proper intrinsic scales for a posteriori multiscale error estimation recently the multiscale a posteriori error estimator has been introduced showing excellent robustness for fluid mechanics problems in this paper a theoretical analysis for element edge exact solutions is conducted in which case the error constant is the norm of a green s function or a residual free bubble this finds application when the solution is computed with a stabilized method one of the features of the technique is that it gives the proper scales for a posteriori error estimation in any norm of interest such as the l2 h1 energy and l norms for fluid transport problems it is shown that the constant for predicting the error in the h1 seminorm is unbounded as the element peclet number tends to infinity making lp norms more suitable for this type of problems furthermore it is shown that the flow intrinsic time scale parameter represents the l1 norm of the error as a function of the l norm of the residual when these scales are employed for one dimensional nodally exact solutions piecewise linear finite element spaces and piecewise constant residuals the multiscale error estimator is shown to be exact

an unusual stabilized finite element method for a generalized stokes problem an unusual stabilized finite element is presented and analyzed herein for a generalized stokes problem with a dominating zeroth order term the method consists in subtracting a mesh dependent term from the formulation without compromising consistency the design of this mesh dependent term as well as the stabilization parameter involved are suggested by bubble condensation stability is proven for any combination of velocity and pressure spaces under the hypotheses of continuity for the pressure space optimal order error estimates are derived for the velocity and the pressure using the standard norms for these unknowns numerical experiments confirming these theoretical results and comparisons with previous methods are presented

on inf sup stabilized finite element methods for transient problems we consider the behavior of inf sup stabilization in the context of transient problems with multiple time scales our motivation for studying this setting is provided by reacting flows problems for which small time steps are necessary in the integration process we show that for algorithms defined through a process wherein spatial and temporal discretizations are separated the coupling of implicit time integration with spatial inf sup stabilization may lead to anomalous pressure behavior including the onset of spurious oscillations for very small time steps effectively this coupling introduces a stability criterion resulting in a dependence between the spatial grid size and the time step we illustrate our theoretical results by numerical examples that demonstrate the stability criterion 2004 elsevier b v all rights reserved

a coupled momentum method for modeling blood flow in three dimensional deformable arteries abstract blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel moreover wave propagation phenomena in the cardiovascular system can only be described considering wall deformability since blood is usually described as an incompressible fluid however computational methods for simulating blood flow in three dimensional models of arteries have either considered a rigid wall assumption for the vessel or significantly simplified or reduced geometries computing blood flow in deformable domains using standard techniques like the ale method remains a formidable problem for large realistic anatomic and physiologic models of the cardiovascular system we have developed a new method to simulate blood flow in three dimensional deformable models of arteries the method couples the equations of the deformation of the vessel wall at the variational level as a boundary condition for the fluid domain we consider a strong coupling of the degrees of freedom of the fluid and the solid domains and a linear membrane model enhanced with transverse shear for the vessel wall the effect of the vessel wall boundary is therefore added in a monolithic way to the fluid equations resulting in a remarkably robust scheme we present here the mathematical formulation of the method and discuss issues related to the fluid solid coupling membrane formulation time integration method and boundary and initial conditions implementation is discussed and results with simple geometries as well as large subject specific models are presented

linear stability analysis in fluid structure interaction with transpiration part ii numerical analysis and applications this paper constitutes the numerical counterpart of the mathematical framework introduced in part i we address the problem of flutter analysis of a coupled fluid structure system involving an incompressible newtonian fluid and a reduced structure we use the linearization principle approach developed in part i particularly suited for fluid structure problems involving moving boundaries thus the stability analysis is reduced to the computation of the leftmost eigenvalues of a coupled eigenproblem of minimal complexity this eigenproblem involves the linearized incompressible navier stokes equations and those of a reduced linear structure the coupling is realized through specific transpiration interface conditions the eigenproblem is discretized using a finite element approximation and its smallest real part eigenvalues are computed by combining a generalized cayley transform and an implicit restarted arnoldi method finally we report three numerical experiments a structure immersed in a fluid at rest a cantilever pipe conveying a fluid flow and a rectangular bridge deck profile under wind effects the numerical results are compared to former approaches and experimental data the quality of these numerical results is very satisfactory and promising

state observers of a vascular fluid structure interaction model through measurements in the solid we analyze the performances of two types of luenberger observers namely the so called direct velocity feedback and schur displacement feedback procedures originally devised for elasto dynamics to estimate the state of a fluid structure interaction model for hemodynamics when the measurements are assumed to be restricted to displacements or velocities in the solid we first assess the observers using hemodynamics inspired test problems with the complete model including the navier stokes equations in arbitrary lagrangian eulerian formulation in particular then in order to obtain more detailed insight we consider several well chosen simplified models each of which allowing a thorough analysis emphasizing spectral considerations while illustrating a major phenomenon of interest for the observer performance namely the added mass effect for the structure the coupling with a lumped parameter boundary condition model for the fluid flow and the fluid dynamics effect per se whereas improvements can be sought when additional measurements are available in the fluid domain in order to more effectively deal with strong uncertainties in the fluid state in the present framework this establishes luenberger observer methods as very attractive strategies compared e g to classical variational techniques to perform state estimation and more generally for uncertainty estimation since other observer procedures can be conveniently combined to estimate uncertain parameters

a multiscale stabilized finite element method for the advection diffusion equation this paper presents a multiscale method that yields a stabilized finite element formulation for the advection diffusion equation the multiscale method arises from a decomposition of the scalar field into coarse resolved scale and fine unresolved scale the resulting stabilized formulation possesses superior properties like that of the supg and the gls methods a significant feature of the present method is that the definition of the stabilization term appears naturally and therefore the formulation is free of any user designed or user defined parameters another important ingredient is that since the method is residual based it satisfies consistency ab initio based on the proposed formulation a family of 2 d elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed numerical results show the good performance of the method on uniform skewed as well as composite meshes and confirm convergence at optimal rates 2004 elsevier b v all rights reserved

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

substitutions and interval exchange transformations of rotation class we propose a method for obtaining the symbolic orbits of interval exchange transformations of rotation class over n intervals by composing a finite set of basic substitutions i e by doing simple parallel rewriting based on surface theory this method is shown to be closely related to rauzy induction sturmian objects are known to correspond to interval exchange transformations over 2 intervals in this respect our n intervals case is shown to be also related to continued fractions and the obtained words have also linear complexity

contraction analysis of nonlinear distributed systems contraction theory is a comparatively recent dynamic analysis and non linear control system design tool based on an exact differential analysis of convergence this paper extends contraction theory to local and global stability analysis of important classes of non linear distributed dynamics such as convection diffusion reaction processes lagrangian and hamilton jacobi dynamics and optimal controllers and observers by contrast with stability proofs based on energy dissipation stability and convergence can be determined for energy based systems excited by time varying inputs the hamilton jacobi bellman controller and a similar optimal non linear observer design are studied based on explicitly computable conditions on the convexity of the cost function these stability conditions extend the well known conditions on controllability and observability grammians for linear time varying systems without requiring the unknown transition matrix of the underlying differential dynamics

brief paper distributed model predictive control of dynamically decoupled systems with coupled cost this paper considers the distributed model predictive control dmpc of systems with interacting subsystems having decoupled dynamics and constraints but coupled costs an easily verifiable constraint is introduced to ensure asymptotic stability of the overall system in the absence of disturbance the constraint introduced has a parameter which allows for the performance of the dmpc system to approach that controlled by a centralized model predictive controller when the subsystems are linear and additive disturbance is present the added constraint ensures the state of each subsystem converges to its respective minimal disturbance invariant set the approach is demonstrated via several numerical examples

compositional contraction analysis of resetting hybrid systems this note develops sufficient conditions for exponential convergence of resetting hybrid nonlinear dynamical systems using nonlinear contraction theory the analysis first develops a unified formulation of continuous time and discrete time nonlinear dynamics based on a differential transition matrix this yields enhanced dwell time based conditions for stability of such systems analogous to those existing for switched systems it turns out that such dwell time based conditions unlike their counterparts for switched systems include arbitrary stability conditions as a special case and are less conservative and much simpler to verify

variational multiscale a posteriori error estimation for multi dimensional transport problems this paper presents an explicit a posteriori error estimator for the multi dimensional transport equation based on an approximation to the variational multiscale theory the technique is adequate for methods with a local error distribution such as stabilized methods yielding efficiencies close to one for both the hyperbolic and diffusive limit regarding the hyperbolic limit previous work is extended to multi dimensions adequate norms are proposed for the computation of the error and proper error intrinsic time scales are calculated for the bilinear quadrilateral and the linear triangle furthermore the model considers the element interface error along the element edges enabling the error prediction in the diffusive limit the success of the method can be explained by the fact that in stabilized methods the element local problem captures most of the error and the proposed error intrinsic time scales are an approximation to the solution of the dual problem the proposed technology which can be implemented straightforwardly in existing codes is extremely economical because it is a simple explicit postprocessing

stability of semidiscrete formulations for parabolic problems at small time steps solutions of direct time integration schemes that converge in time to conventional semidiscrete formulations may be polluted at small time steps by spurious spatial oscillations along with attendant overshoot in time this degradation is not an artifact of the time marching scheme but rather a property of the solution of the semidiscrete formulation itself a critical time step for the onset of spatial oscillations is derived by analogy to singularly perturbed elliptic problems we then propose a simple procedure of spatial stabilization to remove this pathology from implicit time integration schemes without affecting unconditional temporal stability spatially stabilized implicit time integration is free of spurious spatial oscillations at small time steps and numerical experience points to improved temporal accuracy as well

on the stabilization parameter in the subgrid scale approximation of scalar convection diffusion reaction equations on distorted meshes abstract in this paper we revisit the definition of the stabilization parameter in the finite element approximation of the convection diffusion reaction equation the starting point is the decomposition of the unknown into its finite element component and a subgrid scale that needs to be approximated in order to incorporate the distortion of the mesh into this approximation we transform the equation for the subgrid scale within each element to the shape regular reference domain the expression for the subgrid scale arises from an approximate fourier analysis and the identification of the wave number direction where instabilities are most likely to occur the final outcome is an expression for the stabilization parameter that accounts for anisotropy and the dominance of either convection or reaction terms in the equation

a contraction approach to the hierarchical analysis and design of networked systems this brief is concerned with the stability of continuous time networked systems using contraction theory a result is established on the network structure and the properties of the individual component subsystems and their couplings to ensure the overall contractivity of the entire network specifically it is shown that a contraction property on a reduced order matrix that quantifies the interconnection structure coupled with contractivity expansion estimates on the individual component subsystems suffices to ensure that trajectories of the overall system converge towards each other

linearized euler predictions of unsteady aerodynamic loads in cascades a linearized euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and vibratory blade motion is presented using the linearized euler technique one decomposes the flow into a mean or steady flow plus an unsteady harmonically varying small disturbance flow linear variable coefficient equations describe the small disturbance behavior of the flow and are solved using a pseudotime time marching lax wendroff scheme for the blade motion problem a harmonically deforming computational grid that conforms to the motion of vibrating blades eliminates large error producing mean flow gradient terms that would otherwise appear in the unsteady flow tangency boundary condition

a positivity preserving variational method for multi dimensional convectiondiffusionreaction equation a new positivity preserving variational ppv procedure is proposed to solve the convectiondiffusionreaction cdr equation through the generalization of stabilized finite element methods the present variational procedure offers minimal phase and amplitude errors for different regimes associated with convection diffusion and reaction effects by means of fourier analysis we first review the shortcomings of the galerkin least squares gls and the subgrid scale sgs methods during the change in sign of the reaction coefficient that motivates us for the present linear stabilization as a combined gls sgs methodology discrete upwind operator with a solution dependent nonlinear term is then introduced in high gradient regions which enables the positivity preserving property in the variational formulation direct extension to multi dimensions is carried out by considering the principle streamline and crosswind directions the efficacy of the method is demonstrated by the systematic accuracy and stability analyses in one and two dimensions results show the reduction of oscillations in the solution in one and two dimensional cases and a remarkable reduction in the phase error is observed for the cases with negative reaction coefficient the proposed formulation provides a superior solution in the reaction dominated as well as the convection dominated regimes due to the minimization of spurious oscillations and accurate capturing of the high gradient regions

robust distributed model predictive control of constrained dynamically decoupled nonlinear systems a contraction theory perspective abstract this paper considers the robust distributed model predictive control mpc of a group of dynamically decoupled nonlinear systems cooperating via the cost function subject to control constraints inspired by the contraction theory we develop the robust distributed mpc scheme assuming that the dynamics of the cooperating systems satisfy the contraction property they are contracting in a tube centered around a nominal state trajectory compared to conventional robust distributed mpc which uses the lipschitz continuity property the proposed method features the following aspects 1 it can tolerate larger disturbances and 2 it is feasible for a larger prediction horizon and could enlarge the feasible region accordingly the paper evaluates the maximum disturbance which the nonlinear system can tolerate when controlled using the proposed method and derives sufficient conditions for the recursive feasibility of the optimization and for the practical stability of the closed loop system the effectiveness of the proposed method is illustrated using a simulation example

a multiscale a posteriori error estimate we introduce a hierarchic a posteriori error estimate for singularly perturbed reaction diffusion problems the estimator is based on a petrov galerkin method in which the trial space is enriched with nonpolynomial functions or multiscale functions we study the equivalence between the a posteriori estimate and the exact error in the energy norm moreover we prove a relationship between the hierarchic estimator and an explicit residual estimator the approach provides accurate estimates for the boundary layer regions which is confirmed by numerical experiments 2004 elsevier b v all rights reserved

a contraction theory approach to stochastic incremental stability we investigate the incremental stability properties of ito stochastic dynamical systems specifically we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system this bound can be expressed as a function of the noise intensity and the contraction rate of the noise free system we illustrate these results in the contexts of nonlinear observers design and stochastic synchronization

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

variational multiscale a posteriori error estimation for systems application to linear elasticity abstract this paper presents an explicit residual based a posteriori error estimator for linear elasticity the method is derived from the variational multiscale theory where the subgrid scales and the constants of the method are calculated explicitly from fine scale green s functions several numerical examples are presented showing satisfactory local and global efficiencies when the h 1 seminorm is employed the formulation which is applied to plane stress problems can be easily extended to other elasticity problems

implicitly restarted arnoldi with purification for the shift invert transformation the need to determine a few eigenvalues of a large sparse generalised eigenvalue problem az bx with positive semidefinite b arises in many physical situations for example in a stability analysis of the discretised navier stokes equation a common technique is to apply arnoldi s method to the shift invert transformation but this can suffer from numerical instabilities as is illustrated by a numerical example in this paper a new method that avoids instabilities is presented which is based on applying the implicitly restarted arnoldi method with the b semi inner product and a purification step the paper contains a rounding error analysis and ends with brief comments on some extensions

a nonlinear subgrid method for advection diffusion problems abstract this work presents a general framework for approximating advection diffusion equations based on principles of scale separation a two level decomposition of the discrete approximation space is performed and the local problem is modified to capture both local and nonlocal discontinuities the new feature is the local control resulting from decomposing the velocity field into the resolved and unresolved scales and requiring the satisfaction of the discrete model problem at the element level for a minimum kinetic energy associated to the unresolved scales this procedure leads to a nonlinear subgrid model that acts only on the unresolved scales but does not require any tuned up parameter it can be considered a self adaptive method such that the amount of the subgrid viscosity is automatically introduced according to the residual of the resolved scale at element level

bubble functions prompt unusual stabilized finite element methods a second order linear scalar differential equation including a zero th order term is approximated using first the standard galerkin method enriched with bubble functions static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations the method is generalized to allow for a convection operator in the equation this work may be employed as a starting point for simulation of nonlinear equations governing turbulence phenomena flows with chemical reactions and other important problems

a linearized method for the frequency analysis of three dimensional fluid structure interaction problems in all flow regimes abstract we present a computational fluid dynamics cfd based linearized method for the frequency analysis of three dimensional fluid structure interaction problems this method is valid in the subsonic transonic and supersonic flow regimes and is insensitive to the frequency or damping level of the sought after coupled eigenmodes it is based on the solution by an orthogonal iteration procedure of a complex eigenvalue problem derived from the linearization of a three field fluid structure moving mesh formulation the key computational features of the proposed method include the reuse of existing unsteady flow solvers a second order approximation of the flux jacobian matrix and a parallel domain decomposition based iterative solver for the solution of large scale systems of discretized fluid structure equations while the frequency analysis method proposed here is primarily targeted at the extraction of the eigenpairs of a wet structure we validate it with the flutter analysis of the agard wing 445 6 for which experimental data is available

coupled fluid structure interaction hemodynamics in a zero pressure state corrected arterial geometry abstract hemodynamic conditions in large arteries are significantly affected by the interaction of the pulsatile blood flow with the distensible arterial wall a numerical procedure for solving the fluid structure interaction problem encountered in cardiovascular flows is presented we consider a patient specific carotid bifurcation geometry obtained from 3d reconstruction of in vivo acquired tomography images which yields a geometrical representation of the artery corresponding to its pressurized state to recover the geometry of the artery in its zero pressure state which is required for a fluid structure interaction simulation we utilize inverse finite elastostatics time dependent flow simulations with in vivo measured inflow volume flow rate in the 3d undeformed artery are performed through the finite element method the coupled momentum method for fluid structure interaction is adopted to incorporate the influence of wall compliance in the numerical computation of the time varying flow domain to demonstrate the importance in recovering the zero pressure state of the artery in hemodynamic simulations we compute the time varying flow field with compliant walls for the original and the zero pressure state corrected geometric configurations of the carotid bifurcation the most important resulting effects in the hemodynamic environment are evaluated our results show a significant change in the wall shear stress distribution and the spatiotemporal extent of the recirculation regions

analysis of the small viscosity and large reaction coefficient in the computation of the generalized stokes problem by a novel stabilized finite element method abstract in this paper we propose and analyze a novel stabilized finite element method fem for the system of generalized stokes equations arising from the time discretization of transient stokes problem the system involves a small viscosity which is proportional to the inverse of large reynolds number and a large reaction coefficient which is the inverse of small time step the proposed stabilized fem employs the c 0 piecewise linear elements for both velocity field and pressure on the same mesh and uses the residuals of the momentum equation and the divergence free equation to define the stabilization terms the stabilization parameters are fixed and element independent without a comparison of the viscosity the reaction coefficient and the mesh size using the finite element solution of an auxiliary boundary value problem as the interpolating function for velocity and the h 1 seminorm projection for pressure instead of the usual nodal interpolants we derive error estimates for the stabilized finite element approximations to velocity and pressure in the l 2 and h 1 norms and most importantly we explicitly establish the dependence of error bounds on the viscosity the reaction coefficient and the mesh size our analysis reveals that this stabilized fem is particularly suitable for the generalized stokes system with a small viscosity and a large reaction coefficient which has never been achieved before in the error analysis of other stabilization methods in the literature we then numerically confirm the effectiveness of the proposed stabilized fem comparisons made with other existing stabilization methods show that the newly proposed method can attain better accuracy and stability

the discontinuous enrichment method for multiscale analysis computation naturally separates scales of a problem according to the mesh size a variety of improved numerical methods are described by multiscale considerations differing in the treatment of the unresolved fine scales the discontinuous enrichment method provides a unique multiscale approach to computation by employing fine scales that contain solutions of the homogeneous partial differential equation in a discontinuous framework the method thus combines relative ease of implementation with improved numerical performance these properties are demonstrated for both multiscale wave and transport problems pointing to the potential of considerable savings in computational resources

real numbers having ultimately periodic representations in abstract numeration systems using a genealogically ordered infinite regular language we know how to represent an interval of r numbers having an ultimately periodic representation play a special role in classical numeration systems the aim of this paper is to characterize the numbers having an ultimately periodic representation in generalized systems built on a regular language the syntactical properties of these words are also investigated finally we show the equivalence of the classical expansions with our generalized representations in some special case related to a pisot number

a quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability we present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closed loop stability the scheme can be applied to both stable and unstable systems with input constraints the objective functional to be minimized consists of an integral square error ise part over a finite time horizon plus a quadratic terminal cost the terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate lyapunov equation furthermore the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region if the jacobian linearization of the nonlinear system to be controlled is stabilizable we prove that feasibility of the open loop optimal control problem at time t 0 implies asymptotic stability of the closed loop system the size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense

comparison of some finite element methods for solving the diffusion convection reaction equation abstract in this paper we describe several finite element methods for solving the diffusion convection reaction equation none of them is new although the presentation is non standard in an effort to emphasize the similarities and differences between them in particular it is shown that the classical supg method is very similar to an explicit version of the characteristic galerkin method whereas the taylor galerkin method has a stabilization effect similar to a sub grid scale model which is in turn related to the introduction of bubble functions

linear stability of incompressible flow using a mixed finite element method we analyzed the linear stability for incompressible flow using the mixed finite element method first by means of the fractional step finite element method the two dimensional base flows were numerically computed over a range of reynolds numbers and then they were perturbed with three dimensional disturbances by using linear stability and normal mode analysis we obtained the partial differential equations governing the evolution of perturbation from linearized navier stokes equations with slight compressibility in terms of the mixed finite element discretization in which six node quadratic lagrange triangular elements with quadratic interpolation for velocities p2 and three node linear lagrange triangular elements for pressure p1 were used a nonsingular generalized eigenproblem was formulated from these equations whose solution gives the dispersion relationship between the complex growth rate and the wave number we examined the stability of lid driven cavity flow in this study the stability results obtained from thep2p1elements were compared with those fromp1p1elements the spatial distribution of the pressure disturbance can be smoothed by using ap2p1element such as that in the simulation of incompressible flows by the mixed finite element method however the choice of elemental type has little influence on the stability results this study presents stability curves to identify the critical reynolds number and the critical wavelength of the neutral mode and discusses the instability mechanism the taylor goertler like vortices in the cavity were obtained by means of the reconstruction of three dimensional flows the stability results and the reconstructed three dimensional flows were in agreement with the observed ones and the other numerical stability results respectively

modeling of steep layers in singularly perturbed diffusion reaction equation via flexible fine scale basis abstract we present a new stabilized method for the diffusion reaction equation which develops sharp boundary and or internal layers for the reaction dominated case i e singularly perturbed case the method relies on an improved expression for the stabilization parameter that is derived via the fine scale variational formulation facilitated by the variational multiscale vms framework the proposed fine scale basis consists of enrichment functions which may be nonzero at element edges the derived stabilization parameter enjoys spatial variation over element interiors and along inter element boundaries that helps model the rapid variation of the residual of the euler lagrange equations over the domain this feature also facilitates consistent stabilization across boundary and internal layers as well as capturing anisotropic refinement effects the method is able to better satisfy the maximum principle as compared to other existing methods we present a priori mathematical analysis of the stability and convergence of the method for the diffusion reaction equation optimal convergence on meshes comprised of linear triangles and bilinear quadrilateral elements are presented for smooth problems as well as for problems with steep boundary layers stability and accuracy features of the method for problems with discontinuous forcing function internal layers and boundary layers are shown and its performance on unstructured and distorted meshes comprised of quadrilateral and triangular elements is highlighted

stable and time dissipative finite element methods for the incompressible navier stokes equations in advection dominated flows we examine a new galerkin method with scaled bubble functions which replicates the exact artificial diffusion methods in the case of 1 d scalar advection diffusion and that leads to non oscillatory solutions as the streamline upwinding algorithms for 2 d scalar advection diffusion and incompressible navier stokes this method retains the satisfaction of the babuska brezzi condition and thus leads to optimal performance in the incompressible limit this method when combined with the recently proposed linear unconditionally stable algorithms of simo and armero yields a method for solution of the incompressible navier stokes equations ideal for either diffusive or advection dominated flows examples from scalar advection diffusion and the solution of the incompressible navier stokes equations are presented

on the stability of residual free bubbles for convection diffusion problemsand their approximation by a two level finite element method we consider the galerkin finite element method for partial diffferential equations in two dimensions where the finite dimensional space used consists of piecewise isoparametric polynomials enriched with bubble functions writing l for the differential operator we show that for elliptic convection diffusion problems the component of the bubble enrichment that stabilizes the method is essentially equivalent to a petrov galerkin method with an l spline exponentially fitted trial space and piecewise polynomial test space the remaining component of the bubble influences the accuracy of the method a stability inequality recently obtained by brezzi franca and russo for a limiting case of bubbles applied to convection diffusion problems is shown to be slightly weaker than the standard stability inequality that is obtained for the sdfem supg method thereby demonstrating that the bubble approach is in general slightly less stable than the streamline diffusion method when the trial functions are piecewise linear we show that residual free bubbles are as stable as sdfem supg and we extend this stability inequality to include positive mesh peclet numbers in the convection dominated regime approximate computations of the residual free bubbles are performed using a two level finite element method

itineraries of rigid rotations and diffeomorphisms of the circle we examine the itinerary of email protected s 1 r z under the rotation by email protected email protected q the motivating question is if we are given only the itinerary of 0 relative to email protected s 1 a finite union of closed intervals can we recover a and i we prove that the itineraries do determine a and i up to certain equivalences then we present elementary methods for finding a and i moreover if g s 1 s 1 is a c 2 orientation preserving diffeomorphism with an irrational rotation number then we can use the orbit itinerary to recover the rotation number up to certain equivalences

on an improved unusual stabilized finite element method for theadvective reactive diffusive equation an improved unusual finite element method is studied herein for a second order linear scalar differential equation including a zero order term the method consists in subtracting from the standard galerkin method a mesh dependent term suggested by static condensation of the bubbles based on this idea a new stabilized parameter is constructed which improves accuracy of the solution several numerical tests attest the efficiency of the present method and an error analysis is perfomed

a variational multiscale higher order finite element formulation for turbomachinery flow computations abstract the variational multiscale approach for finite elements addresses the inclusion of the effect of fine scales of the solution in the coarse problem in this framework advective diffusive reactive equations modelling turbomachinery flows feature both advection and reaction induced instabilities to be tackled to this end this work deals with a new method called v sgs variable subgrid scale designed for quadratic elements with a variable intrinsic time parameter two dimensional tests have been considered to compare v sgs against supg and other stabilization devices including the flow around a naca 4412 airfoil to assess its reliability in the handling of advanced turbulence closures on cruder meshes

time dependent subgrid scales in residual based large eddy simulation of turbulent channel flow the present study investigates the effect of taking into account the time dependency of the fine subgrid scales in a residual based variational multiscale approach for large eddy simulation the residual based variational multiscale method with time dependent dynamic subgrid scales is presented and the impact of the time dependency is studied for the well known test case of turbulent channel flow results are presented from computations for various values of the reynolds number namely ret 180 ret 395 and ret 590 and several time step sizes a generalized a time integration scheme is employed results from our numerical experiments with dynamic subgrid scales are compared to results obtained with an approximation not explicitly taking the time dependency of the subgrid scales into account for all re t values and time step sizes under consideration results for resolved quantities computed by both approaches are very similar this statement applies to both mean streamwise velocity and root mean square velocity fluctuations however it provides a model for the subgrid scales not depend ing on the time step size and enabling a more robust representation of unresolved scales thus we conclude that the time dependent subgrid scale approximation is not capable of producing more accurate results for this type of flow if the time step size is chosen within an optimal range however we expect it to be more advantageous for more complex problems since our results indicate that it provides a more reliable representation of unresolved scales

analysis of a streamline diffusion finite element method for the stokes and navier stokes equations for the stokes equations with convection and the incompressible navier stokes equations the authors analyze a streamline diffusion finite element method that is capable of balancing both the convection and the pressure thus allowing the use of arbitrary pairs of velocity pressure spaces for the linear problem the authors obtain for all mesh peclet numbers optimal error estimates in natural norms including in particular the l 2 norm of the pressure the same holds for the nonlinear problem which close to a regular branch of solutions i e the linearized operator is an isomorphism of the norm of the inverse of which still depends on the reynolds number consequently the dependence of the error constants on the reynolds number is not completely resolved in this case

linear stability analysis in fluid structure interaction with transpiration part i formulation and mathematical analysis the aim of this work is to provide a new linearization principle approach particularly suited for problems in fluid structure stability the complexity here and the main difference with respect to the classical approach comes from the fact that the full non linear fluid equations are written in a moving i e time dependent domain the underlying idea of our approach uses transpiration techniques j fluid mech 4 1958 383 g mortchelewicz application of linearized euler equations to flutter in 85th agard smp meeting aalborg denmark 1997 p raj b harris using surface transpiration with an euler method for cost effective aerodynamic analysis in aiaa 24th applied aerodynamics conference number 93 3506 monterey canada 1993 aiaa 27 6 1989 777 with the formalization and linearization recently developed in rev europeenne elem finis 9 6 7 2000 681 a dervieux ed fluid structure interaction kogan page science london 2003 chapter 3 this allows us to obtain a new grid independent coupled spectral problem involving the linearized navier stokes equations and those of a reduced linear structure the coupling is realized through specific transpiration conditions acting on a fixed interface while keeping a fixed fluid domain we provide a rigorous mathematical treatment of this eigenproblem we prove that the corresponding eigenmodes characterizing the free evolution of the system can be obtained from the characteristic values of a compact operator acting on a hilbert space moreover we localize the eigenfrequencies of the system in a parabolic region of the complex plan centered along the positive real axis

languages d0l systems sets of curves and surface automorphisms we introduce extend and apply some relationships between formal language theory and surface theory first we show how boundaries of languages topologized with the cantor metric can be mapped to sets of curves on surfaces namely laminations second we present how and when endomorphisms of free monoids i e substitutions can be mapped to automorphisms of surfaces so that d0l systems correspond to iterations of these automorphisms third we apply these ideas to construct sets of non periodic irreducible automorphisms of surfaces following 14 35 43 so that the involved proofs do not use any differential or algebraic tools but accordingly substitution and d0l system theory of 11 12 31 32 37 mainly the decidability for a d0l language 12 to be strongly repetitive or not this construction also yields effective symbolic descriptions of the stable sets of curves associated with these automorphisms

an adaptive stabilized finite element scheme for a water quality model abstract residual type a posteriori error estimators are introduced in this paper for an advection diffusion reaction problem with a dirac delta source term the error is measured in an adequately weighted w 1 p norm these estimators are proved to yield global upper and local lower bounds for the corresponding norms of the error they are used to guide adaptive procedures which are experimentally shown to lead to optimal orders of convergence

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100