a nitsche stabilized finite element method for frictional sliding on embedded interfaces part ii intersecting interfaces abstract we extend the weighted nitsche s method proposed in the first part of this study to include multiple intersecting embedded interfaces these intersections arise either inside a computational domain where two internal interfaces intersect or on the boundary of the computational domain where an internal interface intersects with the external boundary we propose a variational treatment of both the interfacial kinematics and the external dirichlet constraints within nitsche s framework we modify the numerical analysis to account for these intersections and provide an explicit expression for the weights and the method parameters that arise in the nitsche variational form in the presence of junctions finally we demonstrate the performance of the method for both perfectly tied interfaces and perfectly plastic sliding interfaces through several benchmark examples

a reconstruction based chebyshev collocation method for the poisson equation an accurate treatment of the gibbs wilbraham phenomenon on irregular interfaces abstract an accurate numerical solution of the laplace equation and poisson equation is desirable in physical problems related to fluid flows and spectral methods are well suited towards this goal however in the presence of an interface the solution is discontinuous owing to the interface jump conditions and thus the numerical approximation is susceptible to the gibbs wilbraham phenomenon leading to a reduced solution accuracy in order to resolve the discontinuity at the interface we propose a reconstruction technique wherein the approximate solution is expressed as the sum of an infinitely differentiable smooth function and a modified heaviside function the smooth function is composed of chebyshev polynomials while the modified heaviside function is expressed in a weak form using the jump conditions across the interface the reconstruction framework allows us to impose the interfacial conditions exactly to motivate further application of the technique we first present the underlying rationale by revisiting the work of wilbraham 1848 13 followed by the numerical implementation we present numerical solution of four equations to illustrate the application of the proposed technique i an ordinary differential equation ode ii the euler bernoulli equation iii the laplace equation and iv the poisson equation the laplace and poisson equation are solved on a square domain embedded with complex interfacial geometries in two dimensions and on a cube with a spherical interface in three dimensions the method achieves error in the maximum norm o 10 14 using approximately 30 modes in each direction and requires a computational time of less than a second for all the problems we also conduct a sensitivity analysis to demonstrate the robustness of the algorithm under sub grid scale perturbations to interface location an alternate derivation for the modified heaviside function is proposed that is distinct from the taylor series expansion used to treat interface conditions in difference methods the pointwise error plots are subsequently presented to demonstrate that the gibbs wilbraham phenomenon is accurately resolved finally we present concluding thoughts on the potential applications of the reconstruction technique

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

paper error propagation properties of recursive least squares adaptation algorithms the numerical properties of implementations of the recursive least squares identification algorithm are of great importance for their continuous use in various adaptive schemes here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates it is shown that conventional ls algorithms including bierman s ud factorization algorithm are exponentially stable with respect to such errors i e the effect of the error decays exponentially the base of the decay is equal to the forgetting factor the same is true for fast lattice algorithms the fast least squares algorithm sometimes known as the fast kalman algorithm is however shown to be unstable with respect to such errors

a stabilized mixed finite element method for darcy flow we develop new stabilized mixed finite element methods for darcy flow stability and an a priori error estimate in the stability norm are established a wide variety of convergent finite elements present themselves unlike the classical galerkin formulation which requires highly specialized elements an interesting feature of the formulation is that there are no mesh dependent parameters numerical tests confirm the theoretical results 2002 elsevier science b v all rights reserved

a new analytic algorithm of lane emden type equations an reliable ease to use analytic algorithm is provided for lane emden type equation which models many phenomena in mathematical physics and astrophysics this algorithm logically contains the well known adomian decomposition method different from all other analytic techniques this algorithm itself provides us with a convenient way to adjust convergence regions even without pade technique some applications are given to show its validity

recursive identification of switched arx systems we consider the problem of recursively identifying the parameters of a deterministic discrete time switched auto regressive exogenous sarx model under the assumption that the number of models the model orders and the mode sequence are unknown the key to our approach is to view the identification of multiple arx models as the identification of a single though more complex lifted dynamical model built by applying a polynomial embedding to the input output data we show that the dynamics of this lifted model do not depend on the value of the discrete state or the switching mechanism and are linear on the so called hybrid model parameters therefore one can identify the parameters of the lifted model using a standard recursive identifier applied to the embedded input output data the estimated hybrid model parameters are then used to build a polynomial whose derivatives at a regressor give an estimate of the parameters of the arx model generating that regressor the estimated arx model parameters are shown to converge exponentially to their true values under a suitable persistence of excitation condition on a projection of the embedded input output data such a condition is a natural generalization of the well known result for arx models although our algorithm is designed for perfect input output data our experiments also evaluate its performance as a function of the level of noise for different choices of the number of models and model orders we also present an application to temporal video segmentation

mixed finite elements for second order elliptic problems in three variables two families of mixed finite elements one based on simplices and the other on cubes are introduced as alternatives to the usual raviart thomas nedelec spaces these spaces are analogues of those introduced by brezzi douglas and marini in two space variables error estimates inl2 andh s are derived

rls parameter convergence with overparametrized models abstract this paper through the concept of quotient space generalizes the rls parameter convergence results obtained previously using the lyapunov type function approach 14 1 12 7 to overparameterized systems the system signals do not have to be quasi stationary as assumed by ljung 10 and a priori knowledge of the degree of overparameterization is not required the excitation condition is the weakest possible and it is shown that under this excitation condition limiting set of parameter estimates always belongs to a set h each element of which contains the irreducible plant model plus a monic common factor polynomial it is further shown that the common factor polynomials defined by the limiting set of parameter estimates are quantitatively related to the initial conditions of the algorithm for example if the condition number of the initial covariance matrix is unity then the limiting set of parameter estimates is the singleton on h closest to the initial parameter estimate

sufficient excitation and stable reduced order adaptive iir filtering a perturbed error system is used to describe the parameter and output error behaviors of reduced order application of adaptive identifier filters such as the hyperstable adaptive recursive filter harf given satisfaction of a sufficient excitation condition this error system is shown to exhibit a bounded input bounded state bibs property this implies that despite order insufficiency the output and parameter estimates of harf and similar adaptive identifier filter algorithms remain bounded

remarks on persistency of excitation for nonminimal models of systems having purely deterministic disturbances a persistency of excitation result for nonminimal models of systems having purely deterministic disturbances has been given recently in 1 in this note we give a direct and simple proof for the case of bounded signals of the result of 1 and show via a counterexample that an assumption on system signals boundedness which does not appear in 1 is necessary when arbitrary unbounded signals are allowable finally we give a proper persistency of excitation result which does not require signal boundedness for the case when the system input consists of a bounded external signal and of a constant coefficient feedback component

an application of single term haar wavelet series in the solution of nonlinear oscillator equations in this paper a novel single term haar wavelet series sthws method is implemented for the solution of the duffing equation and painleve s transcendents pi and pii the results in the form of a block pulse and a discrete solution are presented unlike classical numerical schemes the sthws method has no restrictions on the coefficients of the duffing equation as regards its solution pi and pii are analysed as regards their solutions up to nearest singularities poles using the sthws also an efficient computational implementation shows the remarkable features of wavelet based techniques

on reduced order adaptive output error identification and adaptive iir filtering the reduced order application of landau s adaptive output error identifier results in a perturbed error system where the perturbation signal is a moving average of the unmodeled portion of the unknown plant output or desired signal in adaptive filter parlance it is proven in this paper that if this perturbation signal is sufficiently small and a reduced order dimension model is sufficiently excited then the output and parameter estimates of this adaptive identifier filter remain bounded the influence of various operating conditions on this quantitatively defined bound are noted this robustness property is crucial in all real applications which due to nonlinearities and distributed effects are subject to reduced order modeling

analysis of a general recursive prediction error identification algorithm a general class of algorithms for recursive identification of stochastic dynamical systems is studied in this class the discrepancy between the measured output and the output predicted from previous data according to a candidate model the prediction error is minimized over the model set using a stochastic approximation approach it is proved that this class of methods has the same convergence properties as its off line counterparts under mild and general assumptions these assumptions do not for example include stationary conditions or conditions that the true system can be exactly represented within the model set the considered class of methods contains as special cases several well known algorithms other common recursive identification methods like the extended least squares method and the extended kalman filter can be interpreted as approximate prediction error methods with simplified gradient calculations therefore the approach taken here may also serve as a basis for unified description of many recursive identification methods

application of optimal homotopy asymptotic method for the analytic solution of singular lane emden type equation abstract in this study optimal homotopy asymptotic method is applied on singular initial value lane emden type problems to check the effectiveness and performance of the method it is observed that the method is easy to implement quite valuable to handle singular phenomena and yield excellent results at minimum computational cost computational results of some of the test problems are presented to demonstrate the viability and practical usefulness of the method

adaptive system stability robustness via burst recovery abstract adaptive systems which are based on a posteriori parameter update algorithms are shown to possess a specific type of self stabilization property termed burst recovery this results in bounded disturbance bounded error stability provided that unbounded parameter drift does not occur persistent excitation prevents unbounded parameter drift but only when both upper and lower bounds on excitation exist for many adaptive systems an upper bound on excitation cannot be assured using standard perturbation analyses which require the disturbance to be suitably small compared to the lower bound on excitation this paper proves that burst recovery in conjunction with only a lower bound on excitation provides bounded disturbance bounded error stability the disturbance need not be small and additional algorithm modifications such as parameter projection are not necessary

a new operational matrix for solving fractional order differential equations abstract fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations for that reason we need a reliable and efficient technique for the solution of fractional differential equations this paper deals with the numerical solution of a class of fractional differential equations the fractional derivatives are described in the caputo sense our main aim is to generalize the legendre operational matrix to the fractional calculus in this approach a truncated legendre series together with the legendre operational matrix of fractional derivatives are used for numerical integration of fractional differential equations the main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus greatly simplifying the problem the method is applied to solve two types of fractional differential equations linear and nonlinear illustrative examples are included to demonstrate the validity and applicability of the presented technique

noise cancellation with improved residuals an effective adaptive scheme for noise cancellation when the signal to be recovered has known autocorrelation is presented two algorithms that exploit a special form of prior information are investigated in this approach the desired signal is removed from the output feedback by linear prediction the prior information used is the desired signal s autocorrelation knowing this one can find a filter that whitens the desired signal screening the error feedback through this filter removes most of the desired signal energy reducing its interference with the coefficient update this is the basis for the first algorithm discussed namely the least mean square algorithm with augmented predictor lms ap proposed by orgren et al 1986 in many applications the whitening filter may not be strictly positive real spr in such cases a different algorithm is needed one which is assuredly convergent regardless of the satisfaction of the spr condition a modified lms algorithm with augmented predictor mlms ap which provides such an alternative is proposed

a new method for solving singular initial value problems in the second order ordinary differential equations singular initial value problems linear and nonlinear homogeneous and nonhomogeneous are investigated by using adomian decomposition method the solutions are constructed in the form of a convergent series a new general formula is established the approach is illustrated with few examples

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

on parameter convergence in adaptive control it is well known that the parameter error as well as the model plant mismatch error in a model reference adaptive scheme tends exponentially to zero iff a certain sufficient richness condition holds for signals inside the time varying plant control loop in this paper we give conditions on the reference signal the exogenous input to the adaptive loop namely that it have as many spectral lines as there are unknown parameters in order to guarantee parameter convergence

recursive parameter identification algorithm stability analysis via pi sharing pi sharing is introduced as an extension of the application of passivity and hyperstability concepts for discrete time systems providing connections between input output and state space stability notions using tools developed within the pi sharing framework new stability results for the output error class identification algorithm are derived this approach offers a clear interpretation of the role of the spr condition in the work of landau and silveira and its absence in the work of tomizuka and altay

application of benveniste s convergence results in the study of adaptive iir filtering algorithms it is shown that the weak convergence results of a benveniste et al ieee trans automat contr vol ac 25 p 1042 58 dec 1980 can be used to prove convergence of some adaptive infinite impulse response iir filtering algorithms the association of the algorithms with some ordinary differential equations for constant gains which parallels the theory of l ljung et al 1983 is suitable for constant gain adaptive filtering applications convergence proofs for a prefiltering algorithm for a simple constant gain version of the recursive maximum likelihood algorithm and for the well known simple hyperstable adaptive recursive filter sharf algorithm are given as examples

computation of eigenvalues and solutions of regular sturm liouville problems using haar wavelets the paper presents a novel method for the computation of eigenvalues and solutions of sturm liouville eigenvalue problems sleps using truncated haar wavelet series this is an extension of the technique proposed by hsiao to solve discretized version of variational problems via haar wavelets the proposed method aims to cover a wider class of problems by applying it to historically important and a very useful class of boundary value problems thereby enhancing its applicability to demonstrate the effectiveness and efficiency of the method various celebrated sturm liouville problems are analyzed for their eigenvalues and solutions also eigensystems are investigated for their asymptotic and oscillatory behavior the proposed scheme unlike the conventional numerical schemes such as rayleigh quotient and rayleigh ritz approximation gives eigenpairs simultaneously and provides upper and lower estimates of the smallest eigenvalue and it is found to have quadratic convergence with increase in resolution

level set topology optimization of fluids in stokes flow we propose the level set method of topology optimization as a viable robust and efficient alternative to density based approaches in the setting of fluid flow the proposed algorithm maintains the discrete nature of the optimization problem throughout the optimization process leading to significant advantages over density based topology optimization algorithms specifically the no slip boundary condition is implemented directly this is accurate removes the need for interpolation schemes and continuation methods and gives significant computational savings by only requiring flow to be modeled in fluid regions topological sensitivity information is utilized to give a robust algorithm in two dimensions and familiar two dimensional power dissipation minimization problems are solved successfully computational efficiency of the algorithm is also clearly demonstrated on large scale three dimensional problems

a variable step vs adaptive filter algorithm in recent work a new version of an lms algorithm has been developed which implements a variable feedback constant for each weight of an adaptive transversal filter this technique has been called the vs variable step algorithm and is an extension of earlier ideas in stochastic approximation for varying the step size in the method of steepest descents the method may be implemented in hardware with only modest increases in complexity approx 15 percent over the lms widrow hoff algorithm it is shown that an upper bound for the convergence time is the classical mean square error time constant and examples are given to demonstrate that for broad signal classes both narrow band and broad band the convergence time is reduced by a factor of up to 50 in noise canceller applications for the proper selection of variable step parameters finally the vs algorithm is applied to an iir filter and simulations are presented for applications of the vs fir and iir adaptive filters

optimal adaptive control and consistent parameter estimate for deterministic systems with quadratic cost in this paper an adaptive control is designed for deterministic systems on the basis of the projection algorithm so that the quadratic loss function approaches its minimum at a rate of n e e 0 and the parameter estimate converges to its true value with a near exponential rate

a structural view of asymptotic convergence speed of adaptive iir filtering algorithms i infinite precision implementation for pt i see ibid vol 41 no 4 p 1493 1517 1993 finite precision fp implementation is the ultimately inevitable reality of all adaptive filters including adaptive infinite impulse response iir filters this paper continues to examine the asymptotic convergence speed of adaptive iir filters of various structures and algorithms including the simple constant gain type and the newton type but under fp implementation a stochastic differential equation sde approach is used in the analysis such an approach not only greatly simplifies the fp analysis which is traditionally very involved algebraically but it also provides valuable information about the first order as well as the second order moments that the latter are not available using the ordinary differential equation ode approach the asymptotic convergence speed as well as the convergent values of the pertinent moments of fp errors are examined in terms of unknown system pole zero locations the adverse effects of lightly damped low frequency ldlf poles resulting from fast sampling on the local transient and convergent behavior of various structures and algorithms are analyzed and compared the new results agree with the existing ones when reduced to the finite impulse response fir case in particular the explosive behavior of pertinent error variances of newton type iir algorithms when the forgetting factor spl lambda 1 is also concluded computer simulation verifies the predicted theoretical results

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

quiver diagrams and signed adaptive filters a graphical technique for exploring the behavior of deterministic discrete time adaptive algorithms excited by periodic inputs is examined the constraint to periodic inputs is convenient the underlying concepts used also apply to stationary inputs drawn from finite alphabets the resulting graph is based on plotting single period parameter trajectories in the parameter error space and is essentially a discrete version of flow diagrams associated with continuous time systems for the least mean square lms adaptive fir filter with the algorithm step size sufficiently small the change of adapted parameters from a particular initial value is given by the total update over the input period with the parameterization frozen at its initial value this results in the familiar elliptical hyperparaboloid surface steepest descent interpretation this method can be extended to the lms adaptive infinite input response iir filter with suitable approximations based on a small step size

convergence analysis of the least squares identification algorithm with a variable forgetting factor the time varying linear systems abstract this paper studies the convergence of the least squares identification algorithm with a variable forgetting factor the evolution of the parameter estimator with respect to initial conditions actual parameter changes and stochastic perturbations is analysed bounds on the deterministic and stochastic parts of their estimator error are found and their relation to a persistent excitation condition is discussed this relation explains the possibility of having bursting phenomena during the identification process special attention is paid to the consistency of these results with the classical ones obtained for the ordinary least squares algorithm when the forgetting factor tends to unity

convergence of the signed output error adaptive identifier this paper considers an adaptive output error identifier with a signum function in its update kernel it is shown that the classical strict positive real spr condition required for the convergence of traditional adaptive identifiers does not suffice for the convergence of this signed identifier instead what is needed is a stronger operator condition called the strict dominant passive sdp condition we give an analog of the kalman yakubovic popov lemma for the sdp conditions and using it give a convergence proof under the assumptions of persistent excitation and sdp

a new algorithm for solving differential equations of lane emden type in this paper a reliable algorithm is employed to investigate the differential equations of lane emden type the algorithm rests mainly on the adomian decomposition method with an alternate framework designed to overcome the difficulty of the singular point the proposed framework is applied to a generalization of lane emden equations so that it can be used in differential equations of the same type

composite adaptive control of robot manipulators abstract adaptive control of linear time invariant single input single output systems has been extensively studied and a number of globally convergent controllers have been derived while extensions of the results to non linear or multivariable systems have rarely been achieved similar global convergence properties can indeed be obtained in the case of robot manipulators an important and unique class of non linear multi input multi output dynamic systems based on the observation that the parameter uncertainty is reflected in both the tracking error in joint motion and the prediction error in the joint torques or the power input we recently proposed a new class of adaptive robot controllers the parameter adaptation of which is driven by both tracking error and prediction error in this paper following a brief review of our earlier globally convergent direct adaptive controller we provide a detailed analysis of these composite adaptive controllers results on global asymptotic and exponential tracking convergence are established and confirmed by simulation

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

persistence of excitation conditions and the convergence of adaptive schemes in the study of the behavior of adaptive filtering algorithms persistence of excitation of the input process arises as a sufficient condition for convergence and perhaps more importantly for convergence rate of the parameter estimates in this paper the underlying nature of the persistence requirement is presented and discussed relating its normal specification in terms of moment conditions with covariance decays etc to sample path properties deterministic and stochastic persistence conditions and persistence measures are treated as well as persistence conditions for output error equation error and adaptive control schemes

globally convergent adaptive iir filters based on fixed pole locations a new class of adaptive filters dubbed fixed pole adaptive filters fpaf s is introduced these adaptive filters have infinite impulse responses yet their adaptation exhibits provable global convergence good filter performance with a relatively small number of adapted parameters is permitted by the new filter structure thus reducing the computational burden needed to implement adaptive filters the implementation and computational complexity of the fpaf is described and its modeling capabilities are determined excitation conditions on the filter input are established that guarantee global convergence of a standard set of adaptive algorithms some methods are described for selecting the fixed pole locations based on a priori information regarding the operating environment of the adaptive filter the fpaf is tailored to applications by such a procedure enabling improved performance in examples the fpaf is shown to achieve a smaller minimum mean square error given an equal number of adapted parameters in comparison with adaptive fir filters and adaptive filters based on laguerre and kautz models

a stabilized mixed finite element method for darcy flow based on a multiscale decomposition of the solution recently masud and hughes proposed a stabilized mixed finite element formulation for darcy flow an interesting feature of this formulation is that there are no mesh dependent parameters in the present work we provide a derivation of this formulation based on a multiscale decomposition of the solution we also extend the work of masud and hughes to three dimensional problems and show the convergence rates for various three dimensional finite elements we also show that this formulation passes three dimensional constant flow patch tests for distorted element geometries i e elements with non constant jacobian robustness of this formulation is illustrated by performing numerical simulations on complex geometries

the composite regressor algorithm for iir adaptive systems an adaptive iir algorithm called the composite regressor algorithm cra is developed the algorithm is a generalization of the common equation error a priori output error and a posteriori output error adaptive iir algorithms the cra is analyzed for convergence in a noiseless environment and for bias in a stochastic setting it is determined that by using a parameter called the regressor composition parameter a tradeoff can be obtained between the automatic convergence but large bias results of the equation error algorithm and the difficult convergence condition but small bias results of the output error algorithms in proving results for the cra it is shown that the a posteriori output error algorithm produces estimates with nonzero bias when the adaptive gain is small but bounded away from zero a convergence condition for the a priori output error algorithm is derived for the first time

numerical solution of differential equations by using chebyshev wavelet operational matrix of integration in this paper we present operational matrix of integration omi of chebyshev wavelets basis and the product operation matrix pom of it some comparative examples are included to demonstrate the superiority of operational matrix of chebyshev wavelets to those of legendre wavelets

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

stabilized continuous and discontinuous galerkin techniques for darcy flow we design stabilized methods based on the variational multiscale decomposition of darcy s problem a model for the subscales is designed by using a heuristic fourier analysis this model involves a characteristic length scale that can go from the element size to the diameter of the domain leading to stabilized methods with different stability and convergence properties these sta bilized methods mimic the different possible functional settings of the continuous problem the optimal method depends on the velocity and pressure approximation order they also involve a subgrid projector that can be either the identity when applied to finite element residuals or can have an image orthogonal to the finite element space in pa rticular we have designed a new stabilized method that allows the use of piecewise constant pressures we consider a general setting in which velocity and pressure can be approximated by either continuous or discontinuous approximations all these methods have been analyzed proving stability and convergence results in some cases duality arguments have been used to obtain error bounds in the l 2 norm

unified stabilized finite element formulations for the stokes and the darcy problems in this paper we propose stabilized finite element methods for both stokes and darcy s problems that accommodate any interpolation of velocities and pressures apart from the interest of this fact the important issue is that we are able to deal with both problems at the same time in a completely unified manner in spite of the fact that the functional setting is different concerning the stabilization formulation we discuss the effect of the choice of the length scale appearing in the expression of the stabilization parameters both in what refers to stability and to accuracy this choice is shown to be crucial in the case of darcy s problem as an additional feature of this work we treat two types of stabilized formulations showing that they have a very similar behavior

a stabilized mixed discontinuous galerkin method for darcy flow abstract a new mixed stabilized discontinuous galerkin formulation for darcy flow is presented the formulation combines several attributes not simultaneously satisfied by other methods it is convergent for any combination of velocity and pressure interpolation higher than first order it exactly satisfies a mass balance on each element and it passes two and three dimensional constant flow patch tests for distorted element geometries the key ingredient in the formulation is a volumetric residual based stabilization term that does not involve any mesh dependent parameters

the non symmetric nitsche method for the parameter free imposition of weak boundary and coupling conditions in immersed finite elements abstract we explore the use of the non symmetric nitsche method for the weak imposition of boundary and coupling conditions along interfaces that intersect through a finite element mesh in contrast to symmetric nitsche methods it does not require stabilization and therefore does not depend on the appropriate estimation of stabilization parameters we first review the available mathematical background recollecting relevant aspects of the method from a numerical analysis viewpoint we then compare accuracy and convergence of symmetric and non symmetric nitsche methods for a laplace problem a kirchhoff plate and in 3d elasticity our numerical experiments confirm that the non symmetric method leads to reduced accuracy in the l 2 error but exhibits superior accuracy and robustness for derivative quantities such as diffusive flux bending moments or stress based on our numerical evidence the non symmetric nitsche method is a viable alternative for problems with diffusion type operators in particular when the accuracy of derivative quantities is of primary interest

brief paper reduced order performance of parallel and series parallel identifiers with weakly observable parasitics the stability properties of discrete time parallel and series parallel identifiers with respect to a specific model plant order mismatch are analyzed while in a deterministic environment with no modeling error the two schemes give identical results when used in a deterministic environment with modeling error their performance is different we assume a singularly perturbed state representation for the plant where the modeling error consists of fast parasitics which are weakly observable in the plant output detailed bounds on parameter and output estimate errors are established and the robustness of the adaptive identifiers is established by showing that the error bound goes to zero as the modeling error goes to zero i e as the parasitics become infinitely fast the dependence of this residual identification error on the input signal the neglected parasitics and the initial error conditions is shown to be crucial the bounds indicate possibilities for reducing the error by a proper choice of the input signal

strong consistency of a class of recursive stochastic gradient algorithms in this work strong consistency results for a class of stochastic gradient algorithms are developed where the system is not necessarily minimum phase or stable and is assumed to be of the carma form the analysis uses only standard martingale results and strong consistency is shown to hold under certain persistent excitation conditions

sharf convergence properties a class of stable algorithms for adapting infinite impulse response iir digital filters based on the concepts of nonlinear stability theory prominent in the control literature is emerging while this class of adaptive filters offers much promise in practical applications little has been done toward providing a characterization that would guide selection of design parameters such as adaptation constants and error smoothing coefficients this paper focuses on the simplest well behaved member of this class of adaptive recursive filters sharf progression from a local linearization of the nonlinear parameter estimate convergence behavior through an idealized eigenvalue eigenvector analysis of the parameter estimate time varying recursion to lyapunov function establishment for the full output and parameter error system reveals the exponential local nongradient descent convergence character of sharf and provides initial insight into the effects of adaptation constants and error smoothing coefficients on these characteristics

modeling flow in porous media with double porosity permeability a stabilized mixed formulation error analysis and numerical solutions abstract the flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon dioxide sequestration the flow within numerous natural and synthetic porous materials that contain multiple scales of pores cannot be adequately described by the classical darcy equations it is for this reason that mathematical models for fluid flow in media with multiple scales of pores have been proposed in the literature however these models are analytically intractable for realistic problems in this paper a stabilized mixed four field finite element formulation is presented to study the flow of an incompressible fluid in porous media exhibiting double porosity permeability the stabilization terms and the stabilization parameters are derived in a mathematically consistent manner and the computationally convenient equal order interpolation of all the field variables is shown to be stable a systematic error analysis is performed on the resulting stabilized weak formulation representative problems patch tests and numerical convergence analyses are performed to illustrate the performance and convergence behavior of the proposed mixed formulation in the discrete setting the accuracy of numerical solutions is assessed using the mathematical properties satisfied by the solutions of this double porosity permeability model moreover it is shown that the proposed framework can perform well under transient conditions and that it can capture well known instabilities such as viscous fingering

imposing dirichlet boundary conditions with nitsche s method and spline based finite elements a key challenge while employing non interpolatory basis functions in finite element methods is the robust imposition of dirichlet boundary conditions the current work studies the weak enforcement of such conditions for b spline basis functions with application to both second and fourth order problems this is achieved using concepts borrowed from nitsche s method which is a stabilized method for imposing constraints on surfaces conditions for the stability of the system of equations are derived for each class of problem stability parameters in the nitsche weak form are then evaluated by solving a local generalized eigenvalue problem at the dirichlet boundary the approach is designed to work equally well when the grid used to build the splines conforms to the physical boundary of interest as well as to the more general case when it does not through several numerical examples the approach is shown to yield optimal rates of convergence copyright 2010 john wiley sons ltd

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear lane emden type equations abstract in this article a new method is generated to solve nonlinear lane emden type equations using legendre hermite and laguerre wavelets we are interested to note that these wavelets will give same solutions with good accuracy theorems on convergence analysis are stated and proved on the spaces which are created by legendre hermite and laguerre wavelets bases and justified these spaces are equivalent to polynomial linear space generated by general polynomial basis the main idea for obtaining numerical solutions depends on converting the differential equation with initial and boundary conditions into a system of linear or nonlinear algebraic equations with unknown coefficients a very high level of accuracy reflects the reliability of this scheme for such problems

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