a new class of higher order mixed finite volume methods for elliptic problems we introduce a new class of higher order mixed finite volume methods for elliptic problems we start from the usual way of changing the given equation into a mixed system using the darcy s law bf u cal k nabla p by integrating the system of equations with some judiciously chosen test spaces on each element we define new mixed finite volume methods of higher order we show that these new schemes are equivalent to the nonconforming finite element spaces used to define them the darcy velocity can be locally recovered from the solution of nonconforming finite element method hence our work opens a way to make higher order mixed method more practicable three dimensional extensions to parallelepiped elements are also presented this work can be viewed as a generalization of earlier works which were devoted to reducing the lowest order mixed finite element method to a corresponding nonconforming finite element method an optimal error analysis is carried out and numerical results are presented w

a parallelized meshfree method with boundary enrichment for large scale cfd a parallel computational implementation of a meshfree method the reproducing kernel particle method rkpm is used for 3 d implicit cfd analysis a novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented using this enrichment along the essential boundaries produces results that more closely match experimental and analytical results for a flow past a cylinder problem than does either the finite element method or other meshfree methods that require matrix inversion for the application of essential boundary conditions this technique also allows the efficient parallelization of the algorithm and leads to higher parallel speedups than do other boundary condition implementations many of which involve inherently serial steps this is important because the expense of meshfree computations makes parallelization crucial for large size problems the performance of the parallelization technique and the accuracy of the implicit cfd algorithm are demonstrated in two example problems

non matching mesh gluing by meshless interpolation an alternative to lagrange multipliers rewards of using non matching meshes are great in many aspects sub meshing a complex structure in a sub structure wise manner separately and or in parallel selective local refinement unlimited scalability guarantee for generating meshes in increasingly large scale finite element simulation etc however when meshes do not match a gluing algorithm is required to enforce inter domain continuity non matching terminologically originates from mesh discretization in nature and the non matching mesh issue is therefore avoidable or does not exist in a node based or meshless discretization in meshless methods motivated by this a gluing algorithm is developed based on meshless interpolation the gluing is accomplished by continuous trial and test functions across non matching meshes constructed using nodes only the developed gluing algorithm is tested in static and wave propagation problems in two and three dimensions it is demonstrated that the gluing algorithm does not deteriorate convergence and accuracy compared with the one piece conforming mesh compared with lagrange multiplier gluing one of the most common approaches the current algorithm has two significant benefits 1 easier implementation in any dimension and 2 positive definite banded system matrices not acting against equation solvers and hence better suited for large scale finite element analysis

a general framework for constructing and analyzing mixed finite volume methods on quadrilateral grids the overlapping covolume case we present a general framework for constructing and analyzing finite volume methods applied to the mixed formulation of second order elliptic problems on quadrilateral grids the control volumes or covolumes in the grids overlap an overlapping finite volume method of this type was first introduced by russell in t f russell tech report 3 reservoir simulation research corp tulsa ok 1995 and was tested for a variety of problems on rectangular and quadrilateral grids in z cai et al comput geosci 1 1997 pp 289 315 later in s h chou and d y kwak siam j numer anal 37 2000 pp 758 771 chou and kwak reformulated it as their mixed covolume method and proved optimal order error estimates using the covolume methodology from s h chou math comp 66 1997 pp 85 104 and s h chou and d y kwak siam j numer anal 35 1998 pp 494 507 however their treatment was restricted to the case of diagonal coefficient tensor and rectangular grids since a different approach was needed for the quadrilateral distorted rectangular case in this paper we give a new framework which can handle not only the rectangular anisotropic case but also the anisotropic and irregular grid cases in which the locally supported test functions are images of the natural unit coordinate vectors under the piola transformation our theory sheds light on how to create new test functions using quadratures and now covers russell s quadrilateral case

mixed covolume methods for elliptic problems on triangular grids we consider a covolume or finite volume method for a system of first order pdes resulting from the mixed formulation of the variable coefficient matrix poisson equation with the neumann boundary condition the system may represent either the darcy law and the mass conservation law in anisotropic porous media flow or fourier law and energy conservation the velocity and pressure are approximated by the lowest order raviart thomas space on triangles we prove its first order optimal rate of convergence for the approximate velocities in the l 2 and h mbox div omega norms as well as for the approximate pressures in the l 2 norm numerical experiments are included

the accuracy of cell vertex finite volume methods on quadrilateral meshes for linear first order hyperbolic equations in two dimensions we restate the cell vertex finite volume scheme as a finite element method on structured meshes consisting of distorted quadrilaterals the global error is shown to be of second order in various mesh dependent norms provided that the quadrilaterals are close to parallelograms in the sense that the distance between the midpoints of the diagonals is of the same order as the measure of the guadrilateral on tensor product nonuniform meshes the cell vertex scheme coincides with the familiar box scheme in this case second order accuracy is shown without any additional assumption on the regularity of the mesh which explains the insensitivity of the cell vertex scheme to mesh stretching in the coordinate directions observed in practice 17 refs

coupling finite and boundary element methods for two dimensional potential problems a finite element boundary element fe be coupling method based on a weighted residual variational method is presented for potential problems governed by either the laplace or the poisson equations in this method a portion of the domain of interest is modeled by finite elements fe and the remainder of the region by boundary elements be because the be fundamental solutions are valid for infinite domains a procedure that limits the effects of the be fundamental solution to a small region adjacent to the fe region called the transition region tr is developed this procedure involves a judicious choice of functions called the transition t functions that have unit values on the be tr interface and zero values on the fe tr interface the present fe be coupling algorithm is shown to be independent of the extent of the transition region and the choice of the transition functions therefore transition regions that extend to only one layer of elements between fe and be regions and the use of simple linear transition functions work well

mixed finite element methods for general quadrilateral grids abstract we study a new mixed finite element of lowest order for general quadrilateral grids which gives optimal order error in the h div norm this new element is designed so that the h div projection h satisfies h p h div a rigorous optimal order error estimate is carried out by proving a modified version of the bramble hilbert lemma for vector variables we show that a local h div projection reproducing certain polynomials suffices to yield an optimal l 2 error estimate for the velocity and hence our approach also provides an improved error estimate for original raviart thomas element of lowest order numerical experiments are presented to verify our theory

mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems we construct and analyze a mixed finite volume method on quadrilateral grids for elliptic problems written as a system of two first order pdes in the state variable e g pressure and its flux e g darcy velocity an important point is that no staggered grids or covolumes are used to stabilize the system only a single primary grid system is adopted and the degrees of freedom are imposed on the interfaces the approximate flux is sought in the lowest order raviart thomas space and the pressure field in the rotated q1 nonconforming space furthermore we demonstrate that the present finite volume method can be interpreted as a rotated q1 nonconforming finite element method for the pressure with a simple local recovery of flux numerical results are presented for a variety of problems which confirm the usefulness and effectiveness of the method

parameter identification of wiener systems with discontinuous nonlinearities abstract the paper deals with modeling and parameter identification of wiener type nonlinear dynamic systems having discontinuous asymmetric piecewise linear characteristics with preloads and dead zones multiple application of a decomposition technique provides a special form of static nonlinearity description its incorporation into the wiener model leads to an input output equation where all the model parameters are separated and can be estimated iteratively using input output data and internal variable estimates more illustrative examples are included to demonstrate the feasibility of the proposed approach

iterative identification of hammerstein systems the iterative method was first proposed to estimate hammerstein system in 9 it is a very simple and efficient algorithm in general the convergence of iterative algorithm can be a problem 12 it was recently shown that iterative algorithms with normalisation possess some global convergence properties in identification of hammerstein system with smooth nonlinearity and finite impulse response fir linear part 3 4 11 the convergence for an infinite impulse response iir system was however not solved in this chapter the results are extended to hammerstein systems with an iir linear part the global convergence for an iir system is established for the odd nonlinearities

flux recovery from primal hybrid finite element methods a flux recovery technique is introduced and analyzed for the computed solution of the primal hybrid finite element method for second order elliptic problems the recovery is carried out over a single element at a time while ensuring the continuity of the flux across the interelement edges and the validity of the discrete conservation law at the element level our construction is general enough to cover all degrees of polynomials and grids of triangular or quadrilateral type we illustrate the principle using the raviart thomas spaces but other well known related function spaces such as the brezzi douglas marini bdm or brezzi douglas fortin marini bdfm space can be used as well an extension of the technique to the nonlinear case is given numerical results are presented to confirm the theoretical results

hierarchical enrichment for bridging scales and mesh free boundary conditions the finite element method when used with a basis made up of piecewise polynomials often requires the generation of a very fine computational mesh in order to capture localized solution phenomena such as boundary layers or near singularities enrichment of the basis with additional functions obtained through analytical or experimental means can allow for a coarser mesh and more accurate solution we introduce an enrichment scheme in which an interaction or bridging scale term is used to separate the basis formed by the enrichment functions from the original set of basis functions in effect making the enrichment hierarchical this separation of scales allows the simple application of essential boundary conditions it also allows a quantification of the effects of the enrichment leading to strategies for error estimation and control of the stiffness matrix condition number we also find that this formulation allows for the simple application of essential boundary conditions for mesh free shape functions which are notoriously problematic we find that for multiple dimensions care must be taken to derive a weak form which is truly consistent with the strong form on the essential boundary copyright 2001 john wiley sons ltd

parameter estimation algorithms for multivariable hammerstein carma systems this paper considers parameter identification problems for multivariable hammerstein controlled autoregressive moving average carma systems we transform a multivariable hammerstein carma system into a new identification model which contains a set of bilinear parameter vectors i e two sets of parameter vectors to solve the difficulty of estimating the two sets of parameter vectors this paper constructs two different forms of the identification model in each of which the output is linear about one set of parameter vectors and presents an extended stochastic gradient algorithm to interactively estimate the two sets of parameter vectors by using the hierarchical identification principle the proposed hierarchical identification algorithm has a higher computational efficiency than the over parametrization model based stochastic gradient algorithm the simulation results indicate that the proposed algorithm is effective and an example of modeling a photovoltaic array system with the multivariable hammerstein model is given

enrichment and coupling of the finite element and meshless methods a mixed hierarchical approximation based on finite elements and meshless methods is presented two cases are considered the first one couples regions where finite elements or meshless methods are used to interpolate continuity and consistency is preserved the second one enriches a finite element mesh with particles thus there is no need to remesh in adaptive refinement processes in both cases the same formulation is used convergence is studied and examples are shown copyright 2000 john wiley sons ltd

global estimates for mixed methods for second order elliptic equations global error estimates in l2 92 l 9 and h s q 2 in r2 or a re derived for a mixed finite element method for the dirichlet problem for the elliptic operator lp div a grad p bp cp based on the raviart thomas nedelec space vh x wh c h div 92 x l2 g2 optimal order estimates are obtained for the approximation of p and the associated velocity field u a grad p bp in l2 g2 and h s 92 0 6 s k 1 and if q c r2 forp in lv2

brief identification of linear systems with hard input nonlinearities of known structure this paper studies identification of systems with input nonlinearities of known structure for input nonlinearities parameterized by one parameter a deterministic approach is proposed based on the idea of separable least squares the identification problem is shown to be equivalent to an one dimensional minimization problem the method is very effective for several common static and nonstatic input nonlinearities for a general input nonlinearity a correlation analysis based identification algorithm is presented which is shown to be convergent

a coupled finite element and meshless local petrov galerkin method for two dimensional potential problems a coupled finite element fe method and meshless local petrov galerkin mlpg method for analyzing two dimensional potential problems is presented in this paper the analysis domain is subdivided into two regions a finite element fe region and a meshless mm region a single weighted residual form is written for the entire domain independent trial and test functions are assumed in the fe and mm regions a transition region is created between the two regions the transition region blends the trial and test functions of the fe and mm regions the trial function blending is achieved using a technique similar to the coons patch method that is widely used in computer aided geometric design the test function blending is achieved by using either fe or mm test functions on the nodes in the transition element the technique was evaluated by applying the coupled method to two potential problems governed by the poisson equation the coupled method passed all the patch test problems and gave accurate solutions for the problems studied

an impes scheme for a two phase flow in heterogeneous porous media using a structured grid abstract we develop a numerical scheme for a two phase immiscible flow in heterogeneous porous media using a structured grid finite element method which has been successfully used for the computation of various physical applications involving elliptic interface equations li et al 2003 2004 chou et al 2010 kwak et al 2010 chang and kwak 2011 the proposed method is based on the implicit pressure explicit saturation procedure to solve the pressure equation we use an ifem based on the rannacher turek rannacher and turek 1992 nonconforming space which is a modification of the work in kwak et al 2010 where broken p 1 nonconforming element of crouzeix raviart 1973 1 was developed for the darcy velocity we apply the mixed finite volume method studied in chou et al 2003 and kwak et al 2010 on the basis of immersed finite element method ifem in this way the darcy velocity of the flow can be computed cheaply locally after we solve the pressure equation the computed darcy velocity is used to solve the saturation equation explicitly the whole procedure can be implemented on a structured grid which is independent of the underlying heterogeneous porous media in fact we apply a new version of multigrid algorithm to solve the pressure equation for which the cpu time grows like o n numerical tests for analytic problems show that our method is almost optimal in all variables problem with sources sinks is also computed and it seems to work well

discrete time adaptive control of linear dynamic systems with a two segment piecewise linear asymmetric nonlinearity in this note a method is presented for doing discrete adaptive control of a nonlinear system which is given by a cascade connection of a two segment piecewise linear asymmetric nonlinearity followed by a linear system a switching gain sequence is introduced to make the parameter identification time invariant the algorithm will ensure that the closed loop system is globally convergent and stable for both the deterministic and stochastic cases

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

a discontinuous finite volume method for a coupled fracture model abstract in this paper we present a discontinuous finite volume method for a hybrid dimensional coupled fracture model on triangular meshes in matrix and fracture the pressure is approximated by the discontinuous and continuous piecewise linear elements and in order to retain local conservation property the velocity is sought in the discontinuous lowest order raviart thomas element space and piecewise linear element space the proposed numerical scheme is only associated with the pressure so we avoid solving an indefinite saddle point problem in addition the discontinuous method eliminates the continuity of approximate functions across the interelement boundary so it has the advantage of high localizability and easy handling of complicated geometries optimal order error estimates for the pressure and velocity are proved and numerical experiments are carried out to confirm our theoretical analysis

a q1 finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh abstract in this paper we study a q 1 finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh it is known that the coercivity is the basement for some other theoretical results stability h 1 and l 2 error estimates etc and the existing results were mainly obtained on h 1 parallelogram meshes with scalar diffusion coefficients for the cases of full diffusion tensors and arbitrary convex quadrilateral meshes we obtain a necessary and sufficient condition for the positive definiteness of the cell matrix related to the cell bilinear form based on this result a sufficient condition is suggested to guarantee the coercivity of the scheme more interesting is that this sufficient condition covers the traditional h 1 parallelogram mesh assumption and has an explicit expression by which one can easily judge on any diffusion tensor and any mesh with arbitrary mesh size h 0 moreover an h 1 error estimate is obtained without the h 1 parallelogram assumption and some numerical results are also provided to validate the theoretical results

recursive identification for wiener model with discontinuous piece wise linear function this paper deals with identification of wiener systems with nonlinearity being a discontinuous piece wise linear function recursive estimation algorithms are proposed to estimate six unknown parameters contained in the nonlinearity and all unknown coefficients of the linear subsystem by using the iid gaussian inputs the estimates are proved to converge to the corresponding true values with probability one a numerical example is given to justify the obtained theoretical results

a multi innovation generalized extended stochastic gradient algorithm for output nonlinear autoregressive moving average systems this paper proposes a generalized extended stochastic gradient gesg algorithm for estimating the parameters of a class of wiener nonlinear autoregressive moving average systems using the gradient search in order to improve the convergence rates of the gesg algorithm a multi innovation gesg algorithm is derived the simulation results indicate that the proposed algorithms can effectively estimate the parameters of a class of output nonlinear systems

coupled meshfree and fractal finite element method for mixed mode two dimensional crack problems this paper presents a coupling technique for integrating the element free galerkin method efgm with the fractal finite element method ffem for analyzing homogeneous isotropic and two dimensional linear elastic cracked structures subjected to mixed mode modes i and ii loading conditions ffem is adopted for discretization of the domain close to the crack tip and efgm is adopted in the rest of the domain in the transition region interface elements are employed the shape functions within interface elements which comprise both the efg and the finite element fe shape functions satisfies the consistency condition thus ensuring convergence of the proposed coupled efgm ffem the proposed method combines the best features of efgm and ffem in the sense that no special enriched basis functions or no structured mesh with special fes are necessary and no post processing employing any path independent integrals is needed to determine fracture parameters such as stress intensity factors sifs and t stress the numerical results show that sifs and t stress obtained using the proposed method are in excellent agreement with the reference solutions for the structural and crack geometries considered in the present study also a parametric study is carried out to examine the effects of the integration order the similarity ratio the number of transformation terms and the crack length to width ratio on the quality of the numerical solutions a numerical example on mixed mode condition is presented to simulate crack propagation as in the proposed coupled efgm ffem at each increment during the crack propagation the ffem mesh around the crack tip is shifted as it is to the new updated position of the crack tip such that ffem mesh center coincides with the crack tip and few meshless nodes are sprinkled in the location where the ffem mesh was lying previously crack propagation analysis can be dramatically simplified copyright 2010 john wiley sons ltd

a posteriori error analysis for locally conservative mixed methods in this work we present a theoretical analysis for a residual type error estimator for locally conservative mixed methods this estimator was first introduced by braess and verfurth for the raviart thomas mixed finite element method working in mesh dependent norms we improve and extend their results to cover any locally conservative mixed method under minimal assumptions in particular avoiding the saturation assumption made by braess and verfurth our analysis also takes into account discontinuous coefficients with possibly large jumps across interelement boundaries the main results are applied to the p1 nonconforming finite element method and the interior penalty discontinuous galerkin method as well as the mixed finite element method

on the convergence of an iterative algorithm used for hammerstein system identification an analytical counterexample to the general convergence of an interative algorithm used for identification of hammerstein systems is given numerical illustration is also included

recursive identification of hammerstein systems with discontinuous nonlinearities containing dead zones this note deals with the recursive parameter identification of hammerstein systems with discontinuous nonlinearities i e two segment piecewise linear with dead zones and preloads a special form of the hammerstein model with this type of nonlinearity is incorporated into the recursive least squares identification scheme supplemented with the estimation of model internal variables the proposed method is illustrated by examples

conservative p 1 conforming and nonconforming galerkin fems effective flux evaluation via a nonmixed method approach given a p1 conforming or nonconforming galerkin finite element method gfem solution ph which approximates the exact solution p of the diffusion reaction equation nabla cdot mathcal k nabla p alpha p f with full tensor variable coefficient mathcal k we evaluate the approximate flux uh to the exact flux bf u mathcal k nabla p by a simple but physically intuitive formula over each finite element the flux is sought in the continuous in normal component or the discontinuous raviart thomas space a systematic way of deriving such a formula is introduced this direct method retains local conservation property at the element level typical of mixed methods finite element or finite volume type but avoids solving an indefinite linear system in short the present method retains the best of the gfem and the mixed method but without their shortcomings thus we view our method as a conservative gfem and demonstrate its equivalence to a certain mixed finite volume box method the equivalence theorems explain how the pressure can decouple basically cost free from the mixed formulation the accuracy in the flux is of first order in the h dive omega norm numerical results are provided to support the theory

an optimal order multigrid method for p1 nonconforming finite elements etude d une methode multigrille d ordre optimal pour la resolution des problemes aux limites elliptiques du second ordre a l aide d elements finis non conformes

on the regularity and uniformness conditions on quadrilateral grids in the literature there are various regularity conditions as well as many different so called almost parallelogram conditions on the subdivisions of quadrilateral grids in this paper we investigate and clarify their relations

a new implementation of the element free galerkin method abstract element free galerkin methods efg are methods for solving partial differential equations with moving least squares interpolants efg methods require only nodal data no element connectivity is needed in a previous implementation of the efg method lagrange multipliers were used to enforce the essential boundary condition however the use of lagrange multipliers increases the cost of solving the linear algebraic equations a new implementation is developed based on a modified variational principle in which the lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are banded in addition weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated numerical examples show that the present implementation effectively computes stress concentrations and stress intensity factors at cracks with very irregular arrangements of nodes the latter makes it very advantageous for modelling progressive cracking

enriching the finite element method with meshfree particles in structural mechanics summary the automatic generation of meshes for the finite element fe method can be an expensive computational burden especially in structural problems with localized stress peaks the use of meshless methods can address such an issue as these techniques do not require the existence of an underlying connection among the particles selected in a general domain this study advances a numerical strategy that blends the fe method with the meshless local petrov galerkin mlpg technique in structural mechanics with the aim at exploiting the most attractive features of each procedure the idea relies on the use of fes to compute a background solution that is locally improved by enriching the approximation space with the basis functions associated to a few meshless points thus taking advantage of the flexibility ensured by the use of particles disconnected from an underlying grid adding the meshless particles only where needed avoids the cost of mesh refining or even of re meshing without the prohibitive computational cost of a thoroughly meshfree approach in the present implementation an efficient integration strategy for the computation of the coefficients taking into account the mutual fe mlpg interactions is introduced moreover essential boundary conditions are enforced separately on both fes and meshless particles thus allowing for an overall accuracy improvement also when the enriched region is close to the domain boundary numerical examples in structural problems show that the proposed approach can significantly improve the solution accuracy at a local level with no re meshing effort and at a low computational cost this article is protected by copyright all rights reserved

element free galerkin methods in combination with finite element approaches element free galerkin efg methods are methods for solving partial differential equations with the help of shape functions coming from moving least squares approximation the efg method is more flexible than the finite element fe method since it requires only nodal data and no element connectivity is needed because the efg method is computationally expensive combinations of the efg method and the fe method are considered implementations based on several weak forms of the problem description are studied numerical examples in elastostatics and fracture mechanics show that the implementations are able to compute both displacement and stress fields accurately

multigrid and multilevel methods for nonconforming q 1 elements in this paper we study theoretical properties of multigrid algorithms and multilevel preconditioners for discretizations of second order elliptic problems using nonconforming rotated q 1 finite elements in two space dimensions in particular for the case of square partitions and the laplacian we derive properties of the associated intergrid transfer operators which allow us to prove convergence of the w cycle with any number of smoothing steps and close to optimal condition number estimates for v cycle preconditioners this is in contrast to most of the other nonconforming finite element discretizations where only results for w cycles with a sufficiently large number of smoothing steps and variable v cycle multigrid preconditioners are available some numerical tests including also a comparison with a preconditioner obtained by switching from the nonconforming rotated q 1 discretization to a discretization by conforming bilinear elements on the same partition illustrate the theory

nonconforming box schemes for elliptic problems on rectangular grids recently courbet and croisille rairo mode l math anal nume r 32 1998 pp 631 649 introduced the finite volume box scheme for the two dimensional 2d poisson problem in the case of triangular meshes generalizations to higher degree box schemes have been published by croisille and greff numer methods partial differential equations 18 2002 pp 355 373 these box schemes are based on the principle of the finite volume method in that they take the average of the equations on each cell of the grid this gives rise to a natural choice of unknowns located at the interface of the mesh these box schemes are conservative and use only one mesh they can be interpreted as a discrete mixed petrov galerkin formulation of the poisson problem in this paper we focus our interest on box schemes for the poisson problem in two dimensions on rectangular grids we discuss the basic finite volume box scheme and analyze and interpret it as three different box schemes the method is demonstrated by numerical examples

on the heterogeneous multiscale method with various macroscopic solvers abstract the heterogeneous multiscale method hmm is a general method for efficient numerical solution of problems with multiscales it consists of two components an overall macroscopic solver for macrovariables on a macrogrid and an estimation of the missing macroscopic data from the microscopic model in this paper we present a state of the art review of the hmm with various macroscopic solvers including finite differences finite elements discontinuous galerkin mixed finite elements control volume finite elements nonconforming finite elements and mixed covolumes the first four solvers have been studied in the hmm setting the others are not as example the hmm with the nonconforming finite element macroscopic solver for nonlinear and random homogenization problems is also studied here

brief paper discrete time adaptive control of linear systems with preload nonlinearity in this note a method is presented for doing discrete time adaptive control of a nonlinear system which is given by a cascade connection of a preload nonlinearity followed by a linear system it is shown that the algorithm will ensure that the closed loop system is globally convergent with a specific residue and stable for both the deterministic and stochastic cases

error estimates for a mixed finite volume method for the p laplacian problem in this work we propose and analyze a mixed finite volume method for the p laplacian problem which is based on the lowest order raviart thomas element for the vector variable and the p1 nonconforming element for the scalar variable it is shown that this method can be reduced to a p1 nonconforming finite element method for the scalar variable only one can then recover the vector approximation from the computed scalar approximation in a virtually cost free manner optimal a priori error estimates are proved for both approximations by the quasi norm techniques we also derive an implicit error estimator of bank weiser type which is based on the local neumann problems

non linear system identification using hammerstein and non linear feedback models with piecewise linear static maps we consider the identification of hammerstein non linear feedback models by approximating internal non linearities using piecewise linear static maps the resulting method utilizes a point slope parameterization that leads to a computationally tractable optimization problem the computational appeal of this technique is derived from the fact that the method only requires a matrix inverse and singular value decomposition furthermore the identification method simultaneously identifies the linear dynamic and static non linear blocks without requiring prior assumptions on the form of the static non linearity

mixed covolume methods on rectangular grids for elliptic problems we consider a covolume method for a system of first order pdes resulting from the mixed formulation of the variable coefficient matrix poisson equation with the neumann boundary condition the system may be used to represent the darcy law and the mass conservation law in anisotropic porous media flow the velocity and pressure are approximated by the lowest order raviart thomas space on rectangles the method was introduced by russell rigorous block centered discretizations on irregular grids improved simulation of complex reservoir systems reservoir simulation research corporation denver co 1995 as a control volume mixed method and has been extensively tested by jones a mixed finite volume elementary method for accurate computation of fluid velocities in porous media university of colorado at denver 1995 and cai et al computational geosciences 1 1997 pp 289 345 we reformulate it as a covolume method and prove its first order optimal rate of convergence for the approximate velocities as well as for the approximate pressures

parameter identification of discontinuous hammerstein systems the paper deals with the parameter identification of hammerstein systems having discontinuous asymmetric nonlinearities two segment piecewise linear with preload and dead zone application of a simple decomposition technique provides a special form of hammerstein model with a minimum number of parameters the identification is carried out with only one record of measured input output data despite the dead zone to demonstrate the feasibility of the identification method some illustrative examples are included

an inexpensive method for the evaluation of the solution of the lowest order raviart thomas mixed method for the model problem operatorname div a nabla u f we show how the approximate solution produced by the raviart thomas lecture notes in mathematics 606 springer verlag berlin 1977 mixed method of lowest degree can be obtained from the solution of the p 1 nonconforming galerkin method modified in a virtually cost free manner

a general mixed covolume framework for constructing conservative schemes for elliptic problems we present a general framework for the finite volume or covolume schemes developed for second order elliptic problems in mixed form i e written as first order systems we connect these schemes to standard mixed finite element methods via a one to one transfer operator between trial and test spaces in the nonsymmetric case convection diffusion equation we show one half order convergence rate for the flux variable which is approximated either by the lowest order raviart thomas space or by its image in the space of discontinuous piecewise constants in the symmetric case diffusion equation a first order convergence rate is obtained for both the state variable e g concentration and its flux numerical experiments are included

a nonconforming covolume method for elliptic problems abstract we consider a control volume covolume method for second order elliptic pdes with the rotated q1 nonconforming finite element on rectangular grids the coefficient may a variable diagonal tensor or discontinuous we prove first order convergence in h1 norm and second order convergence in l2 norm when the partition is square our numerical experiments show that our covolume scheme has about 30 less error than fem even when is discontinuous tensor

superconvergence of new mixed finite element spaces in this paper we prove some superconvergence of a new family of mixed finite element spaces of higher order which we introduced in etna vol 37 pp 189 201 2010 among all the mixed finite element spaces having an optimal order of convergence on quadrilateral grids this space has the smallest unknowns however the scalar variable is only suboptimal in general thus we have employed a post processing technique for the scalar variable as a byproduct we have obtained a superconvergence on a rectangular grid the superconvergence of a velocity variable naturally holds and can be shown by a minor modification of existing theory but that of a scalar variable requires a new technique especially for k 1 numerical experiments are provided to support the theory

identification of hammerstein nonlinear armax systems two identification algorithms an iterative least squares and a recursive least squares are developed for hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by armax carma models the basic idea is to replace unmeasurable noise terms in the information vectors by their estimates and to compute the noise estimates based on the obtained parameter estimates convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition the simulation results validate the algorithms proposed