an inf sup stable and residual free bubble element for the oseen equations we investigate the residual free bubble method for the linearized incompressible navier stokes equations starting with a nonconforming inf sup stable element pair for approximating the velocity and pressure we enrich the velocity space by discretely divergence free bubble functions to handle the influence of strong convection an important feature of the method is that the stabilization does not generate an additional coupling between the mass equation and the momentum equation as is the case for the streamline upwind petrov galerkin method applied to equal order interpolation furthermore the discrete solution is piecewise divergence free a property which is useful for the mass balance in transport equations coupled with the incompressible navier stokes equations

stabilized finite element methods based on multiscale enrichment for the stokes problem this work concerns the development of stabilized finite element methods for the stokes problem considering nonstable different or equal order of velocity and pressure interpolations the approach is based on the enrichment of the standard polynomial space for the velocity component with multiscale functions which no longer vanish on the element boundary on the other hand since the test function space is enriched with bubble like functions a petrov galerkin approach is employed we use such a strategy to propose stable variational formulations for continuous piecewise linear in velocity and pressure and for piecewise linear piecewise constant interpolation pairs optimal order convergence results are derived and numerical tests validate the proposed methods

lower bounds for parallel algebraic decision trees parallel complexity of convex hulls and related problems we show that any parallel algorithm in the fixed degree algebraic decision tree model that answers membership queries in w r n using p processors requires w n log p n rounds where w is the number of connected components of w we further prove a similar result for the average case complexity we give applications of this result to various fundamental problems in computational geometry like convex hull construction and trapezoidal decomposition and also present algorithms with matching upper bounds

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

multiscale seamless domain method for solving nonlinear problems using statistical estimation methodology this article presents a nonlinear solver combining regression analysis and a multiscale simulation scheme first the proposed method repeats microscopic analysis of a local simulation domain which is extracted from the entire global domain to statistically estimate the relation s between the value of a dependent variable at a point and values at surrounding points the relation is called regression function subsequent global analysis reveals the behavior of the global domain with only coarse grained points using the regression function quickly at low computational cost which can be accomplished using a multiscale numerical solver called the seamless domain method sdm the objective of the study is to solve a nonlinear problem accurately and at low cost by combining the two techniques we present an example problem of a nonlinear steady state heat conduction analysis of a heterogeneous material the proposed model using fewer than 1000 points generates a solution with precision similar to that of a standard finite element solution using hundreds of thousands of nodes to investigate the relationship between the accuracy and computational time we apply the sdm under varying conditions such as the number of iterations of the prior analysis for statistical data learning

convergence analysis of a new multiscale finite element method with the element for the incompressible flow abstract in this paper we propose a new multiscale finite element method for the stationary navier stokes problem this new method for the lowest order finite element pairs p 1 p 0 is based on the multiscale enrichment and derived from the navier stokes problem itself therefore the new multiscale finite element method better reflects the nature of the nonlinear problem the well posedness of this new discrete problem is proved under the standard assumption meanwhile convergence of the optimal order in h 1 norm for velocity and l 2 norm for pressure is obtained especially via applying a new dual problem for the incompressible navier stokes problem and some techniques in the process for proof we establish the convergence of the optimal order in l 2 norm for the velocity finally numerical examples confirm our theory analysis for this new multiscale finite element method and validate the high effectiveness of this new method

a conservative stable finite element method for stokes flow and nearly incompressible linear elasticity on rectangular grid abstract in this paper we discuss finite element methods for the incompressible stokes problem and the nearly incompressible linear elasticity problem specifically we present a finite element pair for the incompressible stokes problem which satisfies the discrete inf sup condition and the discrete korn s inequality and moreover which is element wise conservative the pair provides a locking free method for the nearly incompressible linear elasticity problem without reduced integration

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

bubble stabilization of finite element methods for the linearized incompressible navier stokes equations abstract in this paper we discuss the stabilization via bubble functions of a finite element method for stationary linearized incompressible navier stokes equations it is shown that residual free bubbles can reproduce supg

subscales on the element boundaries in the variational two scale finite element method abstract in this paper we introduce a way to approximate the subscales on the boundaries of the elements in a variational two scale finite element approximation to flow problems the key idea is that the subscales on the element boundaries must be such that the transmission conditions for the unknown split as its finite element contribution and the subscale hold in particular we consider the scalar convection diffusion reaction equation the stokes problem and darcy s problem for these problems the transmission conditions are the continuity of the unknown and its fluxes through element boundaries the former is automatically achieved by introducing a single valued subscale on the boundaries for the conforming approximations we consider whereas the latter provides the effective condition for approximating these values the final result is that the subscale on the interelement boundaries must be proportional to the jump of the flux of the finite element component and the average of the subscale calculated in the element interiors

applications of ramsey s theorem to decision tree complexity combinatorial techniques for extending lower bound results for decision trees to general types of queries are presented problems that are defined by simple inequalities between inputs called order invariant problems are considered a decision tree is called k bounded if each query depends on at most k variables no further assumptions on the type of queries are made it is proved that one can replace the queries of any k bounded decision tree that solves an order invariant problem over a large enough input domain with k bounded queries whose outcome depends only on the relative order of the inputs as a consequence all existing lower bounds for comparison based algorithms are valid for general k bounded decision trees where k is a constant an o n log n lower bound for the element uniqueness problem and several other problems for any k bounded decision tree such that k o n c and c n 1 2 bounded decision trees of complexity o n that solve the element uniqueness problem all the lower bounds mentioned above are shown to hold for nondeterministic and probabilistic decision trees as well

residual free bubbles for advection diffusion problems the general error analysis we develop the general a priori error analysis of residual free bubble finite element approximations to linear elliptic convection dominated diffusion problems subject to homogeneous dirichlet boundary condition optimal order error bounds are derived in various norms using piecewise polynomial finite elements of degree greater than or equal to 1

numerical multiscale methods for a reaction dominated model a galerkin enriched finite element method gem is proposed for the singularly perturbed reaction diffusion equation this new method is an improvement on the petrov galerkin enriched method pgem where now the standard piecewise bi linear test space incorporates fine scales this appears as the fundamental ingredient for suppressing oscillations in the numerical solutions also new parameter free stabilized finite element methods derived from both the gem and the pgem are driven by local generalized eigenvalue problems in the process jump stabilizing terms belonging to the class of cip methods emerge as a result of the enriching procedure interestingly numerical results indicate that jump based stabilizations are unnecessary and sometimes undesirable when treating reaction dominated problems finally we establish relationships with more standard enriched and stabilized methods and show that the proposed methods outperform them numerically

brief paper anti windup and bumpless transfer schemes this paper considers the problem of windup which occurs when a controller with unstable integrator modes is subjected to input saturation or multi mode operation an optimal strategy for the so called model based approach is proposed based on an h optimisation framework this has been found to give good results on numerical examples taken from the literature

multiscale hybrid mixed method for the stokes and brinkman equations the method abstract the multiscale hybrid mixed mhm method is extended to the stokes and brinkman equations with highly heterogeneous coefficients the approach is constructive we first propose an equivalent dual hybrid formulation of the original problem using a coarse partition of the heterogeneous domain faces may be not aligned with jumps in the data then the exact velocity and the pressure are characterized as the solution of a global face problem and the solutions of local independent stokes or brinkman problems at the continuous level owing to this decomposition the one level mhm method stems from the standard galerkin approach for the lagrange multiplier space basis functions are responsible for upscaling the unresolved scales of the medium into the global formulation they are the exact solution of the local problems with prescribed neumann boundary conditions on faces driven by the lagrange multipliers we make the mhm method effective by adopting the unusual stabilized finite element method to solve the local problems approximately as such equal order interpolation turns out to be an option for the velocity the pressure and the lagrange multipliers the numerical solutions share the important properties of the continuum such as local equilibrium with respect to external forces and local mass conservation several academic and highly heterogeneous tests infer that the method achieves super convergence for the velocity as well optimal convergence for the pressure and also for the stress tensor in their natural norms

technical communique an anti windup scheme with closed loop stability considerations this paper considers the so called model based approach to anti windup compensation and analyses the stability of the closed loop system for a class of input nonlinearities the degrees of freedom in the anti windup scheme are used to minimise the h norm of the transfer function around the nonlinearity and the small gain theorem is used to prove stability

the complexity of problems on probabilistic nondeterministic and alternating decision trees this work generalizes decision trees in order to study lower bounds on the running times of algorithms that allow probabilistic nondeterministic or alternating control it is shown that decision trees that are allowed internal randomization at the expense of introducing a small probability of error run no faster asymptotically than ordinary decision trees for a collection of natural problems two geometric techniques from the literature for proving lower bounds on the time required by ordinary decision trees are shown to be special cases of one unified technique that in fact applies to nondeterministic decision trees as well finally it is shown that any lower bound on alternating decision tree time also applies to alternating turing machine time

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

explicit solution to the singular lq regulation problem an explicit solution to the multivariable discrete linear quadratic lq regulation problem is obtained in the limiting singular case where the input weighting matrix tends to zero such a solution follows from a suitable spectral factorization of the input spectrum density matrix under the assumption that the system is stabilizable and detectable and that its transfer function matrix is of full rank the suitable spectral factor is shown to be the product of the system s minimum phase image and its unitary interactor matrix the unitary interactor matrix defined is a special case of the nilpotent interactor matrix defined by m w rogozinski et al 1987

parallel comparison merging of many ordered lists we consider the problem of merging m disjoint ordered lists each of size n m we determine up to a constant factor the worst case and average case deterministic and randomized parallel comparison complexity of the problem for all the range of n m and p where p is the number of processors used the worst case deterministic time complexity is log mlog 1 p n loglog nlog 2 p n that means n log mp log log n for p 2n and log mlog p n loglog nlog p n for p 2n clearly merging two equal lists and sorting are special cases of this problem for m 2 and m n respectively we also prove that these bounds hold for randomized algorithms and even for the average case of deterministic or randomized ones therefore the average case of the best deterministic or randomized algorithm for this problem is not faster than the worst case of the best deterministic one by more than a constant factor

a taxonomy of consistently stabilized finite element methods for the stokes problem stabilized mixed methods can circumvent the restrictive inf sup condition without introducing penalty errors for properly chosen stabilization parameters these methods are well posed for all conforming velocity pressure pairs however their variational forms have widely varying properties first stabilization offers a choice between weakly or strongly coercive bilinear forms that give rise to linear systems with identical solutions but very different matrix properties second coercivity may be conditional upon a proper choice of a stabilizing parameter here we focus on how these two aspects of stabilized methods affect their accuracy and efficient iterative solution we present results that indicate a preference of krylov subspace solvers for strongly coercive formulations stability criteria obtained by finite element and algebraic analyses are compared with numerical experiments while for two popular classes of stabilized methods sufficient stability bounds correlate well with numerical stability our experiments indicate the intriguing possibility that the pressure stabilized galerkin method is unconditionally stable

elements of a theory of simulation ii sequential dynamical systems we study a class of discrete dynamical systems that is motivated by the generic structure of simulations the systems consist of the following data a a finite graph y with vertex set 1 n where each vertex has a binary state b functions f i f 2 n f 2 n and c an update ordering p the functions f i update the binary state of vertex i as a function of the state of vertex i and its y neighbors and leave the states of all other vertices fixed the update ordering is a permutation of the y vertices by composing the functions f i in the order given by p one obtains the sequential dynamical system sds f y p email protected i 1nf p i f 2 n f 2 n we derive a decomposition result characterize invertible sds and study fixed points in particular we analyse how many different sds that can be obtained by reordering a given multiset of update functions and give a criterion for when one can derive concentration results on this number finally some specific sds are investigated

analysis of a finite volume element method for the stokes problem in this paper we propose a stabilized conforming finite volume element method for the stokes equations on stating the convergence of the method optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations a superconvergence result is also derived by using a postprocessing projection method in particular the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries finally some numerical experiments that confirm the predicted behavior of the method are provided

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

a residual local projection method for the oseen equation abstract a new residual local projection stabilized method relp is proposed as a result of an enriched petrov galerkin strategy for the oseen problem the p 12 p l pairs l 0 1 with continuous or discontinuous pressures are made stable by enhancing them with solutions of residual based local oseen problems and performing a static condensation procedure afterward this process does not involve the numerical solution of the local problems and maintains the degrees of freedom of the original spaces the method adds symmetric terms to the galerkin formulation which are easy to implement at the element level consistency well posedness and error estimates are demonstrated and an economic way to recover a locally conservative velocity field for the discontinuous pressure case is also proposed extensive numerical experiments attest the theoretical results and compare the relp method to previously existing alternatives

a petrov galerkin enriched method a mass conservative finite element method for the darcy equation starting from the non stable p1 p0 discretization we build enhanced methods for the darcy equation which are stable and locally mass conservative the methods are derived in a petrov galerkin framework where both velocity and pressure trial spaces are enriched with multiscale functions these functions solve local problems correcting the residuals of the strong equations in each element and interior edge which leads to a velocity space enhanced with functions belonging to the lowest order raviart thomas space several numerical tests validate the methods

stabilized mixed methods for the stokes problem the solution of the stokes problem is approximated by three stabilized mixed methods one due to hughes balestra and franca and the other two being variants of this procedure in each case the bilinear form associated with the saddle point problem of the standard mixed formulation is modified to become coercive over the finite element space error estimates are derived for each procedure

some current cfd issues relevant to the incompressible navier stokes equations abstract the goals of this paper are to carefully define a particular class of well set incompressible navier stokes problems in the continuum partial differential equation pde setting and to discuss some relevant and sometimes poorly understood issues related to these well posed pde problems both in the continuum world and in its computer counterpart emphasized are three common formulations used to generate computer codes the primitive variable velocity pressure formulation and two derived variable formulations pressure poisson equation and vorticity transport equation

a unified stabilized method for stokes and darcy s equations we use the lowest possible approximation order piecewise linear continuous velocities and piecewise constant pressures to compute solutions to stokes equation and darcy s equation applying an edge stabilization term to avoid locking we prove that the formulation satisfies the discrete inf sup condition we prove an optimal a priori error estimate for both problems the formulation is then extended to the coupled case using a nitsche type weak formulation allowing for different meshes in the two subdomains finally we present some numerical examples verifying the theoretical predictions and showing the flexibility of the coupled approach

the effect of number of hamiltonian paths on the complexity of a vertex coloring problem a generalization of dobkin and lipton s element uniqueness problem is introduced for any fixed undirected graph g on vertex set v 1 v 2 cdots v n the problem is to determine given n real numbers x 1 x 2 cdots x n whether x i ne x j for every edge upsilon i upsilon j in g this problem is shown to have upper and lower bounds of theta n log n linear comparisons if g is any dense graph the proof of the lower bound involves showing that any dense graph must contain a subgraph with many hamiltonian paths and demonstrating the relevance of these hamiltonian paths to a geometric argument in addition we exhibit relatively sparse graphs for which the same lower bound holds and relatively dense graphs for which a linear upper bound holds

local projection stabilized galerkin approximations for the generalized stokes problem we analyze pressure stabilized finite element methods for the solution of the generalized stokes problem and investigate their stability and convergence properties an important feature of the method is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations although stability of the method has been established for the homogeneous stokes equations the proof given here is based on the existence of a special interpolant with additional orthogonal property with respect to the projection space this makes it a lot simpler and more attractive the resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations

further considerations on residual free bubbles for advective diffusive equations abstract we further consider the galerkin method for advective diffusive equations in two dimensions the finite dimensional space employed is of piecewise polynomials enriched with residual free bubbles rfb we show that in general this method does not coincide with the supg method unless the piecewise polynomials are spanned by linear functions furthermore a simple stability analysis argument displays the effect of the rfb on the reduced space of piecewise polynomials which in some situations is not equivalent to streamline diffusion for bilinears

convergence analysis of a residual local projection finite element method for the navier stokes equations this work presents and analyzes a new residual local projection stabilized finite element method relp for the nonlinear incompressible navier stokes equations stokes problems defined elementwise drive the construction of the residual based terms which make the present method stable for the finite element pairs mathbb p 1 mathbb p l l 0 1 numerical upwinding is incorporated through an extra control on the advective derivative and on the residual of the divergence equation well posedness of the discrete problem as well as optimal error estimates in natural norms are proved under standard assumptions next a divergence free velocity field is provided by a simple postprocessing of the computed velocity and pressure using the lowest order raviart thomas basis functions this updated velocity is proved to converge optimally to the exact solution numerics assess the theoretical results and validate the relp method

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

the l2 l2 bumpless transfer problem for linear plants its definition and solution a novel characterization of bumpless transfer among alternative controllers both in continuous and discrete time is introduced the bumpless transfer problem is to design a compensation scheme guaranteeing an l 2 respectively l 2 bound on the mismatch after the switching time between the actual plant output and a particular target ideal response minimization of the gain from initial plant state mismatch to l 2 respectively l 2 plant output mismatch provides improved transients a solution to the bumpless transfer problem is given both for plants without input saturation and for plants with input saturation the solution guarantees anti windup features in the latter case

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

enhanced rfb method the residual free bubble method rfb is a parameter free stable finite element method that has been successfully applied to a wide range of boundary value problems exhibiting multiple scale behaviour if some local features of the solution are known a priori the approximation properties of the rfb finite element space can be improved by enriching it on selected edges of the partition by edge bubbles that are supported on pairs of neighbouring elements motivated by this idea we define and analyse an enhanced residual free bubble method for the solution of convection dominated convection diffusion problems in 2 d our a priori analysis highlights the limitations of the rfb method and the improved global approximation properties of the new method the theoretical results are supported by detailed numerical experiments

a unified framework for the study of anti windup designs we present a unified framework for the study of linear time invariant lti systems subject to control input nonlinearities the framework is based on the following two step design paradigm design the linear controller ignoring control input nonlinearities and then add anti windup bumpless transfer awbt compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance the resulting awbt compensation is applicable to multivariable controllers of arbitrary structure and order all known lti anti windup and or bumpless transfer compensation schemes are shown to be special cases of this framework it is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model the actual analysis of stability and performance and robustness issues are problems in their own right and hence not detailed here the main result is the unification of existing schemes for awbt compensation under a general framework

on the adaptive selection of the parameter in stabilized finite element approximations a systematic approach is developed for the selection of the stabilization parameter for stabilized finite element approximation of the stokes problem whereby the parameter is chosen to minimize a computable upper bound for the error in the approximation the approach is applied in the context of both a single fixed mesh and an adaptive mesh refinement procedure the optimization is carried out by a derivative free optimization algorithm and is based on minimizing a new fully computable error estimator numerical results are presented illustrating the theory and the performance of the estimator together with the optimization algorithm

on a two level finite element method for the incompressible navier stokes equations we consider the galerkin finite element method for the incompressible navier stokes equations in two dimensions where the finite dimensional space s employed consist of piecewise polynomials enriched with residual free bubble rfb functions to find the bubble part of the solution a two level finite element method tlfem is described and its application to the navier stokes equation is displayed numerical solutions employing the tlfem are presented for three benchmark problems we compare the numerical solutions using the tlfem with the numerical solutions using a stabilized method

a two level enriched finite element method for a mixed problem the simplest pair of spaces is made inf sup stable for the mixed form of the darcy equation the key ingredient is to enhance the finite element spaces inside a petrov galerkin framework with functions satisfying element wise local darcy problems with right hand sides depending on the residuals over elements and edges the enriched method is symmetric locally mass conservative and keeps the degrees of freedom of the original interpolation spaces first we assume local enrichments exactly computed and we prove uniqueness and optimal error estimates in natural norms then a low cost two level finite element method is proposed to effectively obtain enhancing basis functions the approach lays on a two scale numerical analysis and shows that well posedness and optimality is kept despite the second level numerical approximation several numerical experiments validate the theoretical results and compares favourably in some cases our results with the classical raviart thomas element

towards multiscale functions enriching finite element spaces with local but not bubble like functions in this paper we propose a novel way via finite elements to treat problems that can be singular perturbed a reaction diffusion equation in our case we enrich the usual piecewise linear or bilinear finite element trial spaces with local solutions of the original problem as in the residual free bubble rfb setting but do not require these functions to vanish on each element edge a departure from the rfb paradigm such multiscale functions have an analytic expression for triangles and rectangles bubbles are the choice for the test functions allowing static condensation thus our method is of petrov galerkin type we perform several numerical validations which confirm the good performance of the method 2004 elsevier b v all rights reserved

mass lumping emanating from residual free bubbles a nodally exact scheme is derived for a model equation in 1d involving zeroth and second order terms the method is derived using residual free bubbles in conjunction with the galerkin approximation it is shown that this approach leads to the mass lumping scheme for sufficiently small mesh sizes

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

pressure stabilization of finite element approximations of time dependent incompressible flow problems in this paper we develop and analyze pressure stabilized finite element methods for the solution of the transient stokes problem which is a linear model problem of transient incompressible flow a model for the bubble enrichment is proposed to stabilize the numerical solution and an implicit backward euler method is considered for the time approximation different methods are obtained depending on whether bubbles are allowed to evolve with time or they are considered quasi static stability estimates are provided for the two methods considered both for the velocity and the pressure solutions numerical results obtained on test cases are also given which confirm the theoretical stability results

error analysis of some galerkin least squares methods for the elasticity equations the recent technique of stabilizing mixed finite element methods by augmenting the galerkin formulation with least squares terms calculated separately on each element is considered the error analysis is performed in a unified manner yielding improved results for some methods introduced earlier in addition a new formulation is introduced and analyzed method is used within two different contexts the first is in connection with the plain strain or three dimensional problems near the incompressible limit for which the poisson ratio equals one half it is well known that for these problems a standard lower order displacement finite element method will break down by now it is also well known how a working method can be obtained a new unknown the pressure is introduced and discretized with a finite element space different from that used for the displacements the finite element method obtained falls into the class of saddlepoint problems for which there is a general theory developed by brezzi and babuska 5 7 the application of this theory shows that the method converges optimally if the discrete spaces for the displacement and pressure satisfy a stability condition for a particular choice of displacement and pressure approximations it can be a difficult task to verify this babuska brezzi or inf sup condition during the last decade this problem has been intensively studied and the performances of many combinations are now known cf 18 and 23 26 for some recent extensions in addition there exists a general technique utilizing bubble functions by which a stable method can

local projection stabilized method on unsteady navier stokes equations with high reynolds number using equal order interpolation in this paper we propose and analyze a stabilized method for unsteady navier stokes equations with high reynolds number using local projection stabilized method to control spurious oscillations in the velocities due to dominant convection or in the pressure due to the velocity pressure coupling using equal order conforming elements in space and crank nicolson difference in time we derive a fully discrete formulation we prove stability and convergence of the approximate solution the error estimates hold irrespective of the reynolds number provided the exact solution is smooth this result is comparable with the streamline diffusion and continuous interior penalty methods

bounding the maximum size of a packet radio network the author addresses the problem arising in the topology design of packet radio networks prns which use time division multiplexing and have a diameter constraint of what is the maximum number n sub c f k of users which can be contained in a diameter k prn with f time slots per frame the author assumed that users cannot transmit and receive simultaneously and cannot transmit receive more than one packet at a time this assumption implies that no two channels accessed by the same user may be assigned the same time slot it is shown that the problem of determining n sub c f k is identical to the problem of determining the largest number of vertices which can be contained in an f edge colorable directed graph with diameter k lower bounds on n sub c f k for f 2 k 3 4 5 are obtained by generating large graphs of this type the graphs are constructed and colored by simple and fast procedures which are similar for different values of f and k an extensive bibliography on the edge coloring problem is included

a three level finite element method for the instationary incompressible navier stokes equations we present a two and a three level finite element method for the numerical simulation of incompressible flow governed by the navier stokes equations within the theoretical framework of the variational multiscale method and exploiting the concept of residual free bubbles we propose a separation of three different scale groups namely large resolved scales small resolved scales and unresolved scales the resolution of the large and small scales takes place on levels 1 and 2 with the aid of diverse approaches the dynamic calculation of a subgrid viscosity representing the effect of the unresolved scales constitutes level 3 of our algorithm the proposed algorithm is tested for various laminar flow situations and compared to the results obtained via an unusual stabilized finite element method it is supposed to be the basic scheme also for turbulent flow in a subsequent study

a non square sector condition and its application in deferred action anti windup compensator design a sector condition for two connected deadzone nonlinearities is provided by introducing an additional non square operator which exploits their connectivity a more general set of sector like matrix inequalities is obtained this non square matrix inequality condition is applied to an anti windup aw problem in which the aw compensator is not activated until the unconstrained control signal reaches a well defined level beyond that of the physical actuator limits the non square sector condition allows such deferred action aw synthesis to be performed in a manner much closer to traditional immediate sector based aw with either lowered conservatism or decreased computational effort in contrast to recent work the non square condition is applicable to other aw problems

a priori error analysis of residual free bubbles for advection diffusion problems we develop an a priori error analysis of a finite element approximation to the elliptic advection diffusion equation eps delta u conv cdot nabla u f subject to a homogeneous dirichlet boundary condition based on the use of residual free bubble functions an optimal order error bound is derived in the so called stability norm biggl eps nabla v 2 l 2 omega sum t h t conv cdot nabla v 2 l 2 t biggr 1 2 where ht denotes the diameter of element t in the subdivision of the computational domain

analysis of locally stabilized mixed finite element methods for the stokes problem in this paper a locally stabilized finite element formulation of the stokes problem is analyzed a macroelement condition which is sufficient for the stability of locally stabilized mixed methods based on a piecewise constant pressure approximation is introduced by satisfying this condition the stability of the qi po quadrilateral and the pi po triangular element can be established

optimal randomized algorithms for local sorting and set maxima randomized algorithms for two sorting problems are presented in the local sorting problem a graph is given in which each vertex is assigned an element of a total order and the task is to determine the relative order of every pair of adjacent vertices in the set maxima problem a collection of sets whose elements are drawn from a total order is given and the task is to determine the maximum element in each set lower bounds for the problems in the comparison model are described and it is shown that the algorithms are optimal within a constant factor

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

on the number of upward planar orientations of maximal planar graphs we consider the problem of determining the maximum and the minimum number of upward planar orientations a maximal planar graph can have we show that every n vertex maximal planar graph has at least w 1 189 n and at most o 4 n upward planar orientations moreover we show that there exist n vertex maximal planar graphs having o 2 n upward planar orientations and n vertex maximal planar graphs having w 2 599 n upward planar orientations further we present bounds for the maximum and the minimum number of acyclic orientations a maximal planar graph can have

smooth switching lpv controller design for lpv systems abstract this paper presents a method to design a smooth switching gain scheduled linear parameter varying lpv controller for lpv systems the moving region of the gain scheduling variables is divided into a specified number of local subregions as well as subregions for the smooth controller switching and one gain scheduled lpv controller is assigned to each of the local subregions for each switching subregion a function interpolating two local lpv controllers associated with its neighborhood subregions is designed to satisfy the constraint of smooth transition of controller system matrices the smooth switching controller design problem amounts to solving a feasibility problem which involves nonlinear matrix inequalities to find a solution to the feasibility problem an iterative descent algorithm which solves a series of convex optimization problems is proposed the usefulness of the proposed controller design method is demonstrated with a control example of a flexible ball screw drive system

anti windup synthesis using riccati equations the aim of this paper is to give a novel solution to the full order anti windup aw compensation problem for stable systems with input saturation the solution is obtained by completing the square in three steps and requires the solution to a single bounded real riccati equation characterized by the open loop plant s norm the riccati equation plays the role of the lmis usually found in anti windup synthesis but in addition to its numerical advantages it yields a family of anti windup compensators with the same performance this family of compensators is parameterized by a matrix which is intimately linked with both the poles of the anti windup compensator and the robustness properties of the closed loop saturated system thus this matrix allows a robust anti windup problem to be solved in a straightforward and intuitive manner the effectiveness of the proposed technique is demonstrated on a simple example

lq bumpless transfer between two tracking controllers in this article a linear quadratic lq scheme is proposed for bumpless transfer between two tracking controllers the controllers have integral actions which are used to eliminate the steady state tracking errors a compensator is designed using the lq technique to minimise the differences between two sets of signals the differences between two control signals as well as the differences between the two input signals which drive the two controllers under such circumstances complete information of the system is taken into account and utilised for achieving satisfactory control it is shown that the ideal bumpless transfer is achievable with the proposed control scheme moreover the results are extended to discrete time systems finally simulation results are given to demonstrate the effectiveness of the proposed control scheme

global and local error analysis for the residual free bubbles method applied to advection dominated problems we prove the stability and a priori global and local error analysis for the residual free bubbles rfb finite element method applied to advection dominated advection diffusion problems

an adaptive stabilized finite element method for the generalized stokes problem in this work we present an adaptive strategy based on an a posteriori error estimator for a stabilized finite element method for the stokes problem with and without a reaction term the hierarchical type estimator is based on the solution of local problems posed on appropriate finite dimensional spaces of bubble like functions an equivalence result between the norm of the finite element error and the estimator is given where the dependence of the constants on the physics of the problem is explicited several numerical results confirming both the theoretical results and the good performance of the estimator are given

a stabilized nonconfirming finite element method based on multiscale enrichment for the stationary navier stokes equations abstract in the paper we proposed a stabilized nonconforming finite element method for the stationary incompressible navier stokes equations which is a petrov galerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions and we studied the stability of the method for p 1 p 0 triangular element q 1 p 0 quadrilateral element and obtained the optimal error estimates of the stabilized nonconforming finite element method for the stationary navier stokes equations

anti windup synthesis for systems with rate limits using riccati equations this article develops an anti windup aw scheme for systems with rate limited actuators the main results show how a full order aw compensator can be synthesised using an algebraic riccati equation and several free parameters a further result then shows how the free parameters may be chosen to influence in an intuitive way the local gain of the system and the size of the region of attraction the results are of interest due to their low computational burden and hence their applicability to the systems of large state dimension

h bumpless transfer for switched lpv systems and its application in this paper the approach of the control bumps limitation is generalised and applied to the problem of h bumpless transfer for a class of switched linear parameter varying lpv systems the h

bubble enhanced smoothed finite element formulation a variational multi scale approach for volume constrained problems in two dimensional linear elasticity summary this paper presents a bubble enhanced smoothed finite element formulation for the analysis of volume constrained problems in two dimensional linear elasticity the new formulation is derived based on the variational multi scale approach in which unequal order displacement pressure pairs are used for the mixed finite element approximation and hierarchical bubble function is selected for the fine scale displacement approximation an area weighted averaging scheme is employed for the two scale smoothed strain calculation under the framework of edge based smoothed fem the smoothed fine scale solution is shown to naturally contain the stress field jump of the smoothed coarse scale solution across the boundary of edge based smoothing domain and thus provides the possibility to stabilize the global solution for volume constrained problems a global monolithic solution strategy is employed and the fine scale solution is solved without the consideration of approximating the strong form of the fine scale equation several numerical examples are analyzed to demonstrate the accuracy of the present formulation copyright 2014 john wiley sons ltd

brief multivariable anti windup controller synthesis using linear matrix inequalities we present a general formulation of the problem of multi variable anti windup bumpless transfer awbt controller synthesis which provides sufficient conditions for stability covering a large class of typical input nonlinearities such as saturation deadzone and switching override nonlinearities the resulting synthesis method demonstrates graceful performance degradation whenever input nonlinearities are active through minimization of a weighted l 2 gain the main contribution of the paper is that the awbt controller synthesis using static compensation is cast as a convex optimization over linear matrix inequalities

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

convergence analysis of a new multiscale finite element method for the stationary navier stokes problem in this paper we propose a new multiscale finite element method for the stationary navier stokes problem this new method for the lowest equal order finite element pairs p 1 p 1 is based on the multiscale enrichment and derived from the navier stokes problem itself therefore the new multiscale finite element method better reflects the nature of the nonlinear problem the well posedness of this new discrete problem is proved under the standard assumption meanwhile convergence of the optimal order in the h 1 norm for the velocity and the l 2 norm for the pressure is obtained especially via applying a new dual problem and some techniques in the process for proof we establish the convergence of the optimal order in the l 2 norm for the velocity finally numerical examples confirm our theory analysis and validate the effectiveness of this new method

a multiscale finite element method for the incompressible navier stokes equations this paper presents a new multiscale finite element method for the incompressible navier stokes equations the proposed method arises from a decomposition of the velocity field into coarse resolved scales and fine unresolved scales modeling of the unresolved scales corrects the lack of stability of the standard galerkin formulation and yields a method that possesses superior properties like that of the streamline upwind petrov galerkin supg method and the galerkin least squares gls method the multiscale method allows arbitrary combinations of interpolation functions for the velocity and the pressure fields specifically the equal order interpolations that are easy to implement but violate the celebrated babuska brezzi condition a significant feature of the present method is that the structure of the stabilization tensor s appears naturally via the solution of the fine scale problem a family of 2 d elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed convergence studies for the method on uniform skewed as well as composite meshes are presented numerical simulations of the nonlinear steady and transient flow problems are shown that exhibit the good stability and accuracy properties of the method 2005 elsevier b v all rights reserved

bumpless transfer between observer based gain scheduled controllers this paper deals with bumpless transfer between a number of observer based controllers in a gain scheduling architecture linear observer based controllers are designed for a number of linear approximations of a non linear system in a set of operating points and gain scheduling control can subsequently be achieved by interpolating between each controller the youla jabr bongiorno kucera yjbk parameterization is used to achieve a smooth scheduling between the controllers this approach produces a scheduled controller as a linear fractional transformation between a fixed controller and a scheduling parameter the approach is tested on a simple but highly non linear model of a fossil fuel power plant

numerical studies of finite element variational multiscale methods for turbulent flow simulations different realizations of variational multiscale vms methods within the framework of finite element methods are studied in turbulent channel flow simulations one class of vms methods uses bubble functions to model resolved small scales whereas the other class contains the definition of the resolved small scales by an explicit projection in its set of equations all methods are employed with eddy viscosity models of smagorinsky type the simulations are performed on grids for which a direct numerical simulation blows up in finite time

consistent local projection stabilized finite element methods this work establishes a formal derivation of local projection stabilized methods as a result of an enriched petrov galerkin strategy for the stokes problem the initial unstable mathbb p 1 times mathbb p l l 0 1 finite element space is enhanced with solutions of residual based local problems and then the static condensation procedure is applied to derive new methods the approach keeps degrees of freedom unchanged while giving rise to new stable and consistent methods for continuous and discontinuous approximation spaces for the pressure the resulting methods do not need the use of a macroelement grid structure and are parameter free the numerical analysis is carried out showing optimal convergence in natural norms and moreover two ways of rendering the velocity field locally mass conservative are proposed some numerics validate the theoretical results

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

p1 p0 elements for incompressible flows with discontinuous material properties abstract we present a 3 noded triangle and a 4 noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown constant pressure field and a prescribed linear field that satisfies the steady state momentum equations for a constant body force the elements are termed p1 p0 as the effective pressure field is linear although the unknown pressure field is piecewise constant within each element the elements have an excellent behavior for incompressible viscous flow problems with discontinuous material properties formulated in either eulerian or lagrangian descriptions the necessary numerical stabilization for dealing with the inf sup condition imposed by the incompressibility constraint and high convective effects in eulerian flows is introduced via the finite calculus fic approach for the sake of clarity the element derivation is presented first for the simpler stokes equations written in the standard eulerian frame the extension of the formulation to the navier stokes equations written in the eulerian and lagrangian frameworks is straightforward and is presented in the second part of the paper the efficiency and accuracy of the new p1 p0 triangle is verified by solving a set of incompressible multifluid flow problems using a lagrangian approach and a classical eulerian description the excellent performance of the new triangular element in terms of mass conservation and general accuracy for analysis of fluids with discontinuous material properties is highlighted

numerical verification of a non residual orthogonal term by term stabilized finite element formulation for incompressible convective flow problems abstract the modeling of turbulent flows is relevant in many engineering applications and is an active field of research on numerical methods convergence and stability of proposed formulations are crucial to predict transitional flows from laminar to turbulent flows in this work a recently developed stabilized finite element formulation is used as a powerful tool to describe such kind of problems the essential point of the formulation is the time dependent nature of the subscales and contrary to residual based formulations the introduction of two velocity subscale components the theoretical rate of convergence of the method is verified numerically using linear and quadratic equal order finite element discretizations to this end a standard convergence test of l 2 norm is presented where the computed solutions are compared when manufactured solutions are imposed at gauss point level moreover the hopf bifurcation is studied for two well known benchmark problems flow past a cylinder and the three dimensional lid driven cavity flow for the flow past a cylinder case the hopf bifurcation is verified using dynamic subscales and is assessed so that they do not disturb the solution in particular a dominant convective problem re 4000 is solved using both the quasistatic and dynamic versions of the method evaluating the performance of each one in the quality of the solution and in the cpu time needed to obtain a converged solution for the 3d lid driven cavity flow problem the hopf bifurcation is determined using two different boundary conditions analyzing their effect on the dynamics of the problem and on the thickness and shape of the boundary layer the final test case is the turbulent 3d lid driven cavity problem re 12000 where velocity profiles are compared with experimental les and dns reference solutions additionally pressure and velocity spectra are shown at certain representative points of the domain as well as phase diagrams correlation function graphs the poincare map and the lyapunov exponent typical mathematical tools used in dynamical system analysis from the results the method is robust and accurate for all the numerical tests both in viscous dominant problems as in dominant convective ones

commuting matrices equilibrium points for control systems with single saturated input in this paper commutative matrices of multiple input multiple output mimo linear systems are considered the existence of the feedback matrices of a commutative state matrix set in the mimo closed loops is reduced to the existence of an invariant subspace of a matrix a the existence of feedback matrices in systems in open loop is equivalent to the existence of the solution of matrix equations denoted by kronecker products by defining new equilibrium points the relationship between equilibrium points are discussed for a linear system with a single saturated input four criteria for equilibrium points are outlined for such linear systems finally four interesting examples including their corresponding simulink plots are shown to illustrate the above results

a symmetric nodal conservative finite element method for the darcy equation this work introduces and analyzes novel stable petrov galerkin enriched methods pgem for the darcy problem based on the simplest but unstable continuous mathbb p 1 mathbb p 0 pair stability is recovered inside a petrov galerkin framework where elementwise dependent residual functions named multiscale functions enrich both velocity and pressure trial spaces unlike the velocity test space that is augmented with bubble like functions multiscale functions correct edge residuals as well the multiscale functions turn out to be the well known lowest order raviart thomas basis functions for the velocity and discontinuous quadratics polynomial functions for the pressure the enrichment strategy suggests the way to recover the local mass conservation property for nodal based interpolation spaces we prove that the method and its symmetric version are well posed and achieve optimal error estimates in natural norms numerical validations confirm claimed theoretical results