weak and strong solutions for the incompressible navier stokes equations with damping in this paper we show that the cauchy problem of the navier stokes equations with damping u 1u 0 has global weak solutions for any 1 global strong solution for any 7 2 and that the strong solution is unique for any 7 2 5

numerical discretization of a darcy forchheimer model we solve a steady darcy forchheimer flow in a bounded region by means of piecewise constant velocities and nonconforming piecewise mathbb p 1 pressures for the computation we solve the nonlinearity by an alternating directions algorithm and we decouple the computation of the velocity from that of the pressure by a gradient algorithm we prove a priori error estimates of the scheme and convergence of the alternating directions algorithm

stabilized multiscale finite element method for the stationary navier stokes equations abstract in the paper a stabilized multiscale finite element method for the stationary incompressible navier stokes equations is considered the method is a petrov galerkin approach based on the multiscale enrichment of the standard polynomial space enriched with the unusual bubble functions which no longer vanish on every element boundary for the velocity space the stability of the p 1 p 0 triangular element or the q 1 p 0 quadrilateral element is established and the optimal error estimates of the stabilized multiscale finite element method for the stationary navier stokes equations are obtained

a new mixed finite element formulation and the mac method for the stokes equations a new mixed finite element method is formulated for the stokes equations in which the two components of the velocity and the pressure are defined on different meshes first order error estimates are obtained for both the velocity and the pressure also the well known mac method is derived from the resulting finite element method

entropy constrained halftoning using multipath tree coding we suggest an optimization based method for halftoning that involves looking ahead before a decision for each binary output pixel is made we first define a mixture distortion criterion that is a combination of a frequency weighted mean square error mse and a measure depending on the distances between minority pixels in the halftone a tree coding approach with the ml algorithm is used for minimizing the distortion criterion to generate a halftone while this approach generates halftones of high quality these halftones are not very amenable to lossless compression we introduce an entropy constraint into the cost function of the tree coding algorithm that optimally trades off between image quality and compression performance in the output halftones

on convergence of block centered finite differences for elliptic problems we consider linear selfadjoint elliptic problems with neumann boundary conditions in rectangular domains we demonstrate that with sufficiently smooth data the discrete l 2 norm errors for tensor product block centered finite differences in both the approximate solution and its first derivatives are second order for all nonuniform grids extensions to nonselfadjoint and parabolic problems are discussed

existence of a solution of the wave equation with nonlinear damping and source terms abstract we study the nonlinear wave equation involving the nonlinear damping term u t u t m 1 and a source term of type u u p 1 for 1 p m we prove a global existence theorem with large initial data for 1 m p a blow up result is established for sufficiently large initial data

existence of global weak solutions for a 2d viscous shallow water equations and convergence to the quasi geostrophic model we consider a two dimensional viscous shallow water model with friction term existence of global weak solutions is obtained and convergence to the strong solution of the viscous quasi geostrophic equation with free surface term is proven in the well prepared case the ill prepared data case is also discussed

stability and superconvergence of mac scheme for stokes equations on nonuniform grids the marker and cell mac method a class of finite volume schemes based on staggered grids has been one of the simplest and most effective numerical schemes for solving the stokes and navier sto

convergence of the mac scheme for the compressible stokes equations we prove in this paper the convergence of the marker and cell mac scheme for the discretization of the steady state compressible stokes equations on two or three dimensional cartesian grids the existence of a solution to the scheme is proven followed by estimates on approximate solutions which yield the convergence of the approximate solutions up to a subsequence and in an appropriate sense we then prove that the limit of the approximate solutions satisfies the mass and momentum balance equations as well as the equation of state which is the main difficulty of this study

a new stabilized finite element method for the transient navier stokes equations abstract this paper is concerned with the development and analysis of a new stabilized finite element method based on two local gauss integrations for the two dimensional transient navier stokes equations by using the lowest equal order pair of finite elements this new stabilized finite element method has some prominent features parameter free avoiding higher order derivatives or edge based data structures and stabilization being completely local at the element level an optimal error estimate for approximate velocity and pressure is obtained by applying the technique of the galerkin finite element method under certain regularity assumptions on the solution compared with other stabilized methods using the same pair of mixed finite elements for the two dimensional transient navier stokes equations through a series of numerical experiments it is shown that this new stabilized method has better stability and accuracy results

a stabilized implicit fractional step method for the time dependent navier stokes equations using equal order pairs abstract a stabilized implicit fractional step method for numerical solutions of the time dependent navier stokes equations is presented in this paper the time advancement is decomposed into a sequence of two steps the first step has the structure of the linear elliptic problem the second step can be seen as the generalized stokes problem the two problems satisfy the full homogeneous dirichlet boundary conditions on the velocity on the other hand a locally stabilized term is added in the second step of the schemes it allows one to enhance the numerical stability and efficiency by using the equal order pairs convergence analysis and error estimates for the velocity and pressure of the schemes are established via the energy method some numerical experiments are also used to demonstrate the efficiency of this new method

analysis and convergence of the mac scheme i the linear problem the mac marker and cell discretization of fluid flow is analysed for the stationary stokes equations it is proved that the discrete approximations do in fact converge to the exact solutions of the flow equations estimates using mesh dependent norms analogous to the standard bf h 1 and l 2 norms are given for the velocity and pressure respectively

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

a block centered finite difference method for the darcy forchheimer model a block centered finite difference scheme is introduced to solve the nonlinear darcy forchheimer equation in which the velocity and pressure can be approximated simultaneously the second order error estimates for both pressure and velocity are established on a nonuniform rectangular grid numerical experiments using the scheme show the consistency of the convergence rates of our method with the theoretical analysis

discontinuous galerkin methods for the stokes equations with nonlinear damping term on general meshes abstract this paper presents the interior penalty discontinuous galerkin ipdg methods to solve the stationary stokes equations with nonlinear damping term the ipdg discrete schemes are established on general meshes the corresponding consistency and stabilization of those schemes are proved subsequently we analyze the existence boundedness and uniqueness of the discrete solutions then the optimal error estimates are derived in the l 2 norm and h 1 like dg norm for the velocity variable and l 2 norm for the pressure variable respectively finally some numerical experiments in two dimensional are reported to demonstrate the theoretical results and show the robustness of our discrete schemes

a high order compact mac finite difference scheme for the stokes equations augmented variable approach this paper deals with the steady stokes flow on a rectangular domain a high order compact mac finite difference scheme based on the staggered grid is developed for solving stokes equations with a dirichlet boundary condition on the velocity a novel high order boundary treatment is developed via introducing a suitable augmented variable the accuracy of the proposed method is demonstrated in test problems creeping flow solutions for driven cavity problem are obtained numerically and compared with published results

duality methods for solving variational inequalities abstract methods of maximal monotone operators are used in order to study from a general point of view duality numerical algorithms for solving variational inequalities with classical algorithms such as uzawa s method for the standard and augmented lagrangian this paper presents some new algorithms which appear to have very good numerical performances

two level mixed finite element methods for the navier stokes equations with damping abstract in this paper the mixed finite element methods are considered for the navier stokes equations with damping optimal error estimates of the h 1 norm and l 2 norm for the velocity and the l 2 norm for the pressure are obtained moreover two kinds of two level methods based on the oseen correction and newton correction are presented finally two numerical examples are implemented to confirm the analysis

introduction to causal inference the goal of many sciences is to understand the mechanisms by which variables came to take on the values they have that is to find a generative model and to predict what the values of those variables would be if the naturally occurring mechanisms were subject to outside manipulations the past 30 years has seen a number of conceptual developments that are partial solutions to the problem of causal inference from observational sample data or a mixture of observational sample and experimental data particularly in the area of graphical causal modeling however in many domains problems such as the large numbers of variables small samples sizes and possible presence of unmeasured causes remain serious impediments to practical applications of these developments the articles in the special topic on causality address these and other problems in applying graphical causal modeling algorithms this introduction to the special topic on causality provides a brief introduction to graphical causal modeling places the articles in a broader context and describes the differences between causal inference and ordinary machine learning classification and prediction problems

a new class of b w halftoning algorithms a new class of dithering algorithms for black and white b w images is presented the basic idea behind the technique is to divide the image into small blocks and minimize the distortion between the original continuous tone image and its low pass filtered halftone this corresponds to a quadratic programming problem with linear constraints which is solved via standard optimization techniques examples of b w halftone images obtained by this technique are compared to halftones obtained via existing dithering algorithms

duality methods with an automatic choice of parameters application to shallow water equations in conservative form in 3 a duality numerical algorithm for solving variational inequalities based on certain properties of the yosida approximation of maximal monotone operators has been introduced the performance of this algorithm strongly depends on the choice of two constant parameters in this paper we consider a new class of algorithms where these constant parameters are replaced by functions we show that convergence properties are preserved and look for optimal values of these two functions in general these optimal values cannot be computed as they depend on the exact solution therefore we propose some strategies in order to approximate them the resulting algorithms are applied to three variational inequalities in order to compare their performance with that of the original algorithm

superclose and superconvergence of finite element discretizations for the stokes equations with damping a class of conforming mixed finite element methods fems are applied to the stokes equations with damping with the help of the prior estimates for the exact and approximated solutions and the appropriate choice of the parameters a n and r appeared in the problem the superclose and superconvergence results for the velocity in h 1 norm and the pressure in l 2 norm are derived to our best knowledge this is the first superconvergence analysis of conforming mixed fems for this kind nonlinear problem

analysis of some finite elements for the stokes problem we study some finite elements which are used in the approximation of the stokes problem so as to obtain error estimates of optimal order resume nous etudions deux elements finis utilises pour l approximation du probleme de stokes et obtenons des estimations d erreur d ordre optimal

markov properties for linear causal models with correlated errors a linear causal model with correlated errors represented by a dag with bi directed edges can be tested by the set of conditional independence relations implied by the model a global markov property specifies by the d separation criterion the set of all conditional independence relations holding in any model associated with a graph a local markov property specifies a much smaller set of conditional independence relations which will imply all other conditional independence relations which hold under the global markov property for dags with bi directed edges associated with arbitrary probability distributions a local markov property is given in richardson 2003 which may invoke an exponential number of conditional independencies in this paper we show that for a class of linear structural equation models with correlated errors there is a local markov property which will invoke only a linear number of conditional independence relations for general linear models we provide a local markov property that often invokes far fewer conditional independencies than that in richardson 2003 the results have applications in testing linear structural equation models with correlated errors

joint response graphs and separation induced by triangular systems summary we consider joint probability distributions generated recursively in terms of univariate conditional distributions satisfying conditional independence restrictions the independences are captured by missing edges in a directed graph a matrix form of such a graph called the generating edge matrix is triangular so the distributions that are generated over such graphs are called triangular systems we study consequences of triangular systems after grouping or reordering of the variables for analyses as chain graph models i e for alternative recursive factorizations of the given density using joint conditional distributions for this we introduce families of linear triangular equations which do not require assumptions of distributional form the strength of the associations that are implied by such linear families for chain graph models is derived the edge matrices of chain graphs that are implied by any triangular system are obtained by appropriately transforming the generating edge matrix it is shown how induced independences and dependences can be studied by graphs by edge matrix calculations and via the properties of densities some ways of using the results are illustrated

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

mac finite difference scheme for stokes equations with damping on non uniform grids abstract in this paper we consider the numerical methods for stationary stokes equations with damping the mark and cell mac method has been applied to discretize the problem on non uniform grids we establish the lbb condition and the stability for the mac scheme then we obtain the second order super convergence in l2 norm for both velocity and pressure on non uniform grids we also obtain the second order convergence for some terms of h1 norm of the velocity and the other terms of h1 norm are second order convergence on uniform grids numerical experiments using the mac scheme show agreement of the numerical results with theoretical analysis

ancestral graph markov models this paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all dag independence models this class of graphs called maximal ancestral graphs has two attractive features there is at most one edge between each pair of vertices every missing edge corresponds to an independence relation these features lead to a simple parameterization of the corresponding set of distributions in the gaussian case

stabilized low order finite elements for frictional contact with the extended finite element method abstract contact problem suffers from a numerical instability similar to that encountered in incompressible elasticity in which the normal contact pressure exhibits spurious oscillation this oscillation does not go away with mesh refinement and in some cases it even gets worse as the mesh is refined using a lagrange multipliers formulation we trace this problem to non satisfaction of the lbb condition associated with equal order interpolation of slip and normal component of traction in this paper we employ a stabilized finite element formulation based on the polynomial pressure projection ppp technique which was used successfully for stokes equation and for coupled solid deformation fluid diffusion using low order mixed finite elements for the frictional contact problem the polynomial pressure projection approach is applied to the normal contact pressure in the framework of the extended finite element method we use low order linear triangular elements tetrahedral elements for 3d for both slip and normal pressure degrees of freedom and show the efficacy of the stabilized formulation on a variety of plane strain plane stress and three dimensional problems

what can we learn from the path equations identifiability constraints equivalence procedures are given for determining identified parameters finding constraints on the covariances and checking equivalence in acyclic recursive linear path models with correlated error terms disturbances by inspection of the path equations aided by simple recursions this provides a useful and general alternative to the employment of directed acyclic graph theory for such purposes

fully discrete mixed finite element approximations for non darcy flows in porous media a numerical approximation procedure is proposed to solve equations describing non darcy flow of a single phase fluid in a porous medium in two or three spacial dimensions including the generalized forchheimer equation fully discrete mixed finite element methods are considered and analyzed for the approximation existence and uniqueness of the approximation are discussed and optimal order error estimates in l2 are derived for the three relevant functions

a generalized mac scheme on curvilinear domains we propose a simple finite difference scheme for navier stokes equations in primitive formulation on curvilinear domains with proper boundary treatment and interplay between covariant and contravariant components the spatial discretization admits exact hodge decomposition and energy identity as a result the pressure can be decoupled from the momentum equation with explicit time stepping no artificial pressure boundary condition is needed in addition it can be shown that this spatially compatible discretization leads to uniform inf sup condition which plays a crucial role in the pressure approximation of both dynamic and steady state calculations numerical experiments demonstrate the robustness and efficiency of our scheme

stabilized finite element method for the transient navier stokes equations based on a pressure gradient projection abstract in this paper we present a stabilized finite element formulation for the transient incompressible navier stokes equations the main idea is to introduce as a new unknown of the problem the projection of the pressure gradient onto the velocity space and to add to the incompresibility equation the difference between the laplacian of the pressure and the divergence of this new vector field this leads to a pressure stabilization effect that allows the use of equal interpolation for both velocities and pressures in the case of the transient equations we consider the possibility of treating the pressure gradient projection either implicitly or explicity in the first case the number of unknowns of the problem is substantially increased with respect to the standard galerkin formulation nevertheless iterative techniques may be used in order to uncouple the calculation of the pressure gradient projection from the rest of unknowns velocity and pressure when this vector field is treated explicitly the increment of computational cost of the stabilized formulation with respect to the galerkin method is very low we provide a stability estimate for the case of the simple backward euler time integration scheme for both the implicit and the explicit treatment of the pressure gradient projection

stabilization of low order mixed finite elements for the stokes equations we present a new family of stabilized methods for the stokes problem the focus of the paper is on the lowest order velocity pressure pairs while not lbb compliant their simplicity and attractive computational properties make these pairs a popular choice in engineering practice our stabilization approach is motivated by terms that characterize the lbb deficiency of the unstable spaces the stabilized methods are defined by using these terms to modify the saddle point lagrangian associated with the stokes equations the new stabilized methods offer a number of attractive computational properties in contrast to other stabilization procedures they are parameter free do not require calculation of higher order derivatives or edge based data structures and always lead to symmetric linear systems furthermore the new methods are unconditionally stable achieve optimal accuracy with respect to solution regularity and have simple and straightforward implementations we present numerical results in two and three dimensions that showcase the excellent stability and accuracy of the new methods

stabilized low order finite elements for stokes equations with damping abstract in this paper we consider the stationary stokes equations with damping low order mixed finite element spaces are used to approximate the velocity and the pressure and a local pressure projection stabilization method is used for the pairs to overcome the lack of the inf sup condition the stability of this method is proved and the optimal order error estimates are derived by some nonlinear analysis techniques at last two numerical examples are implemented to test the stability and effectiveness of the proposed method

analysis of ordered dither for arbitrary sampling lattices and screen periodicities ordered dither is considered a simple and effective method of image binarization for rectangular lattices it has been shown that this method of spatially periodic quantization causes aliasing in the frequency domain resulting in a degradation of halftone image quality this result is extended by deriving an expression for the spectrum of the halftoned image generalized for any sampling lattice and any screen periodicity this expression will show the explicit relationship between screen function and halftone image quality using this expression the nonlinearities associated with four optimized screens are analyzed to determine which screens are best suited to halftone rectangularly and hexagonally sampled images