a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

mass lumping emanating from residual free bubbles a nodally exact scheme is derived for a model equation in 1d involving zeroth and second order terms the method is derived using residual free bubbles in conjunction with the galerkin approximation it is shown that this approach leads to the mass lumping scheme for sufficiently small mesh sizes

an analysis of the discontinuous galerkin method for a scalar hyperbolic equation we prove lp stability and error estimates for the discontinuous galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain using finite element analysis techniques we obtain l2 estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials lp estimates for p 2 are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree the latter estimates are proved by combining finite difference and finite element analysis techniques

dispersion analysis and element free galerkin solutions of second and fourth order gradient enhanced damage models gradient dependent damage formulations incorporate higher order derivatives of state variables in the constitutive equations different formulations have been derived for this gradient enhancement comparison of which is difficult in a finite element context due to higher order continuity requirements for certain formulations on the other hand the higher order continuity requirements are met naturally by element free galerkin efg shape functions thus the efg method provides a suitable tool for the assessment of gradient enhanced continuum models dispersion analyses have been carried out to compare different gradient enhanced models with the non local damage model the formulation of the additional boundary conditions is addressed numerical examples show the objectivity with respect to the discretization and the differences between various gradient formulations with second and fourth order derivatives it is shown that with the same underlying internal length scale very different results can be obtained copyright 2000 john wiley sons ltd

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

continuous discontinuous finite element approximations of fourth order elliptic problems in structural and continuum mechanics with applications to thin beams and plates and strain gradient elasticity abstract a new finite element method for fourth order elliptic partial differential equations is presented and applied to thin bending theory problems in structural mechanics and to a strain gradient theory problem the method combines concepts from the continuous galerkin cg method the discontinuous galerkin dg method and stabilization techniques a brief review of the cg method the dg method and stabilization techniques highlights the advantages and disadvantages of these methods and suggests a new approach for the solution of fourth order elliptic problems a continuous discontinuous galerkin c dg method is proposed which uses c 0 continuous interpolation functions and is formulated in the primary variable only the advantage of this formulation over a more traditional mixed approach is that the introduction of additional unknowns and related difficulties can be avoided in the context of thin bending theory the c dg method leads to a formulation where displacements are the only degrees of freedom and no rotational degrees of freedom need to be considered the main feature of the c dg method is the weak enforcement of continuity of first and higher order derivatives through stabilizing terms on interior boundaries consistency stability and convergence of the method are shown analytically numerical experiments verify the theoretical results and applications are presented for bernoulli euler beam bending poisson kirchhoff plate bending and a shear layer problem using toupin mindlin strain gradient theory

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

combining probability distributions from dependent information sources inferences or decisions in the face of uncertainty should be based on all available information thus when probability distributions for an uncertain quantity are obtained from experts models or

unlocking with residual free bubbles residual free bubbles are derived for the timoshenko beam problem eliminating these bubbles the resulting formulation is form identical in using the following tricks to the standard variational formulation i one point reduced integration on the shear energy term ii replace its coefficient 1 2 by 1 2 hk212 in each element iii modify consistently the right hand side this final formulation is legally obtained in that the galerkin method enriched with residual free bubbles is developed using full integration throughout furthermore this method is nodally exact by construction

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

modelling agent forecast distributions problems in the analysis and interpretation of uncertain inferences obtained from individuals or agents are considered in the context of forecasting a scalar random quantity based on new theoretical results presented by west and crosse bayesian updating is developed for cases in which agents opinions are proveded in terms of full forecast distributions discrete or continuous or parital summaries such as forecast means and variances a particular focus is on problems in which partial agent information is communicated in terms of a few sumary probabilities or alternatively quantiles of the agent s distribution example models highlight the key features of the theory and illustrate applications

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

analysis of quantization error in line based stereo matching abstract quantization error generated by the quantization process of an image is inherent in computer vision because especially in stereo vision the quantization error in 2d digital images results in position errors in a reconstructed 3d scene it is necessary to analyze stochastically quantization error in stereo vision in this paper an analysis of the probability density function pdf of quantization error in line based stereo matching is presented it is shown that the theoretical pdfs of quantization errors of the reconstructed 3d point positions in line based stereo matching show general forms compared to those of the conventional error analysis in pixel based stereo matching computer simulations are observed to support the theoretical pdfs

modelling probabilistic agent opinion summary a single agent an individual expert or model provides a decision maker with probabilistic information partially or completely describing the agent s opinion about a collection of uncertain quantities or events this paper discusses ways in which the decision maker may model the agent s opinion to provide rules for updating his own probability for a related event or random quantity of particular interest concepts discussed include the relevance of the agent s information and experience the accord between the agent and decision maker in terms of common or conflicting information and calibration of probability assessments new theory develops and extends that of genest and schervish requiring only a partial specification of the decision maker s prior over the agent s opinion several illustrative examples are developed

reconciliation of probability distributions several people each express their opinion of an uncertain quantity by providing their mean and standard deviation of it in this paper we discuss the problem of incorporating all these opinions into a single reconciled probability distribution for the quantity the usual procedure is least squares based on normality the paper illustrates the advantages of using t distributions instead and clarifies the role of the information provided by the standard deviations suitable approximations are provided for many cases

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

bayesian nonparametric calibration and combination of predictive distributions abstractwe introduce a bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights building on the work of ranjan and gneiting we use infinite beta mixtures for the calibration the proposed bayesian nonparametric approach takes advantage of the flexibility of dirichlet process mixtures to achieve any continuous deformation of linearly combined predictive distributions the inference procedure is based on combination gibbs and slice sampling we provide some conditions under which the proposed probabilistic calibration converges in terms of weak posterior consistency to the true underlying density for both cases of iid and markovian observations this calibration property improves upon the earlier calibration approaches we study the methodology in simulation examples with fat tails and multimodal densities and apply it to density forecasts of dail

modeling expert judgments for bayesian updating this paper examines how a bayesian decision maker would update his her probability p for the occurrence of an event a in the light of a number of expert opinions expressed as probabilities q 1 cdots q n of a it is seen among other things that the linear opinion pool lambda 0p sum n i 1 lambda iq i corresponds to an application of bayes theorem when the decision maker has specified only the mean of the marginal distribution for q 1 cdots q n and requires his her formula for the posterior probability of a to satisfy a certain consistency condition a product formula similar to that of bordley 1982 is also derived in the case where the experts are deemed to be conditionally independent given a and given its complement