on the poincare friedrichs inequality for piecewise h 1 functions in anisotropic discontinuous galerkin finite element methods the purpose of this paper is to propose a proof for the poincare friedrichs inequality for piecewise h 1 functions on anisotropic meshes by verifying suitable assumptions involved in the newly proposed proof we show that the poincare friedrichs inequality for piecewise h 1 functions holds independently of the aspect ratio which characterizes the shape regular condition in finite element analysis in addition under the maximum angle condition we establish the poincare friedrichs inequality for the crouzeix raviart non conforming linear finite element counterexamples show that the maximum angle condition is only sufficient

the interpolation theorem for narrow quadrilateral isoparametric finite elements the interpolation theorem for convex quadrilateral isoparametric finite elements is proved in the case when the condition varrho k h k ge varrho 0 0 is not satisfied where h k is the diameter of the element k and varrho k is the radius of an inscribed circle in k the interpolation error is o h k 2 in the l 2 k norm and o h k in the h 1 k norm provided that the interpolated function belongs to h 2 k in the case when the long sides of the quadrilateral k are parallel the constants appearing in the estimates are evaluated

error estimates for the raviart thomas interpolation under the maximum angle condition the classical error analysis for the raviart thomas interpolation on triangular elements requires the so called regularity of the elements or equivalently the minimum angle condition however in the lowest order case optimal order error estimates have been obtained in g acosta and r g duran siam j numer anal 37 2000 pp 18 36 replacing the regularity hypothesis by the maximum angle condition which was known to be sufficient to prove estimates for the standard lagrange interpolation in this paper we prove error estimates on triangular elements for the raviart thomas interpolation of any order under the maximum angle condition also we show how our arguments can be extended to the three dimensional case to obtain error estimates for tetrahedral elements under the regular vertex property introduced in g acosta and r g duran siam j numer anal 37 2000 pp 18 36

layer adapted meshes for convection diffusion problems abstract in the present paper a classification and a survey are given of layer adapted meshes for stationary convection dominated convection diffusion problems for a number of standard numerical schemes theoretical results are presented that demonstrate that the use of properly layer adapted meshes yields robust methods i e methods that perform equally well no matter how dominant the convection we review a number of techniques used in the convergence analysis of these methods

piecewise polynomial interpolation in muckenhoupt weighted sobolev spaces and applications we develop a constructive piecewise polynomial approximation theory in weighted sobolev spaces with muckenhoupt weights for any polynomial degree the main ingredients to derive optimal error estimates for an averaged taylor polynomial are a suitable weighted poincare inequality a cancellation property and a simple induction argument we also construct a quasi interpolation operator built on local averages over stars which is well defined for functions in l 1 l1 we derive optimal error estimates for any polynomial degree on simplicial shape regular meshes on rectangular meshes these estimates are valid under the condition that neighboring elements have comparable size which yields optimal anisotropic error estimates over n n rectangular domains the interpolation theory extends to cases when the error and function regularity require different weights we conclude with three applications nonuniform elliptic boundary value problems elliptic problems with singular sources and fractional powers of elliptic operators

an anisotropic pressure stabilized finite element method for incompressible flow problems we consider a pressure stabilized finite element approximation of incompressible flow problems in primitive velocity pressure variables which is based on a projection of the gradient of the discrete pressure onto the space of discrete functions equal order interpolation for the velocity and the pressure can be employed with this formulation the method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios

anisotropic error bounds of lagrange interpolation with any order in two and three dimensions abstract in this paper using the newton s formula of lagrange interpolation we present a new proof of the anisotropic error bounds for lagrange interpolation of any order on the triangle rectangle tetrahedron and cube in a unified way

an approach to refining three dimensional tetrahedral meshes based on delaunay transformations a technique for refining three dimensional tetrahedral meshes is proposed in this paper the proposed technique is capable of treating arbitrary unstructured tetrahedral meshes convex or non convex with multiple regions resulting in high quality constrained delaunay triangulations the tetrahedra generated are of high quality nearly equilateral sliver tetrahedra which present a real problem to many algorithms are not produced with the new method the key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the voronoi delaunay theory and a reposition of nodes technique the computational requirements of the proposed technique are in linear relationship with the number of nodes and tetrahedra making it ideal for direct employment in a fully automatic finite element analysis system for 3 d adaptive mesh refinement application to some test problems is presented to show the effectiveness and applicability of the new method

hierarchical decomposition of domains with fractures we consider the efficient and robust numerical solution of elliptic problems with jumping coefficients occuring on a network of fractures these thin geometric structures are resolved by anisotropic trapezoidal elements we present an iterative solution concept based on a hierarchical separation of the fractures and the surrounding rock matrix upper estimates for the convergence rates are independent of the the jump of coefficients and of the width of the fractures and depend only polynomially on the number of refinement steps the theoretical results are illustrated by numerical experiments

uniform error estimates for certain narrow lagrange finite elements error estimates of dupont and scott are used to derive uniform error estimates for lagrange finite elements in jrn n 2 under the following conditions 1 the elements can be arbitrarily narrow in any coordinate direction such that a sufficient number of interpolation points are grouped on lines parallel to that coordinate axis and 2 the space of approximating functions ft in each element t must include the space of polynomials of degree 1 n 2 if n is odd this does not cover elements of lowest degree that are normally considered with the shape regularity requirement that the ratio of their outer and inner diameters be bounded for example if n 3 the usual requirement with shape regularity is that each ft contain all first degree polynomials the result of this paper requires that each ft contain all quadratic polynomials and consequently does not apply to linear courant elements in tetrahedrons or trilinear tensor elements in rectangular boxes counterexamples in these two cases are included

interpolation error estimates in w 1 p for degenerate q 1 isoparametric elements optimal order error estimates in h 1 for the q 1 isoparametric interpolation were obtained in acosta and duran siam j numer anal37 18 36 1999 for a very general class of degenerate convex quadrilateral elements in this work we show that the same conlusions are valid in w 1 p for 1 p 3 and we give a counterexample for the case p 3 showing that the result cannot be generalized for more regular functions despite this fact we show that optimal order error estimates are valid for any p 1 keeping the interior angles of the element bounded away from 0 and independently of the aspect ratio we also show that the restriction on the maximum angle is sharp for p 3

anisotropic interpolation error estimate for arbitrary quadrilateral isoparametric elements the aim of this paper is to show that for any p in 1 infty the w 1 p anisotropic interpolation error estimate holds on quadrilateral isoparametric elements verifying the maximum angle condition mac and the property of comparable lengths for opposite sides clos i e on all those quadrilaterals with interior angles uniformly bounded away from pi and with both pairs of opposite sides having comparable lengths for rectangular elements our interpolation error estimate agrees with the usual one whereas for perturbations of rectangles the most general quadrilateral elements previously considered as far as we know our result has some advantages with respect to the pre existing ones the interpolation error estimate that we proved is written by using two neighboring sides of the element instead of the sides of the unknown perturbed rectangle and on the other hand conditions mac and clos are much simpler requirements to verify and with a clearer geometrical sense than those involved in the definition of perturbations of a rectangle

an anisotropic superconvergent nonconforming plate finite element the classical finite element convergence analysis relies on the following regularity condition there exists a constant c independent of the element k and the mesh such that h k r k

anisotropic mesh refinement in stabilized galerkin methods the numerical solution of a convection diffusion reaction model problem is considered in two and three dimensions a stabilized finite element method of galerkin least square type accomodates diffusion dominated as well as convection and or reaction dominated situations the resolution of boundary layers occuring in the singularly perturbed case is achieved using anisotropic mesh refinement in boundary layer regions in this paper the standard analysis of the stabilized galerkin method on isotropic meshes is extended to more general meshes with boundary layer refinement simplicial lagrangian elements of arbitrary order are used

on friedrichs poincare type inequalities friedrichs and poincare type inequalities are important and widely used in the area of partial differential equations and numerical analysis most of their proofs appearing in references are the argument of reduction to absurdity in this paper we give direct proofs of friedrichs type inequalities in h 1 and poincare type inequalities in some subspaces of w 1 p the dependencies of the inequality coefficients on the domain and some sub domains are illustrated explicitly

error estimates for cq_1 isoparametric elements satisfying a weak angle condition we prove optimal order error estimates in the h1 norm for the cq 1 isoparametric interpolation on convex quadrilateral elements under rather weak hypotheses improving previously known results choose one diagonal and divide the element into two triangles we show that if the chosen diagonal is the longest one then the constant in the error estimate depends only on the maximum angle of the two triangles otherwise the constant depends on that maximum angle and on the ratio between the two diagonals in particular we obtain the optimal order error estimate under the maximum angle condition as in the case of triangular elements consequently the error estimate is uniformly valid for a rather general class of degenerate quadrilaterals

on the interpolation error estimates for q_1 quadrilateral finite elements in this paper we study the relation between the error estimate of the bilinear interpolation on a general quadrilateral and the geometric characters of the quadrilateral some explicit bounds of the interpolation error are obtained based on some sharp estimates of the integral over frac 1 j p 1 for 1 leq p leq infty on the reference element where j is the jacobian of the nonaffine mapping this allows us to introduce weak geometric conditions depending on p leading to interpolation error estimates in the w 1 p norm for any p in 1 infty which can be regarded as a generalization of the regular decomposition property rdp condition introduced in g acosta and r g duran siam j numer anal 38 2000 pp 1073 1088 for p 2 and new rdp conditions nrdp for p neq2 we avoid the use of the reference family elements which allows us to extend the results to a larger class of elements and to introduce the nrdp condition in a more unified way as far as we know the mesh condition presented in this paper is weaker than any other mesh conditions proposed in the literature for any p with 1 leq p leq infty

on nonobtuse simplicial partitions this paper surveys some results on acute and nonobtuse simplices and associated spatial partitions these partitions are relevant in numerical mathematics including piecewise polynomial approximation theory and the finite element method special attention is paid to a basic type of nonobtuse simplices called path simplices the generalization of right triangles to higher dimensions in addition to applications in numerical mathematics we give examples of the appearance of acute and nonobtuse simplices in other areas of mathematics

lagrange and average interpolation over 3d anisotropic elements abstract an average interpolation is introduced for 3 rectangles and tetrahedra and optimal order error estimates in the h1 norm are proved the constant in the estimate depends weakly improving the results given in duran math comp 68 1999 187 199 on the uniformity of the mesh in each direction for tetrahedra the constant also depends on the maximum angle of the element on the other hand merging several known results acosta and duran siam j numer anal 37 1999 18 36 duran math comp 68 1999 187 199 krizek siam j numer anal 29 1992 513 520 al shenk math comp 63 1994 105 119 we prove optimal order error for the p 1 lagrange interpolation in w1 p p 2 with a constant depending on p as well as the maximum angle of the element again under the maximum angle condition optimal order error estimates are obtained in the h1 norm for higher degree interpolations

an anisotropic gls stabilized finite element method for incompressible flow problems abstract we consider a stabilized finite element approximation of incompressible flow problems in primitive velocity pressure variables which is based on a gls formulation equal order interpolation for the velocity and the pressure can be employed with this formulation the method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios rather than using a single stabilization parameter within each element the jacobian matrix of the affine transformation from the reference element is employed for stabilization purposes stability and anisotropic error estimates in a suitable mesh dependent norm are proved for the linear stokes problem numerical results confirm the accuracy and robustness of the proposed method compared to similar previous stabilized schemes

error estimates on anisotropic elements for functions in weighted sobolev spaces in this paper we prove error estimates for a piecewise q 1 average interpolation on anisotropic rectangular elements i e rectangles with sides of different orders in two and three dimensions our error estimates are valid under the condition that neighboring elements have comparable size this is a very mild assumption that includes more general meshes than those allowed in previous papers in particular strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses moreover we generalize the error estimates allowing on the right hand side some weighted sobolev norms this extension is of interest in singularly perturbed problems finally we consider the approximation of functions vanishing on the boundary by finite element functions with the same property a point that was not considered in previous papers on average interpolations for anisotropic elements as an application we consider the approximation of a singularly perturbed reaction diffusion equation and show that as a consequence of our results almost optimal order error estimates in the energy norm valid uniformly in the perturbation parameter can be obtained

acute type refinements of tetrahedral partitions of polyhedral domains we present a new technique to perform refinements on acute type tetrahedral partitions of a polyhedral domain provided that the center of the circumscribed sphere around each tetrahedron belongs to the tetrahedron the resulting family of partitions is of acute type thus all the tetrahedra satisfy the maximum angle condition both these properties are highly desirable in finite element analysis

the maximum angle condition for mixed and nonconforming elements application to the stokes equations for the lagrange interpolation it is known that optimal order error estimates hold for elements satisfying the maximum angle condition the objective of this paper is to obtain similar results for the raviart thomas interpolation arising in the analysis of mixed methods we prove that optimal order error estimates hold under the maximum angle condition for this interpolation both in two and three dimensions and moreover that this condition is indeed necessary to have these estimates error estimates for the mixed approximation of second order elliptic problems and for the nonconforming piecewise linear approximation of the stokes equations are derived from our results

an interface fitted mesh generator and virtual element methods for elliptic interface problems abstract a simple and efficient interface fitted mesh generation algorithm which can produce a semi structured interface fitted mesh in two and three dimensions quickly is developed in this paper elements in such interface fitted meshes are not restricted to simplices but can be polygons or polyhedra especially in 3d the polyhedra instead of tetrahedra can avoid slivers virtual element methods are applied to solve elliptic interface problems with solutions and flux jump conditions algebraic multigrid solvers are used to solve the resulting linear algebraic system numerical results are presented to illustrate the effectiveness of our method

interpolation error estimates of a modified 8 node serendipity finite element interpolation error estimates for a modified 8 node serendipity finite element are derived in both regular and degenerate cases the latter of which includes the case when the element is of triangular shape for u in w 3 p k defined over a quadrilateral k the error for the interpolant pi k u is estimated as u pi k u w alpha p k le ch 3 alpha k u w 3 p k alpha 0 1 where 1 le p le infty in the regular case and 1 le p 3 in the degenerate case respectively thus the obtained error estimate in the degenerate case is of the same quality as in the regular case at least for 1 le p 3 results for some related elements are also given

on the maximum angle condition for linear tetrahedral elements synge s maximum angle condition for triangular elements is generalized to tetrahedral elements for the generalized condition it is proved that tetrahedra may degenerate in a certain way and the error of the standard linear interpolation remains o h in the w p 1 omega norm for sufficiently smooth functions and p in 1 infty

modeling rationality to control self organization of crowds an environmental approach in this paper we propose a classification of crowd models in built environments based on the assumed pedestrian ability to foresee the movements of other walkers at the same time we introduce a new family of macroscopic models which make it possible to tune the degree of predictiveness i e rationality of the individuals by means of these models we describe both the natural behavior of pedestrians i e their expected behavior according to their real limited predictive ability and a target behavior i e a particularly efficient behavior one would like them to assume e g for logistic or safety reasons then we tackle a challenging shape optimization problem which consists in controlling the environment in such a way that the natural behavior is as close as possible to the target one thereby inducing pedestrians to behave more rationally than they naturally would we present numerical tests which elucidate the role of rational predictive abilities and show some promising results about the

trefftz difference schemes on irregular stencils the recently developed flexible local approximation method flame produces accurate difference schemes by replacing the usual taylor expansion with trefftz functions local solutions of the underlying differential equation this paper advances and casts in a general form a significant modification of flame proposed recently by pinheiro and webb a least squares fit instead of the exact match of the approximate solution at the stencil nodes as a consequence of that flame schemes can now be generated on irregular stencils with the number of nodes substantially greater than the number of approximating functions the accuracy of the method is preserved but its robustness is improved for demonstration the paper presents a number of numerical examples in 2d and 3d electrostatic magnetostatic particle interactions scattering of electromagnetic acoustic waves and wave propagation in a photonic crystal the examples explore the role of the grid and stencil size of the number of approximating functions and of the irregularity of the stencils

on the least squares fit by radial functions to multidimensional scattered data this paper investigates some aspects of discrete least squares approximation by translates of certain classes of radial functions its specific aims are i to provide conditions under which the associated least squares matrix is invertible and ii to give upper bounds for the euclidean norms of the inverses of these matrices when they exist

error estimates for 3 d narrow finite elements we obtain error estimates for finite element approximations of the lowest degree valid uniformly for a class of three dimensional narrow elements first for the lagrange interpolation we prove optimal error estimates both in order and regularity in l p for p 2 for p 2 it is known that this result is not true applying extrapolation results we obtain an optimal order error estimate for functions sligthly more regular than h 2 these results are valid both for tetrahedral and rectangular elements second for the case of rectangular elements we obtain optimal in order and regularity error estimates for an average interpolation valid for functions in w 1 s p with 1 p and 0 s 1

applicability of the bramble hilbert lemma in interpolation problems of narrow quadrilateral isoparametric finite elements two approaches to deriving the interpolation theorem for narrow quadrilateral isoparametric finite elements not satisfying the condition rho k h k greater than or equal to rho 0 0 rho k and h k being the radius of inscribed circle and the diameter of the quadrilateral k respectively are presented the first one using the bramble hilbert lemma is successful only in deriving the l 2 k estimate the nonapplicability of the standard approach via the bramble hilbert lemma in the case of h 1 k estimate is presented and a fully efficient method giving the optimum rate of convergence o h in the h 1 k norm is described in the end the dependence of the interpolation error on the geometry of a quadrilateral is demonstrated by an example

on mesh geometry and stiffness matrix conditioning for general finite element spaces the performance of finite element computation depends strongly on the quality of the geometric mesh and the efficiency of the numerical solution of the linear systems resulting from the discretization of partial differential equation pde models it is common knowledge that mesh geometry affects not only the approximation error of the finite element solution but also the spectral properties of the corresponding stiffness matrix in this paper for typical second order elliptic problems some refined relationships between the spectral condition number of the stiffness matrix and the mesh geometry are established for general finite element spaces defined on simplicial meshes the derivation of such relations for general high order elements is based on a new trace formula for the element stiffness matrix it is shown that a few universal geometric quantities have the same dominant effect on the stiffness matrix conditioning for different finite element spaces these results provide guidance to the studies of both linear algebraic solvers and the unstructured geometric meshing

local high order regularization and applications to hp methods we develop a regularization operator based on smoothing on a spatially varying length scale this operator is defined for functions u l 1 and has approximation properties that are given by the local sobolev regularity of u and the local smoothing length scale additionally the regularized function satisfies inverse estimates commensurate with the approximation orders by combining this operator with a classical h p interpolation operator we obtain an h p clement type quasi interpolation operator i e an operator that requires minimal smoothness of the function to be approximated but has the expected approximation properties in terms of the local mesh size and polynomial degree as a second application we consider residual error estimates in h p boundary element methods that are explicit in the local mesh size and the local approximation order

on polynomial approximation in sobolev spaces we obtain new bounds for the error in the polynomial approximation in sobolev spaces in an open bounded set which is star shaped with respect to every point in a set of positive measure b subset omega this estimate follows by applying the hardy littlewood maximal function

on the equivalence of regularity criteria for triangular and tetrahedral finite element partitions in this note we examine several regularity criteria for families of simplicial finite element partitions in r d email protected 2 3 these are usually required in numerical analysis and computer implementations we prove the equivalence of four different definitions of regularity often proposed in the literature the first one uses the volume of simplices the others involve the inscribed and circumscribed ball conditions and the minimal angle condition

optimization of the multigrid convergence rate on semi structured meshes by local fourier analysis in this paper a local fourier analysis for multigrid methods on tetrahedral grids is presented different smoothers for the discretization of the laplace operator by linear finite elements on such grids are analyzed a four color smoother is presented as an efficient choice for regular tetrahedral grids whereas line and plane relaxations are needed for poorly shaped tetrahedra a novel partitioning of the fourier space is proposed to analyze the four color smoother numerical test calculations validate the theoretical predictions a multigrid method is constructed in a block wise form by using different smoothers and different numbers of pre and post smoothing steps in each tetrahedron of the coarsest grid of the domain some numerical experiments are presented to illustrate the efficiency of this multigrid algorithm

the maximum angle condition is not necessary for convergence of the finite element method we show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems this condition is only sufficient in fact finite element approximations may converge even though some dihedral angles of simplicial elements tend to

a geometrical approach to mesh smoothing we study the problem of smoothing finite element meshes of triangles and tetrahedra where vertices are recursively moved to improve the overall quality of the elements with respect to a given shape quality metric we propose a geometric approach to solving the local optimization problem level sets of the given metric are used to characterize the set of optimal point s we also introduce a new mesh quality metric for tetrahedra

strictly positive definite functions on spheres in euclidean spaces in this paper we study strictly positive definite functions on the unit sphere of the m dimensional euclidean space such functions can be used for solving a scattered data interpolation problem on spheres since positive definite functions on the sphere were already characterized by schoenberg some fifty years ago the issue here is to determine what kind of positive definite functions are actually strictly positive definite the study of this problem was initiated recently by xu and cheney proc amer math soc 116 1992 977 981 where certain sufficient conditions were derived a new approach which is based on a critical connection between this problem and that of multivariate polynomial interpolation on spheres is presented here the relevant interpolation problem is subsequently analyzed by three different complementary methods the first is based on the de boor ron general least solution for the multivariate polynomial interpolation problem the second which is suitable only for m 2 is based on the connection between bivariate harmonic polynomials and univariate analytic polynomials and reduces the problem to the structure of the integer zeros of bounded univariate exponentials finally the last method invokes the realization of harmonic polynomials as the polynomial kernel of the laplacian thereby exploiting some basic relations between homogeneous ideals and their polynomial kernels

the minimal angle condition for quadrilateral finite elements of arbitrary degree we study w1 p lagrange interpolation error estimates for general quadrilateralqk finite elements with k2 for the most standard case of p 2 it turns out that the constant c involved in the error estimate can be bounded in terms of the minimal interior angle of the quadrilateral moreover the same holds for any p in the range 1p 3 on the other hand for 3p we show that c also depends on the maximal interior angle we provide some counterexamples showing that our results are sharp

an immersed finite element method based on a locally anisotropic remeshing for the incompressible stokes problem abstract in the present paper we study a finite element method for the incompressible stokes problem with a boundary immersed in the domain on which essential constraints are imposed such type of methods may be useful to tackle problems with complex geometries interfaces such as multiphase flow and fluid structure interaction the method we study herein consists in locally refining elements crossed by the immersed boundary such that newly added elements called subelements fit the immersed boundary in this sense this approach is of a fitted type but with an original mesh given independently of the location of the immersed boundary we use such a subdivision technique to build a new finite element basis which enables us to represent accurately the immersed boundary and to impose strongly dirichlet boundary conditions on it however the subdivision process may imply the generation of anisotropic elements which for the incompressible stokes problem may result in the loss of inf sup stability even for well known stable element schemes we therefore use a finite element approximation which appears stable also on anisotropic elements we perform numerical tests to check stability of the chosen finite elements several numerical experiments are finally presented to illustrate the capabilities of the method the method is presented for two dimensional problems

residence time of symmetric random walkers in a strip with large reflective obstacles we study the effect of a large obstacle on the so called residence time i e the time that a particle performing a symmetric random walk in a rectangular two dimensional 2d domain needs to cross the strip we observe complex behavior we find out that the residence time does not depend monotonically on the geometric properties of the obstacle such as its width length and position in some cases due to the presence of the obstacle the mean residence time is shorter with respect to the one measured for the obstacle free strip we explain the residence time behavior by developing a one dimensional 1d analog of the 2d model where the role of the obstacle is played by two defect sites having smaller probability to be crossed with respect to all the other regular sites the 1d and 2d models behave similarly but in the 1d case we are able to compute exactly the residence time finding a perfect match with the monte carlo simulations

calibration of smooth camera models generic imaging models can be used to represent any camera current generic models are discrete and define a mapping between each pixel in the image and a straight line in 3d space this paper presents a modification of the generic camera model that allows the simplification of the calibration procedure the only requirement is that the coordinates of the 3d projecting lines are related by functions that vary smoothly across space such a model is obtained by modifying the general imaging model using radial basis functions rbfs to interpolate image coordinates and 3d lines thereby allowing both an increase in resolution due to their continuous nature and a more compact representation using this variation of the general imaging model we also develop a calibration procedure this procedure only requires that a 3d point be matched to each pixel in addition not all the pixels need to be calibrated as a result the complexity of the procedure is significantly decreased normalization is applied to the coordinates of both image and 3d points which increases the accuracy of the calibration results with both synthetic and real datasets show that the model and calibration procedure are easily applicable and provide accurate calibration results

residence time estimates for asymmetric simple exclusion dynamics on strips abstract the target of our study is to approximate numerically and in some particular physically relevant cases also analytically the residence time of particles undergoing an asymmetric simple exclusion dynamics on a two dimensional vertical strip the sources of asymmetry are twofold i the choice of boundary conditions different reservoir levels and ii the strong anisotropy from a drift nonlinear in density with prescribed directionality we focus on the effect of the choice of anisotropy on residence time we analyze our results by means of two theoretical models a mean field and a one dimensional birth and death one for positive drift we find a striking agreement between monte carlo and theoretical results in the zero drift case we still find agreement as long as particles can freely escape the strip through the bottom boundary otherwise the two models give different predictions and their ability to reproduce numerical results depends on the horizontal displacement probability the topic is relevant for situations occurring in pedestrian flows or biological transport in crowded environments where lateral displacements of the particles occur predominantly affecting therefore in an essentially way the efficiency of the overall transport mechanism

nonconforming mixed finite element approximation to the stationary navier stokes equations on anisotropic meshes abstract the main aim of this paper is to study the error estimates of a rectangular nonconforming finite element for the stationary navier stokes equations under anisotropic meshes that is the nonconforming rectangular element is taken as approximation space for the velocity and the piecewise constant element for the pressure the convergence analysis is presented and the optimal error estimates both in a broken h 1 norm for the velocity and in an l 2 norm for the pressure are derived on anisotropic meshes