a stabilized element based finite volume method for poroelastic problems abstract the coupled equations of biot s poroelasticity consisting of stress equilibrium and fluid mass balance in deforming porous media are numerically solved the governing partial differential equations are discretized by an element based finite volume method ebfvm which can be used in three dimensional unstructured grids composed of elements of different types one of the difficulties for solving these equations is the numerical pressure instability that can arise when undrained conditions take place in this paper a stabilization technique is developed to overcome this problem by employing an interpolation function for displacements that considers also the pressure gradient effect the interpolation function is obtained by the so called physical influence scheme pis typically employed for solving incompressible fluid flows governed by the navier stokes equations classical problems with analytical solutions as well as three dimensional realistic cases are addressed the results reveal that the proposed stabilization technique is able to eliminate the spurious pressure instabilities arising under undrained conditions at a low computational cost

finite calculus formulation for incompressible solids using linear triangles and tetrahedra summary many finite elements exhibit the so called volumetric locking in the analysis of incompressible or quasi incompressible problems in this paper a new approach is taken to overcome this undesirable effect the starting point is a new setting of the governing differential equations using a finite calculus fic formulation the basis of the fic method is the satisfaction of the standard equations for balance of momentum equilibrium of forces and mass conservation in a domain of finite size and retaining higher order terms in the taylor expansions used to express the different terms of the differential equations over the balance domain the modified differential equations contain additional terms which introduce the necessary stability in the equations to overcome the volumetric locking problem the fic approach has been successfully used for deriving stabilized finite element and meshless methods for a wide range of advective diffusive and fluid flow problems the same ideas are applied in this paper to derive a stabilized formulation for static and dynamic finite element analysis of incompressible solids using linear triangles and tetrahedra examples of application of the new stabilized formulation to linear static problems as well as to the semi implicit and explicit 2d and 3d non linear transient dynamic analysis of an impact problem and a bulk forming process are presented copyright 2004 john wiley sons ltd

approachability and fixed points for non convex set valued maps this paper studies the approachability of upper semicontinuous nonconvex set valued maps by single valued continuous functions and its applications to fixed point theory the use of approximate selections was initiated by j von neumann 41 in the proof of his well known minimax principle this remarkable property was extended to the normed space setting by cellina s and cellina and lasota 9 in the context of a degree theory for upper semicontinuous convex compact valued maps it also holds for maps with compact contractible values defined on finite polyhedra of iw ma cole11 40 and more generally defined on compact anrs mclennan 39 it was recently taken up by gbrniewicz granas and kryszewski 22 241 in the context of an index theory for non convex maps defined on compact anrs the content of this paper is divided into three parts the first part is devoted to background material concerning the types of spaces and set valued maps studied herein in the second part we define the abstract class d of approachable set valued maps that is the class of maps a x y

some remarks on the structure of the solution set for differential inclusions in banach spaces abstract in this paper we show the general scheme of the proof the solution set of differential inclusions is r in general only if it is nonempty and compact new results are also obtained

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

scalable algorithms for three field mixed finite element coupled poromechanics abstract we introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three field formulation the use of a displacement velocity pressure mixed finite element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 3 unsymmetric and indefinite block matrix the preconditioners are obtained by approximating the two level schur complement with the aid of physically based arguments that can be also generalized in a purely algebraic approach a theoretical and experimental analysis is presented that provides evidence of the robustness efficiency and scalability of the proposed algorithm the performance is also assessed for a real world challenging consolidation experiment of a shallow formation

note to the asymptotic behaviour of solutions of damped pendulum equations under forcing although the mathematical or the physical pendulum seems to be one of the most popular objects in modelling see the nice exposition lo and therefore no wonder that for the related autonomous equations studied by means of the planar geometrical methods a vast literature exists see the monographs 2 3 151 or more recently the beautiful modern article 4 there are still several white places of its study in the case of forcing recently the big activity is devoted for proving the existence of harmonics to its equation for the survey of results in this field see s lo or chaotic behaviour of the dynamics see e g 6 or the different approaches in 12 is nevertheless we have found only one reference 16 on the asymptotic behaviour of solutions of the pendulum type equations under forcing which is already 30 years old hence our aim is to extend the results in this field for the equation

efficient solvers for hybridized three field mixed finite element coupled poromechanics abstract we consider a mixed hybrid finite element formulation for coupled poromechanics a stabilization strategy based on a macro element approach is advanced to eliminate the spurious pressure modes appearing in undrained incompressible conditions the efficient solution of the stabilized mixed hybrid block system is addressed by developing a class of block triangular preconditioners based on a schur complement approximation strategy robustness computational efficiency and scalability of the proposed approach are theoretically discussed and tested using challenging benchmark problems on massively parallel architectures

measurability and integrability of the weak upper limit of a sequence of multifunctions we provide several properties of the weak upper limit of a sequence of subsets of a separable banach space such as a criterion of non vacuity of closedness etc we also examine the measurability of the multifunction defined as the weak upper limit of a sequence of multifunctions at last applications to the existence of a measurable and bochner integrable selector for this multifunction are presented

stabilized mixed finite element formulations for materially nonlinear partially saturated two phase media standard and enhanced bbar or eas low order finite elements applied to the problem of consolidation of two phase nonlinear continua do not satisfy the lbb condition when the same interpolation functions are used for both displacement and pore pressure fields strong spatial pressure oscillations are the main consequence of the lbb condition violation the class of direct stabilized methods widely used in the field of fluid mechanics is a powerful tool to circumvent violation of the aforementioned condition three stabilized formulations designed for the problem of consolidation of fully or partially saturated media are presented galerkin least squares gls with the least squares term construction based on the residuum of the local fluid mass conservation equation the pressure stabilized formulation fpl in which the rate of the pore pressure laplacian residual free in the incompressibility limit is added to the fluid mass conservation equation and finally a stabilized formulation in which the stabilization term is constructed based on the rate of the residuum of the local momentum equation an h convergence study and test problems for the three stabilized schemes are discussed

numerical and experimental investigations of the nonlinear dynamics and chaos in non smooth systems nature is full of non smooth nonlinearities that are usually related to either friction phenomena or the discontinuous characteristics of intermittent contacts in general non smooth characteristics cause difficulties in the modeling and simulation of natural systems a smoothed switch model is used in this contribution in order to analyze non smooth systems the procedure is shown to be an effective method of dealing with this kind of system and has advantages in numerical implementation as an application of the general formulation a single degree of freedom oscillator with discontinuous support is analyzed an experimental apparatus is developed in order to verify the capability of the mathematical formulation and the numerical procedure used to describe the system general behavior this apparatus is instrumented to obtain all system state variables making it possible to compare experimental results with those obtained through numerical simulations the system s dynamical behavior shows a rich response that includes dynamical jumps bifurcations and chaos different aspects related to nonlinear dynamics are carried out showing that numerical simulations are in close agreement with experimental data

boundary value problems on infinite intervals and semiconductor devices the nonlinear differential equation y f x y y 0 x f satisfying bernstein type growth conditions we also examine an important application which occurs in the theory of semiconductor devices

a topological method for bounded solutions of nonautonomous ordinary differential equations the existence of bounded solutions to nonlinear nonautonomous ordinary differential equations is studied this is done by associating the given equation to nonlinear autonomous ones by means of a family of skew product flows related by homotopy the existence of a bounded solution to the original differential equation is then related to the nontriviality of a certain conley index associated with the autonomous differential equations the existence of nontrivial bounded solutions is also considered the differential equations studied are perturbations of homogeneous ones

corner bifurcations in non smoothly forced impact oscillators abstract we consider an impacting mechanical system in which a particle at position u t impacts with a periodically moving obstacle at position z t the motion of which is non smooth in particular we look at corner events when u impacts with z very close to a point where z loses smoothness we show that this leads through a corner bifurcation to complex dynamics in u which can include periodic orbits of arbitrary period and period adding cascades by analysing associated maps close to the corner event we show that this dynamics can be understood in terms of the iterations of a two dimensional piecewise linear discontinuous map we also show some links between this analysis and the difficult problem of understanding the motion of three objects which may have simultaneous impacts

stability and monotonicity for some discretizations of the biot s consolidation model abstract we consider finite element discretizations of the biot s consolidation model in poroelasticity with mini and stabilized p1 p1 elements we analyze the convergence of the fully discrete model based on spatial discretization with these types of finite elements and implicit euler method in time we also address the issue related to the presence of non physical oscillations in the pressure approximation for low permeabilities and or small time steps we show that even in 1d a stokes stable finite element pair fails to provide a monotone discretization for the pressure in such regimes we then introduce a stabilization term which removes the oscillations we present numerical results confirming the monotone behavior of the stabilized schemes

derivation of stabilized equations for numerical solution of advective diffusive transport and fluid flow problems abstract the concept of the so called artificial or balancing diffusion used to stabilize the numerical solution of advective diffusive transport and fluid flow problems is revised in this paper it is shown that the standard forms of the balancing diffusion terms usually chosen in a heuristic manner can be naturally found by introducing higher order approximations in the derivation of the governing differential equations via standard conservation or equilibrium principles this allows us to reinterpret many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter

existence of positive solutions to some singular and nonsingular second order boundary value problems abstract the topological transversality theorem is employed to study existence of solutions to a variety of singular and nonsingular second order boundary value problems of the form y f t y y 0 0 t t 0 t 1 y 0 and or y 0 the principal tools are the arzela ascoli theorem essential maps and a priori bounds on solutions

extracting information from interimpact intervals in a mechanical oscillator monitoring all the state variables in dynamic experiments may be difficult or even impossible it is also desirable to reduce the coupling between the system under study and the measuring device to as low a level as possible to these ends we investigated the use of interimpact interval as a discrete state variable it is well established that topological information can be obtained from delay coordinate embedding and thus not all of the state variables or even a continuous set of a single variable need to be measured in the case of impacting systems the impacts can be viewed as discrete events that can then be used to reconstruct more general features of the behavior the success of such reconstruction techniques will be assessed in this paper

ill conditioning of finite element poroelasticity equations abstract the solution to biot s coupled consolidation theory is usually addressed by the finite element fe method thus obtaining a system of first order differential equations which is integrated by the use of an appropriate time marching scheme for small values of the time step the resulting linear system may be severely ill conditioned and hence the solution can prove quite difficult to achieve under such conditions efficient and robust projection solvers based on krylov s subspaces which are usually recommended for non symmetric large size problems can exhibit a very slow convergence rate or even fail the present paper investigates the correlation between the ill conditioning of fe poroelasticity equations and the time integration step t an empirical relation is provided for a lower bound tcrit of t below which ill conditioning may suddenly occur the critical time step is larger for soft and low permeable porous media discretized on coarser grids a limiting value for the rock stiffness is found such that for stiffer systems there is no ill conditioning irrespective of t however small as is also shown by several numerical examples finally the definition of a different tcrit as suggested by other authors is reviewed and discussed

using solution sets for solving boundary value problems for ordinary differential equations where f e c i x r r s c c z r consists of finding fixed points of a solution map e for a suitable linearized problem associated to bv see e g 2 5 6 71 in these problems the map x is either continuous and single valued or upper semicontinuous set valued with convex values these are rather strong restrictions because the set of solutions of a general boundary value problem may well be neither a singleton nor a convex set the case in which the solution map is upper semicontinuous but with nonnecessarily convex values is considered in this paper more precisely we want to consider the case when the values of x form an acyclic set and the case when the values of c are sets with a finite number of elements an application to the existence of periodic solutions for a licnard type equation is also given moreover an existence theorem for a boundary value problem of the following form f l x x x teicr x e r

cell centered finite volume method for heterogeneous anisotropic poromechanics problem abstract the article introduces a finite volume method for the poromechanics problem for heterogeneous anisotropic media the media are characterized by the full tensors of elasticity permeability and biot coefficient the pressure and displacement unknowns are collocated at centers of cells poromechanics represents a multi physics problem of darcy flow and linear elasticity coupled via biot terms based on the flux and the displacement and pressure continuity conditions we derive the coupled block expression for the flux the flux expression is split into a block harmonic part a transversal part and an additional contribution due to gravity the block harmonic part is equivalent to the two point flux approximation method for the darcy problem for the approximation of the transversal part we derive an interpolation method for the coupled pressure and displacement fields valid over discontinuities of the tensors finally we derive the flux expression for generalized boundary conditions the flux expression does not require introduction of auxiliary unknowns at the boundary we evaluate the performance of the proposed method on a number of numerical tests and apply the method to a problem on a grid corresponding to a real oil field

bifurcations in nonsmooth dynamical systems a review is presented of the one parameter nonsmooth bifurcations that occur in a variety of continuous time piecewise smooth dynamical systems motivated by applications a pragmatic approach is taken to defining a discontinuity induced bifurcation dib as a nontrivial interaction of a limit set with respect to a codimension one discontinuity boundary in phase space only dibs that are local are considered that is bifurcations involving equilibria or a single point of boundary interaction along a limit cycle for flows three classes of systems are considered involving either state jumps jumps in the vector field or jumps in some derivative of the vector field a rich array of dynamics are revealed involving the sudden creation or disappearance of attractors jumps to chaos bifurcation diagrams with sharp corners and cascades of period adding for each kind of bifurcation identified where possible a kind of normal form or discontinuity mapping dm is given together with a canonical example and an application the goal is always to explain dynamics that may be observed in simulations of systems which include friction oscillators impact oscillators dc dc converters and problems in control theory

a global continuation theorem and bifurcation from infinity for infinite dimensional dynamical systems a general continuation theorem for isolated sets in infinite dimensional dynamical systems is proved for a class of semiflows this result is then used to prove the existence of continua of full bounded solutions bifurcating from infinity for systems of reaction diffusion equations

on the structure of fixed point sets of compact maps in b0 spaces with applications to integral and differential equations in unbounded domain abstract in this paper we present certain applications of the topological degree theory in locally convex linear topological spaces as a result we obtain two generalizations of the krasnosielski perov rabinovitz theorem on the characterization of sets of solutions of functional equations known for the banach space case onto the case of a locally convex space on the other hand we make use of such consequences of the degree theory as the borsuk theorem and browder domain invariance theorem in order to reach a certain generalization of the lasota opial covering theorem and a new theorem on the characterization of sets of solutions of functional equations at the end we apply the abstract topological theorems to study the structure of sets of solutions of a certain integral equation and the darboux problem for a hyperbolic equation in an unbounded domain a general assumption is that the kernel of the integral equation and the right hand side of the hyperbolic equation satisfy the caratheodory conditions

on stability and convergence of finite element approximations of biot s consolidation problem stability and convergence analysis of finite element approximations of biot s equations governing quasistatic consolidation of saturated porous media are discussed a family of decay functions parametrized by the number of time steps is derived for the fully discrete backward euler galerkin formulation showing that the pore pressure oscillations arising from an unstable approximation of the incompressibility constraint on the initial condition decay in time error estimates holding over the unbounded time domain for both semidiscrete and fully discrete formulations are presented and a post processing technique is employed to improve the pore pressure accuracy

on the qualitative theory of lower semicontinuous differential inclusions on etudie les proprietes qualitatives de l ensemble des solutions de caratheodory pour une inclusion differentielle de la forme x t f t x t t 0 t x 0 r n

asymptotic properties of solutions to quasi linear differential systems abstract using some previous author s results or their slight modifications two theorems concerning the existence of a bounded and a periodic solution are presented for the system whose one part of components is uniformly ultimately bounded while the other tends mostly to infinity this type of results seems to be new