulation of the steady state coercive maxwell equations with a discrete sobolev embedding type estimates for the discontinuous polynomials we provide a priori error estimates for the electric field and the lagrange multiplier in the energy norm with the smooth or minimal regularity assumption on the exact solution we have optimal convergence rate for the electric field and the lagrange multiplier in the energy norm the a priori error estimate for the electric field in the l 2 norm is also obtained by the duality argument and the approximation is also optimal for the electric field in the l 2 norm moreover by employing suitable helmholtz decompositions of the error together with the upper bound estimate for the lagrange multiplier we provide a computable residual based a posteriori error estimator which is derived based on the error measured in terms of a mesh dependent energy norm the efficiency of the a posteriori error estimator is also established three dimensional numerical results testing the performance of the a priori and a posteriori error estimates for the maxwell equations are given

asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity consider a sample of size n from a regular exponential family in p n dimensions let hat theta n denote the maximum likelihood estimator and consider the case where p n tends to infinity with n and where theta n is a sequence of parameter values in r p n moment conditions are provided under which hat theta n theta n o p sqrt p n n and hat theta n theta n overline x n o p p n n where overline x n is the sample mean the latter result provides normal approximation results when p 2 n n rightarrow 0 it is shown by example that even for a single coordinate of hat theta n theta n p 2 n n rightarrow 0 may be needed for normal approximation however if p 3 2 n n rightarrow 0 the likelihood ratio test statistic lambda for a simple hypothesis has a chi square approximation in the sense that 2 log lambda p n sqrt 2p n rightarrow d mathscr n 0 1

a simple method for the adjustment of profile likelihoods summary we propose a simple adjustment for profile likelihoods the aim of the adjustment is to alleviate some of the problems inherent in the use of profile likelihoods such as bias inconsistency and overoptimistic variance estimates the adjustment is applied to the profile loglikelihood score function at each parameter value so that its mean is zero and its variance is the negative expected derivative matrix of the adjusted score function for cases in which explicit calculation of the adjustments is difficult we give two methods to simplify their computation an automatic simulation method that requires as input only the profile loglikelihood and its first few derivatives first order asymptotic expressions some examples are provided and a comparison is made with the conditional profile log likelihood of cox and reid

asymptotics for panel quantile regression models with individual effects this paper studies panel quantile regression models with individual fixed effects we formally establish sufficient conditions for consistency and asymptotic normality of the quantile regression estimator when the number of individuals n and the number of time periods t jointly go to infinity the estimator is shown to be consistent under similar conditions to those found in the nonlinear panel data literature nevertheless due to the non smoothness of the objective function we had to impose a more restrictive condition on t to prove asymptotic normality than that usually found in the literature the finite sample performance of the estimator is evaluated by monte carlo simulations

smoothed quantile regression for panel data abstract this paper studies fixed effects estimation of quantile regression models for panel data under an asymptotic framework where both the numbers of individuals and time periods grow at the same rate we show that the fixed effects estimator for the smoothed objective function has a limiting normal distribution with a bias in the mean and provide the analytic form of the asymptotic bias we propose a one step bias correction estimator based on the analytic bias formula obtained from the asymptotic analysis importantly our results cover the case that observations are dependent over time we illustrate the effects of the bias correction through simulations

mixed discontinuous galerkin approximation of the maxwell operator we introduce and analyze a discontinuous galerkin discretization of the maxwell operator in mixed form here all the unknowns of the underlying system of partial differential equations are approximated by discontinuous finite element spaces of the same order for piecewise constant coefficients the method is shown to be stable and optimally convergent with respect to the mesh size numerical experiments highlighting the performance of the proposed method for problems with both smooth and singular analytical solutions are presented

stabilized interior penalty methods for the time harmonic maxwell equations we propose stabilized interior penalty discontinuous galerkin methods for the indefinite time harmonic maxwell system the methods are based on a mixed formulation of the boundary value problem chosen to provide control on the divergence of the electric field we prove optimal error estimates for the methods in the special case of smooth coefficients and perfectly conducting boundary using a duality approach

on the unbiased asymptotic normality of quantile regression with fixed effects abstract nonlinear panel data models with fixed individual effects provide an important set of tools for describing microeconometric data in a large class of such models including probit proportional hazard and quantile regression to name just a few it is impossible to difference out the individual effects and inference is usually justified in a large n large t asymptotic framework however there is a considerable gap in the type of assumptions that are currently imposed in models with smooth score functions such as probit and proportional hazard and quantile regression in the present paper we show that this gap can be bridged and establish unbiased asymptotic normality for fixed effects quantile regression panels under conditions on n t that are very close to what is typically assumed in standard nonlinear panels our results considerably improve upon existing theory and show that quantile regression is applicable to the same type of panel data in terms of n t as other commonly used nonlinear panel data models thorough numerical experiments confirm our theoretical findings

an absolutely stable discontinuous galerkin method for the indefinite time harmonic maxwell equations with large wave number this paper develops and analyzes an interior penalty discontinuous galerkin ipdg method using piecewise linear polynomials for the indefinite time harmonic maxwell equations with the impedance boundary condition in the three dimensional space the main novelties of the proposed ipdg method include the following first the method penalizes not only the jumps of the tangential component of the electric field across the element faces but also the jumps of the tangential component of its vorticity field second the penalty parameters are taken as complex numbers of negative imaginary parts for the differential problem we prove that the sesquilinear form associated with the maxwell problem satisfies a generalized weak stability i e inf sup condition for star shaped domains such a generalized weak stability readily infers wave number explicit a priori estimates for the solution of the maxwell problem which plays an important role in the error analysis for the ipdg method for the proposed ipdg metho

projection as a method for increasing sensitivity and eliminating nuisance parameters l article analyse des methodes statistiques basees sur les fonctions d estimation qui sont des fonctions de parametres et de donnees a la fois destinees a permettre une inference sur un parametre inconnu une methode de projection peut etre utilisee pour la reduction de ces fonctions afin d accroitre la puissance d un test et l efficacite d un estimateur ponctuel ou bien de rendre une fonction d inference insensible a la valeur d un parametre de nuisance

hybridizable discontinuous galerkin methods for the time harmonic maxwell s equations we present two hybridizable discontinuous galerkin hdg methods for the numerical solution of the time harmonic maxwell s equations the first hdg method explicitly enforces the divergence free condition and thus necessitates the introduction of a lagrange multiplier it produces a linear system for the degrees of freedom of the approximate traces of both the tangential component of the vector field and the lagrange multiplier the second hdg method does not explicitly enforce the divergence free condition and thus results in a linear system for the degrees of freedom of the approximate trace of the tangential component of the vector field only for both hdg methods the approximate vector field converges with the optimal order of k 1 in the l 2 norm when polynomials of degree k are used to represent all the approximate variables we propose elementwise postprocessing to obtain a new h c u r l conforming approximate vector field which converges with order k 1 in the h c u r l norm we present extensive numerical examples to demonstrate and compare the performance of the hdg methods

incidental versus random nuisance parameters let p vartheta eta vartheta eta in theta times h with theta subset mathbb r and h arbitrary be a family of mutually absolutely continuous probability measures on a measurable space x mathscr a the problem is to estimate vartheta based on a sample x 1 cdots x n from times n 1 p vartheta eta nu if eta 1 cdots eta n are independently distributed according to some unknown prior distribution gamma then the distribution of n 1 2 vartheta n vartheta under p n vartheta gamma p vartheta gamma being the gamma mixture of p vartheta eta eta in h cannot be more concentrated asymptotically than a certain normal distribution with mean 0 say n 0 sigma 2 0 vartheta gamma folklore says that such a bound is also valid if eta 1 cdots eta n are just unknown values of the nuisance parameter in this case the distribution cannot be more concentrated asymptotically than n 0 sigma 2 0 vartheta e n eta 1 cdots eta n where e n eta 1 cdots eta n is the empirical distribution of eta 1 cdots eta n the purpose of the present paper is to discuss to which extent this conjecture is true the results are summarized at the end of sections 1 and 3

an a posteriori error estimate for the variable degree raviart thomas method we propose a new a posteriori error analysis of the variable degree hybridized version of the raviart thomas method for second order elliptic problems on conforming meshes made of simplexes we establish both the reliability and eciency of the estimator for the l2 norm of the error of the ux we also nd the explicit dependence of the estimator on the order of the local spaces k 0 the only constants that are not explicitly computed are those depending on the shape regularity of the simplexes in particular the constant of the local eciency in equality is proven to behave like k 2 3 2 however we present numer ical experiments suggesting that such constant is actually independent of k

jackknife and analytical bias reduction for nonlinear panel models fixed effects estimators of panel models can be severely biased because of the well known incidental parameters problem we show that this bias can be reduced by using a panel jackknife or an analytical bias correction motivated by large t we give bias corrections for averages over the fixed effects as well as model parameters we find large bias reductions from using these approaches in examples we consider asymptotics where t grows with n as an approximation to the properties of the estimators in econometric applications we show that if t grows at the same rate as n the fixed effects estimator is asymptotically biased so that asymptotic confidence intervals are incorrect but that they are correct for the panel jackknife we show t growing faster than n 1 3 suffices for correctness of the analytic correction a property we also conjecture for the jackknife

conditional score functions some optimality results summary the conditional score function has previously been shown to generate the optimal estimating equation for a parameter of interest when the conditioning statistic is complete and sufficient for the nuisance parameters godambe 1976 the present paper generalizes these results to partial likelihood factorizations and then examines the nature of the problem when the appropriate conditioning statistics depend on the parameter of interest in this case globally optimal estimating functions are impossible a weaker criterion of optimal weighting leads to a class of estimated conditional score functions which satisfy an information equality the purpose of this paper is to develop and justify an approach based on conditional likelihood to estimation in the presence of nuisance parameters the arguments focus on the case when there is a complete and sufficient statistic s 0 for the nuisance parameters when the parameter of interest 0 is fixed an extended notion of completeness will be presented in the context of partial likelihoods the problem takes on two separate natures depending on whether the statistic s 0 truly depends on 0 or not if s s 0 is free of 0 then the conditional likelihood of the data given s has been shown to generate optimal inferential procedures giving a best estimating equation godambe 1976 and a best asymptotically normal estimator in a mixture setting lindsay 1980 if s 0 depends on 0 then it will be shown that the best estimating equation also a conditional likelihood score will generally be only locally optimal leaving no single best strategy consideration of an optimal weighting strategy yields estimators which have second order properties similar to the conditional likelihoods of the first type

a posteriori error estimates for maxwell equations maxwell equations are posed as variational boundary value problems in the function space h curl and are discretized by nedelec finite elements in beck et al 2000 a residual type a posteriori error estimator was proposed and analyzed under certain conditions onto the domain in the present paper we prove the reliability of that error estimator on lipschitz domains the key is to establish new error estimates for the commuting quasi interpolation operators recently introduced in j schoberl commuting quasi interpolation operators for mixed finite elements similar estimates are required for additive schwarz preconditioning to incorporate boundary conditions we establish a new extension result

convergence and quasi optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems recently an adaptive nonconforming finite element method anfem has been developed by carstensen and hoppe in numer math 103 251 266 2006 in this paper we extend the result to some nonsymmetric and indefinite problems the main tools in our analysis are a posteriori error estimators and a quasi orthogonality property in this case we need to overcome two main difficulties one stems from the nonconformity of the finite element space the other is how to handle the effect of a nonsymmetric and indefinite bilinear form an appropriate adaptive nonconforming finite element method featuring a marking strategy based on the comparison of the a posteriori error estimator and a volume term is proposed for the lowest order crouzeix raviart element it is shown that the anfem is a contraction for the sum of the energy error and a scaled volume term between two consecutive adaptive loops moreover quasi optimality in the sense of quasi optimal algorithmic complexity can be shown for the anfem the results of numerical experiments confirm the theoretical findings

a posteriori error estimates for a discontinuous galerkin approximation of second order elliptic problems several a posteriori error estimators are introduced and analyzed for a discontinuous galerkin formulation of a model second order elliptic problem in addition to residual type estimators we introduce some estimators that are couched in the ideas and techniques of domain decomposition results of numerical experiments are presented

robust a posteriori error estimation for the maxwell equations we consider a robust a posteriori error estimator of residual type for the maxwell equations in a bounded two and three dimensional domain the continuous problem is approximated using conforming approximated spaces the main goal is to express the lower and upper bounds with respect to appropriate norms for that purpose a new interpolant of clement nedelec type is introduced and some interpolation error estimates are proved numerical tests are presented which confirm our theoretical results

generalizations of ancillarity completeness and sufficiency in an inference function space on introduit l e ancillarite et l e exhaustivite complete des extensions naturelles des definitions d ancillarite et d exhaustivite complete a l espace des fonctions d estimation ou d inference

poincare friedrichs inequalities for piecewise h 1 functions poincare friedrichs inequalities for piecewise h1 functions are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

breaking spaces and forms for the dpg method and applications including maxwell equations discontinuous petrov galerkin dpg methods are made easily implementable using broken test spaces i e spaces of functions with no continuity constraints across mesh element interfaces broken spaces derivable from a standard exact sequence of first order unbroken sobolev spaces are of particular interest a characterization of interface spaces that connect the broken spaces to their unbroken counterparts is provided stability of certain formulations using the broken spaces can be derived from the stability of analogues that use unbroken spaces this technique is used to provide a complete error analysis of dpg methods for maxwell equations with perfect electric boundary conditions the technique also permits considerable simplifications of previous analyses of dpg methods for other equations reliability and efficiency estimates for an error indicator also follow finally the equivalence of stability for various formulations of the same maxwell problem is proved including the strong form the ultraweak form and various forms in between

adaptive finite element techniques for the maxwell equations using implicit a posteriori error estimates we consider an implicit a posteriori error estimation technique for the adaptive solution of the maxwell equations with nedelec edge finite element methods on three dimensional domains on each element of the tessellation an equation for the error is formulated and solved with a properly chosen local finite element basis the discrete bilinear form of the local problems is shown to satisfy an inf sup condition which ensures the well posedness of the error equations an adaptive solution algorithm is developed based on the obtained error estimates the performance of the method is tested on various problems including non convex domains with non smooth boundaries the numerical results show that the estimated error computed by the implicit a posteriori error estimation technique correlates well with the actual error on the meshes generated adaptively with the help of the error estimator the achieved accuracy is higher than on globally refined meshes with comparable number degrees of freedom moreover the rate of the error convergence on the locally adapted meshes is faster than that on the globally refined meshes

convergence and optimality of adaptive edge finite element methods for time harmonic maxwell equations we consider a standard adaptive edge finite element method aefem based on arbitrary order nedelec edge elements for three dimensional indefinite time harmonic maxwell equations we prove that the aefem gives a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops provided the initial mesh is fine enough using the geometric decay we show that the aefem yields the best possible decay rate of the error plus oscillation in terms of the number of degrees of freedom the main technical contribution of the paper is in the establishment of a quasi orthogonality and a localized a posteriori error estimator

secure erasure codes with partial reconstructibility we design p reconstructible mu secure n k erasure coding schemes 0 leq mu which encode k mu information symbols into n coded symbols and moreover satisfy the k out of n property and the following two properties p1 strongly mu secure an adversary that accesses at most mu coded symbols gains no information about the information symbols p2 p reconstructible a legitimate user can reconstruct each predetermined group of p information symbols by accessing a predetermined group of mu p coded symbols the scheme is perfectly p reconstructible mu secure if apart from p1 p2 it also satisfies the following additional property p3 weakly mu p 1 secure an adversary that accesses at most mu p 1 coded symbols cannot reconstruct any single information symbol in contrast with most related work in the literature our codes guarantee partial reconstructibility due to p2 once the user accesses p more coded symbols than the threshold mu it can reconstruct a specific group of p information symbols we provide an explicit construction of p reconstructible mu secure coding schemes for all mu and p over any field of size at least n 1 we also establish a randomized construction for perfectly p reconstructible mu secure coding schemes for all mu and p satisfying k geq 2 mu p 1 over any field of size at least n k k 3 4

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

locally divergence free discontinuous galerkin methods for the maxwell equations in this paper we develop the locally divergence free discontinuous galerkin method for numerically solving the maxwell equations the distinctive feature of the method is the use of approximate solutions that are exactly divergence free inside each element as a consequence this method has a smaller computational cost than that of the discontinuous galerkin method with standard piecewise polynomial spaces we show that in spite of this fact it produces approximations of the same accuracy we also show that this method is more efficient than the discontinuous galerkin method using globally divergence free piecewise polynomial bases finally a post processing technique is used to recover 2k 1 th order of accuracy when piecewise polynomials of degree k are used

efficiency of projected score methods in rectangular array asymptotics summary the paper considers a rectangular array asymptotic embedding for multistratum data sets in which both the number of strata and the number of within stratum replications increase and at the same rate it is shown that under this embedding the maximum likelihood estimator is consistent but not efficient owing to a non zero mean in its asymptotic normal distribution by using a projection operator on the score function an adjusted maximum likelihood estimator can be obtained that is asymptotically unbiased and has a variance that attains the cram6r rao lower bound the adjusted maximum likelihood estimator can be viewed as an approximation to the conditional maximum likelihood estimator

a convergent nonconforming adaptive finite element method with quasi optimal complexity in this paper we prove convergence and quasi optimal complexity of a simple adaptive nonconforming finite element method in each step of the algorithm the iterative solution of the discrete system is controlled by an adaptive stopping criterion and the local refinement is based on either a simple edge residual or a volume term depending on an adaptive marking strategy we prove that this marking strategy guarantees a strict reduction of the error augmented by the volume term and an additional oscillation term and quasi optimal complexity of the generated sequence of meshes

discrete functional analysis tools for discontinuous galerkin methods with application to the incompressible navier stokes equations two discrete functional analysis tools are established for spaces of piecewise polynomial functions on general meshes i a discrete counterpart of the continuous sobolev embeddings in both hilbertian and non hilbertian settings ii a compactness result for bounded sequences in a suitable discontinuous galerkin norm together with a weak convergence property for some discrete gradients the proofs rely on techniques inspired by the finite volume literature which differ from those commonly used in finite element analysis the discrete functional analysis tools are used to prove the convergence of discontinuous galerkin approximations of the steady incompressible navier stokes equations two discrete convective trilinear forms are proposed a non conservative one relying on temam s device to control the kinetic energy balance and a conservative one based on a nonstandard modification of the pressure

energy norm a posteriori error estimation for mixed discontinuous galerkin approximations of the maxwell operator in this paper we develop the a posteriori error estimation of mixed discontinuous galerkin finite element approximations of the maxwell operator in particular by employing suitable helmholtz decompositions of the error together with the conservation properties of the underlying method computable upper bounds on the error measured in terms of a natural mesh dependent energy norm are derived numerical experiments testing the performance of our a posteriori error bounds for problems with both smooth and singular analytical solutions are presented

an adaptive multilevel method for time harmonic maxwell equations with singularities we develop an adaptive edge finite element method based on reliable and efficient residual based a posteriori error estimates for low frequency time harmonic maxwell equations with singularities the resulting discrete problem is solved by the multigrid preconditioned minres minimum residual iteration algorithm we demonstrate the efficiency and robustness of the proposed method by extensive numerical experiments for cavity problems with singular solutions which include in particular scattering over screens

a posteriori error estimation and adaptive mesh refinement techniques abstract we analyse three different a posteriori error estimators for elliptic partial differential equations they are based on the evaluation of local residuals with respect to the strong form of the differential equation on the solution of local problems with neumann boundary conditions and on the solution of local problems with dirichlet boundary conditions we prove that all three are equivalent and yield global upper and local lower bounds for the true error thus adaptive mesh refinement techniques based on these estimators are capable to detect local singularities of the solution and to appropriately refine the grid near these singularities some numerical examples prove the efficiency of the error estimators and the mesh refinement techniques