a residual based a posteriori error estimator for the stokes darcy coupled problem in this paper we develop an a posteriori error analysis of a new conforming mixed finite element method for the coupling of fluid flow with porous media flow the flows are governed by the stokes and darcy equations respectively and the transmission conditions are given by mass conservation balance of normal forces and the beavers joseph saffman law the finite element subspaces consider bernardi raugel and raviart thomas elements for the velocities piecewise constants for the pressures and continuous piecewise linear elements for a lagrange multiplier defined on the interface we derive a reliable and efficient residual based a posteriori error estimator for this coupled problem the proof of reliability makes use of suitable auxiliary problems diverse continuous inf sup conditions satisfied by the bilinear forms involved and local approximation properties of the clement interpolant and raviart thomas operator on the other hand helmholtz decomposition inverse inequalities and the localization technique based on triangle bubble and edge bubble functions are the main tools for proving the efficiency of the estimator up to minor modifications our analysis can be extended to other finite element subspaces yielding a stable galerkin scheme

coupling fluid flow with porous media flow the transport of substances back and forth between surface water and groundwater is a very serious problem we study herein the mathematical model of this setting consisting of the stokes equations in the fluid region coupled with the darcy equations in the porous medium coupled across the interface by the beavers joseph saffman conditions we prove existence of weak solutions and give a complete analysis of a finite element scheme which allows a simulation of the coupled problem to be uncoupled into steps involving porous media and fluid flow subproblems this is important because there are many legacy codes available which have been optimized for uncoupled porous media and fluid flow

a numerical framework for material characterisation of inhomogeneous hyperelastic membranes by inverse analysis an inverse method for estimating the distributions of the elastic properties of hyperelastic inhomogeneous membranes is proposed the material description of the membrane is based on a versatile constitutive model in which two stiffness parameters govern the nonlinear elastic behaviour of the material the estimation procedure includes a finite element framework the two stiffness parameters in the constitutive law are assumed to vary continuously over the inhomogeneous membrane and in the finite element framework the distributions of the two parameters are approximated using standard linear shape functions experimental results are assumed to exist in terms of nodal displacements from a test with known geometry and boundary conditions the experimental membrane is modelled in the finite element framework and the deformation of it is predicted an error function quantifying the discrepancy between the experimentally obtained deformation pattern and the numerically predicted pattern is then minimised with respect to the nodal values of the two interpolated parameters in a number of numerical examples the proposed procedure is assessed by attempting to reproduce the given random reference distributions of material properties the proposed estimation method is fully able to reproduce the reference distributions of the two material parameters with excellent accuracy

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

limits for the precision and value of information from dependent sources in many inferential and decision making situations information is obtained from a number of information sources and the separate pieces of information are often not independent this paper investigates the impact of dependence on the precision and value of information the results indicate that positive dependence among information sources can have a serious detrimental effect on the precision and value of the information differences in precision between the dependent and independent cases can be remarkably large with dependence the incremental value of information can decrease very rapidly and the limiting value of information as more sources are considered can be considerably less than the expected value of perfect information the results of this paper have implications for the acquisition and use of information in decision making problems

marginalization and linear opinion pools abstract suppose a decision maker has asked a group of experts to assess subjective probability distributions over some space and he wishes to find a consensus probability distribution as a function of these the assumption that finding the consensus distribution commutes with marginalization of the distributions implies that the consensus must be found using a linear opinion pool weighted average provided the space being considered contains three or more points some of the consequences of this result are discussed

correlations and copulas for decision and risk analysis the construction of a probabilistic model is a key step in most decision and risk analyses typically this is done by defining a joint distribution in terms of marginal and conditional distributions for the model s random variables we describe an alternative approach that uses a copula to construct joint distributions and pairwise correlations to incorporate dependence among the variables the approach is designed specifically to permit the use of an expert s subjective judgments of marginal distributions and correlations the copula that underlies the multivariate normal distribution provides the basis for modeling dependence but arbitrary marginals are allowed we discuss how correlations can be assessed using techniques that are familiar to decision analysts and we report the results of an empirical study of the accuracy of the assessment methods the approach is demonstrated in the context of a simple example including a study of the sensitivity of the results to the assessed correlations

probability judgments for continuous quantities linear combinations and calibration expert judgment elicitation is often required in probabilistic decision making and the evaluation of risk one measure of the quality of probability distributions given by experts is calibration the faithfulness of the probabilities in an empirically verifiable sense a method of measuring calibration for continuous probability distributions is presented here a discussion of the impact of using linear rules for combining such judgments is given and an empirical demonstration is given using data collected from experts participating in a large scale risk study it is shown by theoretical argument that combining well calibrated distributions of individual experts using linear rules can only result in reducing calibration in contrast it is demonstrated both by example and empirically that an equally weighted linear combination of experts who tend to be overconfident can produce distributions that are better calibrated than the experts individual distributions using data from training exercises it is shown that the improvement in calibration is rapid as the number of experts is increased from one to five or six but there is only modest improvement from increasing the number of experts beyond that point

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

note on the aggregation of individual probability estimates this note considers the problem of aggregating individual probability estimates of an event to obtain a group estimate norman dalkey has argued that no rigorous theory of probability aggregation is possible for the following reasons 1 there is no consistent way of aggregating individual probability estimates dalkey s impossibility theorem but dalkey s impossibility theorem makes what we call the context free assumption namely that the group estimate of an event s probability is a function only of the estimates of the individuals and in particular is not dependent on the event in question we argue that the context free assumption is unreasonable and present several known aggregation methods which don t make it 2 although there is a bayesian approach to the problem it requires that the estimates of all but at most one of the experts be independent of the event in question to make this argument dalkey assumed both a1 the individual estimates are independent random variables and a2 given the occurrence or nonoccurrence of the event the individual estimates are independent random variables this paper presents an alternate derivation of the result abstracting from dalkey s context the point is that dalkey s result is simply a consequence of assuming both a1 and a2 it is unreasonable to assume both a1 and a2 and hence dalkey s result does not discredit the bayesian approach thus this paper resolves some theoretical objections to the possibility of a rigorous theory of aggregation furthermore it clarifies the nature of the context free assumption and the independence assumptions a1 and a2

maximum principle preserving schemes for interface problems with discontinuous coefficients new finite difference methods using cartesian grids are developed for elliptic interface problems with variable discontinuous coefficients singular sources and nonsmooth or even discontinuous solutions the new finite difference schemes are constructed to satisfy the sign property of the discrete maximum principle using quadratic optimization techniques the methods are shown to converge under certain conditions using comparison functions the coefficient matrix of the resulting linear system of equations is an m matrix and is coupled with a multigrid solver numerical examples are also provided to show the efficiency of the proposed methods

a conflict between two axioms for combining subjective distributions with the development of multi agent statistical decision theory weerahandi and zidek 1981 1983 considerable attention has recently been paid to the problem of combining the diverse beliefs of a group of individuals more specifically if n 2 bayesians formulate their opinions about some quantity 0 in terms of subjective probability densities fi fn on e the parameter space a consensual density t fi fn is desired which could then be used in a conventional uni bayesian analysis owing in part to the complexity of existing solution schemes based on the bayesian inferential framework morris 1974 1977 french 1980 various axioms have been proposed in the literature which purport to embrace the minimal requirements that a pooling formula t should satisfy this note points out a serious incompatibility between two such conditions which are often individually imposed on pooling operators when the two are used simultaneously the resulting procedure is seen to depend on the opinion of a single expert

expert elicitation of adversary preferences using ordinal judgments we introduce a simple elicitation process where subject matter experts provide only ordinal judgments of the attractiveness of potential targets and the adversary utility of each target is assumed to involve multiple attributes probability distributions over the various attribute weights are then mathematically derived using either probabilistic inversion or bayesian density estimation this elicitation process reduces the burden of time consuming orientation and training in traditional methods of attribute weight elicitation and explicitly captures the existing uncertainty and disagreement among experts rather than attempts to achieve consensus by eliminating them we identify the relationship between the two methods and conduct sensitivity analysis to elucidate how these methods handle expert consensus or disagreement we also present a real world application on elicitation of adversarial preferences over various attack scenarios to show the applicability of our proposed methods

characterization of the mechanical properties of skin by inverse analysis combined with the indentation test this study proposes a new method to determine the mechanical properties of human skin by the use of the indentation test pailler mattei 2004 caracterisation mecanique et tribologique de la peau humaine in vivo ph d thesis ecl no 2004 31 pailler mattei zahouani 2004 journal of adhesion science and technology 18 1739 1758 the principle of the measurements consists in applying an in vivo compressive stress zhang et al 1994 proceedings of the institution of mechanical engineers 208 217 222 bosboom et al 2001 journal of biomechanics 34 1365 1368 oomens et al 1984 selected proceedings of meetings of european society of biomechanics pp 227 232 oomens et al 1987 journal of biomechanics 20 9 877 885 on the skin tissue of an individual s forearm these measurements show an increase in the normal contact force as a function of the indentation depth the interpretation of such results usually requires a long and tedious phenomenological study we propose a new method to determine the mechanical parameters which control the response of skin tissue this method is threefold experimental numerical and comparative it consists combining experimental results with a numerical finite elements model in order to find out the required parameters this process uses a scheme of extended kalman filters ekf gu et al 2003 materials science and engineering a345 223 233 nakamura et al 2000 acta mater 48 4293 4306 leustean and rosu 2003 certifying kalman filters riacs technical report 03 02 27pp http gureni cs uiuc edu grosu download luta leo pdf welch and bishop an introduction to kalman filter university of north carolina at chapel hill 16p http www cs unc edu welch kalman the first results presented in this study correspond to a simplified numerical modeling of the global system the skin is assumed to be a semi infinite layer with an isotropic linear elastic mechanical behavior zhang et al 1994 proceedings of the institution of mechanical engineers 208 217 222 this analysis will be extended to more realistic models in further works

numerical solution to a mixed navier stokes darcy model by the two grid approach we study numerical methods for a coupled navier stokes darcy model which describes a fluid flow filtrating through porous media a decoupled and linearized two grid algorithm is proposed numerical analysis and experiments are presented to show the efficiency and effectiveness of the decoupled and linearized algorithm

an augmented cartesian grid method for stokes darcy fluid structure interactions summary a new finite difference method based on cartesian meshes is proposed for solving the fluid structure interaction between a fluid flow modeled by the stokes equations and a porous media modeled by the darcy s law the idea is to introduce several augmented variables along the interface between the fluid flow and the porous media so that the problem can be decoupled as several poisson equations the augmented variables should be chosen so that the beavers joseph saffman and other interface conditions are satisfied in the discretization the augmented variables have co dimension one compared with that of the primitive variables and are solved through the schur complement system a non trivial analytic solution with a circular interface is constructed to check second order convergency of the proposed method numerical examples with various interfaces and parameters are also presented some simulations show interesting behaviors of the fluid structure interaction between the fluid flow and the porous media the computational framework can be applied to other multi phase and multi physics problems copyright 2015 john wiley sons ltd

a mixture approach to the mechanics of skin skin can be considered to be a mixture of a solid and a fluid a general theory for the description of the behaviour of mixtures is presented and applied to a mixture of a solid and a fluid a numerical procedure is presented to solve the non linear field equations describing such a mixture the abilities of the procedure are demonstrated by means of a confined compression test

a strongly conservative finite element method for the coupling of stokes and darcy flow we consider a model of coupled free and porous media flow governed by stokes and darcy equations with the beavers joseph saffman interface condition this model is discretized using divergence conforming finite elements for the velocities in the whole domain discontinuous galerkin techniques and mixed methods are used in the stokes and darcy subdomains respectively this discretization is strongly conservative in h d i v w and we show convergence numerical results validate our findings and indicate optimal convergence orders

elastic properties of anisotropic vascular membranes examined by inverse analysis an inverse method for estimating the distributions of the nonlinear elastic properties of inhomogeneous and anisotropic vascular membranes such as cerebral aneurysms is proposed the material description of the membrane is based on a versatile structural model able to represent multiple collagen layers and the passive response of the vascular wall each individual layer is assumed to behave transversely isotropic following exponential stiffening with increasing loading the model includes four parameters to be explainable physically two initial stiffnesses of the collagen fabric a parameter related to the nonlinearity of the collagen fabric angle between the principal directions of the collagen fabric and a reference coordinate system for this finite deformation problem a finite element framework for membranous structures considering pressure boundary loading is outlined i e the principle of virtual work its linearisation and the related spatial discretisation the estimation procedure consists of the following three steps i in vivo or in vitro approaches record the mechanical responses of membranous structures whose properties are to be determined ii define a corresponding finite element model iii minimise an error function regarding the unknown parameters that quantifies the deviation of the numerical prediction from the recorded data to achieve a robust parameter estimation an element partition method is employed the outcome of the procedure is affected by the number of nodes defined on the membrane surface and the number of load steps in a numerical example the proposed procedure is assessed by reestablishing given reference distributions in a reference membrane the deviations of the estimated material parameter distributions from the related reference fields are within just a few percent in most of the investigated cases the standard deviation for the resulting maximum principal stress was even below 1 which is accurate enough for rupture risk assessment of vascular membranes

an analytic method for evaluating the performance of aggregation rules for probability densities it is shown how infinite sequences of densities with defined properties can be used to evaluate the expected performance of mathematical aggregation rules for elicited densities the performance of these rules is measured through the average variance calibration and average brier score of the aggregates a general result for the calibration of the arithmetic average of densities from well calibrated independent experts is given arithmetic and geometric aggregation rules are compared using sequences of normal densities sequences are developed that exhibit dependence among experts and lack of calibration the impact of correlation number of experts and degree of calibration on the performance of the aggregation is demonstrated