explicit residual based a posteriori error estimation for finite element discretizations of the helmholtz equation computation of the constant and new measures of error estimator quality abstract this paper continues the study of an explicit residual based a posteriori error estimator developed for finite element discretizations of the helmholtz equation in the context of time harmonic exterior acoustics problems in previous papers 1 3 the error estimator was derived and subsequently applied to h adaptive computations of model problems in two dimensions in the present paper a methodology is established for computing error estimates these error estimates are then analyzed in detail the error estimates are made possible by computing the scaling constant which exists in error estimators of this type in our case this constant is difficult to obtain an algorithm for computing the constant is described it is noted that the error indicators used for adaptive computations do not require knowledge of this constant several measures are used to analyze the quality of the error estimates providing a complete description of the error estimator in the context of these problems we compute global effectivity indices and utilize the local element wise effectivity index in computing three additional measures the first of these is the robustness index the others are the modified robustness index and the distribution index which are introduced for the first time it is found that the global effectivity index varies with problem parameters in particular the wave number robustness indices also vary due to the local error definition and wave number values of the distribution index are much better however indicating the suitability of the error estimator in guiding efficient adaptive mesh refinement the analysis of the error estimator is carried out on relatively coarse meshes typical of those used in practical engineering computations

an adaptive finite element method for transient compressible flows with moving boundaries a description is given of an adaptive finite element method for the simulation of two dimensional compressible flows with moving boundaries the method is implemented on an unstructured triangular grid and the mesh adaptation is achieved by local grid regeneration using an error estimation procedure coupled to an automatic triangular mesh generator two numerical examples are included to illustrate the numerical performance of the method

implicit discrete time systems and accessibility an intrinsic description for dynamic systems whose evolution along discrete time is governed by nonlinear implicit difference equations in one independent variable and zero order algebraic equations is presented by means of differential geometrical methods where systems are associated with appropriate geometric objects reflecting their dynamics dynamic systems given in implicit form have the peculiarity that they may contain so called hidden restrictions a normal form is presented which is characterized by the circumstances that there are no further restrictions in addition it is illustrated that such a normal form allows for an equivalent system representation in explicit form based on the geometric picture of implicit discrete time systems the qualitative property of accessibility along a fixed trajectory is discussed by applying symmetry groups of discrete time systems and studying invariants of these groups a formal approach is provided that allows us to gather local accessibility criteria successively which can be tested by computer algebra several examples illustrate the results

adaptive mesh finite volume calculation of 2d lid cavity corner vortices abstract an anisotropic refinement criterion suitable for finite volume methods is presented and navier stokes solutions are reported for the lid driven cavity flow configuration at re 1000 with adaptive anisotropic meshes h refinement the a posteriori error estimation criterion is based on the assessment of the goodness of fit of the least squares regression used to perform the variables profile reconstruction and it is capable of detecting both large scale and small scale flow phenomena the criterion allowed to capture in detail the large scale flow structure and also the sequence of creeping flow small sharp corner s 1 eddies up to the fourth corner vortex in addition to the primary cavity vortex the smallest corner vortex detected is o 10 16 smaller in velocity magnitude compared with the cavity primary recirculation flow

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

assessment of discretized errors and adaptive refinement with quadrilateral finite elements this paper studies discretized errors and their estimation in conjunction with quadrilateral finite element meshes which are generated by the intelligent mesh generator xformq 1 the exact energy error is used to evaluate the distortion effect of the quadrilateral mesh the zienkiewicz zhu2 error estimate and actaptive procedure are applied to the short cantilever and the square plate problems using the quadrilateral mesh generator xformq it is shown that the multistage quadrilateral element refinement produces results superior to the triangular element refinement in the test cases

non oscillatory and non diffusive solution of convection problems by the iteratively reweighted least squares finite element method in this paper we first introduce the least squares finite element method lsfem for two dimensional steady state pure convection problems with smooth solutions and compare the lsfem with other finite element methods we prove that the lsfem has the same stability estimate as the original equation i e the lsfem has better control of the streamline derivative than the streamline upwinding petrov galerkin method numerical convergence rates are given to show that the lsfem is almost optimal then we use this lsfem as a framework to develop an iteratively reweighted least squares finite element method irlsfem to obtain non oscillatory and non diffusive solutions for problems with contact discontinuities this new method produces a highly accurate numerical solution that has a sharp discontinuity in one element a number of examples solved by using triangular and bilinear elements are presented to show that the method can convect contact discontinuities without error

forward and backward shifts of vector fields towards the dual algebraic framework an algebraic framework for discrete time nonlinear control systems is introduced based on the forward and backward shifts of the vector fields it appears to be the dual of the framework based on the differential 1 forms as applications the characterization of accessibility and the solution to the static state feedback linearization problem are stated in terms of the given vector fields

stabilized low order finite elements for failure and localization problems in undrained soils and foundations abstract geomaterials in general and soils in particular are highly nonlinear materials presenting a very strong coupling between solid skeleton and intersticial water in the limit of zero compressibility of water and soil grains and zero permeability which correspond to the classical undrained assumption of soil mechanics the functions used to interpolate displacements and pressures must fulfill either the babuska brezzi conditions or the much simpler patch test proposed by zienkiewicz and taylor these requirements exclude the use of elements with equal order interpolation for pressures and displacements for which spurious oscillations may appear the simplest elements with continuous pressures which can be used in 2d are the quadratic triangle and quadrilateral with linear and bilinear pressures respectively the purpose of this paper is to present a stabilization technique allowing the use of both linear triangles for displacements and pressures t3p3 and bilinear quadrilaterals q4p4 the proposed element will be applied to obtain limit loads and failure surfaces in simple boundary value problems for which analytical solutions exist

error estimator and adaptive moving grids for finite volumes schemes a new adaptation technique has been developed for two and three dimensional grids based on relocation of the mesh nodes the flow is governed by the euler equations expressed in an euler lagrange form and the discretization uses a first order finite volume scheme based on roe s approximate riemann solver the grid is unstructured and its motion and evolution obey the physical and geometrical conservation laws the error is evaluated by a reconstructed higher order solution which is used to derive a forcing term to drive the motion of the grid nodes this is formulated so as to uniformly distribute the error while keeping the same grid connectivity the development is made for two and three dimensional grids although results are presented only for two dimensional flows he adaptation of the grid to the flow characteristics is widely recognized as a method to improve the solution accuracy and the overall computing efficiency of numerical schemes the moti vation is that since the grid is normally generated before knowing the flow behavior it is possible that the nodes distribution does not correspond to the solution requirements the adaptivity process is made up of two key elements an error estimator and an adaptation procedure the simplest error estimator used for finite volume schemes 1 2 is based on the physical behavior of the flowfield more specifically on the gradient of the density or the mach number the adaptation consists in refining and coarsening the mesh in regions of higher or lower gradients respectively the projection method developed by zienkiewicz and zhu3 4 is based on the observation that for finite elements discretization the solution is continuous whereas the derivatives are discontinuous at the interface of two elements those derivatives are projected in a space of continuous functions and the norm of the difference be tween this projection and the derivatives is used as a measure of the computational error for some problems the fluxes instead of derivatives are physically continuous in all of the domain and con sequently more appropriate to be projected in a space of continuous functions 5 babuska and rheinboldt6 propose an error estimator based on the solution of a local variational problem where the unknowns are the approximation errors the advantage consists in the reduction of the size of the linear system to be solved in compressible flows with shock waves or contact discontinu ities the variables can no longer be considered continuous the computed errors based on the solution gradient increase unbound edly with the adaptation of the discontinuity this acts as permanent source for grid refinement and could produce wrong results 7 paillere et al 8 use a wave model to evaluate the error for com pressible flows the model combines the effects of the divergence and rotational of the velocity to reduce the influence of disconti nuities the error is multiplied by a power of a characteristic length of the grid cell the adaptation procedure also considers a minimal local grid size

an adaptive finite element procedure for compressible high speed flows abstract a two step explicit finite element procedure for obtaining time accurate solutions to the compressible euler equations is described the method is coupled with an adaptive mesh refinement process which enables steady state solutions of improved quality to be obtained

adaptive recovery of near optimal meshes in the finite element method for parameter dependent problems abstract a method for adaptive construction of nearly optimal finite element meshes is presented the method is based on the notion of mesh density for parametrized problems optimal meshes for new parameter values can be predicted from previous meshes the method is of the one shot type normally giving a sufficiently good approximation to the optimal mesh at the first attempt but when the first shot is unsuccessful the method can be iterated for parametrized problems no coarse mesh solutions are required except for the very first problem and whenever the method fails in providing an acceptable mesh and iteration becomes necessary

an implicit explicit scheme for compressible viscous high speed flows abstract an implicit explicit finite element based algorithm for the solution of 2d steady compressible viscous high speed flows is presented a structured grid is employed in the vicinity of solid walls and the implicit form of the algorithm is implemented in this region the explicit form of the algorithm is used in the remainder of the flow domain which is discretised with an unstructured assembly of triangles the quality of the computed solution is improved by the application of solution adaptive remeshing the computed results for two examples are compared with experimental observations to illustrate the performance of the proposed scheme

adaptive finite element analysis of fractal interfaces in contact problems abstract structures involving interfaces with fractal geometry are referred here as a sequence of classical interfaces problems which result from the consideration of the fractal interfaces as the unique fixed point or the deterministic attractor of a given iterated function system ifs on the interface unilateral contact conditions are assumed to hold the approximations of the fractal interfaces are combined with a penalty regularization based on the minimization of the potential energy after some appropriate transformations are performed for this type of contact problems there often result singular points on the interfaces which lead to possible stress concentrations further more the convergence of finite element solution under a sufficient discretization can not be determined from the outset an adaptive finite element strategy appears to be suitable for such kind of contact problems in that it possesses the properties of adjusting automatically the mesh sizes both in the interior of the bodies and on the contact zone in this spirit both the goals of exactly determining the real contact areas and of enhancing the accuracy of finite element solution meanwhile consuming reasonable computational costs may be achieved the error estimator based on the residual stress analysis is discussed numerical examples illustrate the validity and effectiveness of the method proposed in this paper

adaptive finite element method for turbulent flow near a propeller we present an adaptive finite element method based on remeshing to solve incompressible turbulent free shear flow near a propeller solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids turbulence is modeled by a mixing length formulation two general purpose error estimators which take into account swirl and the variation or the eddy viscosity are presented and applied to the turbulent wake or a propeller the proposed adaptive scheme is robust reliable and cost effective

optimal two dimensional finite difference grids providing superconvergence a novel multidimensional grid adaptation method based on minimization of the leading truncation error term of arbitrary second and higher order finite difference approximations is proposed the method does not explicitly require the truncation error estimate but increases the design order of approximation globally by one so that the same finite difference operator is superconvergent on the optimal grid if the differential operator and the metric coefficients are evaluated identically by some hybrid approximation the single optimal grid generator can be used in the entire computational domain and does not depend on points where the hybrid discretization switches from one approximation to another if one family of the coordinate lines is given a priori then the analytical optimal mapping is constructed for any consistent second order finite difference approximation of nabla f in two dimensions the present approach can be extended directly to nonlinear partial differential equations and three dimensions numerical calculations show that the truncation error obtained on the two dimensional optimal grid is both superconvergent and reduced by several orders of magnitude in comparison with the uniform grid results for all the test examples considered

two dimensional mesh generation adaptive remeshing and refinement this paper discusses the generation of unstructured triangular meshes by the advancing front technique we also employ the technique to discretize surfaces a simple and effective algorithm for the specification of element sizes is described a similar idea is then applied to adaptive remeshing where a completely new mesh is created on the basis of the isolines of a certain important variable the isolines are obtained from the fe calculation based on the previous mesh in this paper attention is focused on the poisson s equation the optimal a priori error estimate for the problem is used to estimate the number of isolines needed for the remeshing when the estimated error exceeds the tolerance in only a small part of the domain the adaptive procedure is switched automatically to an adaptive refinement

adjoint a posteriori error measures for anisotropic mesh optimisation in this paper an adjoint or sensitivity based error measure is formulated which measures the error contribution of each solution variable to an overall goal the goal is typically embodied in an integral functional e g the solution in a small region of the domain of interest the resulting a posteriori error measures involve the solution of both primal and adjoint problems a comparison of a number of important a posteriori error measures is made in this work there is a focus on developing relatively simple methods that refer to information from the discretised equation sets often readily accessible in simulation codes and do not explicitly use equation residuals this method is subsequently used to guide anisotropic mesh adaptivity of tetrahedral finite elements mesh adaptivity is achieved here with a series of optimisation heuristics of the landscape defined by mesh quality mesh quality is gauged with respect to a riemann metric tensor embodying an a posteriori error measure such that an ideal element has sides of unit length when measured with respect to this metric tensor this results in meshes in which each finite element node has approximately equal subject to certain boundary conforming constraints and the performance of the mesh optimisation heuristics error contribution to the functional goal

blockwise adaptivity for time dependent problems based on coarse scale adjoint solutions we describe and test an adaptive algorithm for evolution problems that employs a sequence of blocks consisting of fixed though nonuniform space meshes this approach offers the advantages of adaptive mesh refinement but with reduced overhead costs associated with load balancing remeshing matrix reassembly and the solution of adjoint problems used to estimate discretization error and the effects of mesh changes a major issue with a block adaptive approach is determining block discretizations from coarse scale solution information that achieve the desired accuracy we describe several strategies for achieving this goal using adjoint based a posteriori error estimates and we demonstrate the behavior of the proposed algorithms as well as several technical issues in a set of examples

anisotropic mesh refinement in stabilized galerkin methods the numerical solution of a convection diffusion reaction model problem is considered in two and three dimensions a stabilized finite element method of galerkin least square type accomodates diffusion dominated as well as convection and or reaction dominated situations the resolution of boundary layers occuring in the singularly perturbed case is achieved using anisotropic mesh refinement in boundary layer regions in this paper the standard analysis of the stabilized galerkin method on isotropic meshes is extended to more general meshes with boundary layer refinement simplicial lagrangian elements of arbitrary order are used

discrete time transitivity and accessibility analytic systems a basic open question for discrete time nonlinear systems is that of determining when in analogy with the classical continuous time positive form of chow s lemma accessibility follows from transitivity of a natural group action this paper studies the problem and establishes the desired implication for analytic systems in several cases i compact state space ii under a poisson stability condition and iii in a generic sense in addition the paper studies accessibility properties of the controllability sets recently introduced in the context of dynamical systems studies finally various examples and counterexamples are provided relating the various lie algebras introduced in past work

linearization of discrete time systems the algebraic formalism developed in this paper unifies the study of the accessibility problem and various notions of feedback linearizability for discrete time nonlinear systems the accessibility problem for nonlinear discrete time systems is shown to be easy to tackle by means of standard linear algebraic tools whereas this is not the case for nonlinear continuous time systems in which case the most suitable approach is provided by differential geometry the feedback linearization problem for discrete time systems is recasted through the language of differential forms in the event that a system is not feedback linearizable the largest feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a pfaffian system a discrete time system may be linearizable by dynamic state feedback though it is not linearizable by static state feedback necessary and sufficient conditions are given for the existence of a so called linearizing output which in turn is a sufficient condition for dynamic state feedback linearizability

numerical comparison of some hessian recovery techniques derivative recovery techniques are used in a posteriori error indicators to drive mesh adaptation their behaviour in the core of the computational domain and on boundaries constitutes an important efficiency factor for a subsequent mesh adaptation process a methodology to compare recovery techniques for second order derivatives from a piecewise linear approximation is presented in this paper a systematic approach to measuring the performance of recovery techniques using analytical functions interpolated on a series of meshes is proposed the asymptotic behaviour of some recently published recovery techniques as well as new ones is numerically assessed on various type of meshes recommendations are done on the choice of a recovery technique

high order unstructured curved mesh generation using the winslow equations we propose a method to generate high order unstructured curved meshes using the classical winslow equations we start with an initial straight sided mesh in a reference domain and fix the position of the nodes on the boundary on the true curved geometry in the interior of the domain we solve the winslow equations using a new continuous galerkin finite element discretization this formulation appears to produce high quality curved elements which are highly resistant to inversion in addition the corresponding nonlinear equations can be solved efficiently using picard iterations even for highly stretched boundary layer meshes compared to several previously proposed techniques such as optimization and approaches based on elasticity analogies this can significantly reduce the computational cost while producing curved elements of similar quality we show a number of examples in both two and three space dimensions including complex geometries and stretched boundary layers and demonstrate the high quality of the generated meshes and the performance of the nonlinear solver

anisotropic mesh adaptation for 3d flows on structured and unstructured grids abstract this paper presents a mesh optimization methodology in three dimensions mom3d an initial mesh is continually adapted during the solution process without the need for global remeshing the adaptation procedure uses an interpolation error estimate whose magnitude and direction are controlled by the hessian the matrix of second derivatives of the solution this metric error is projected over mesh edges and drives the nodal movement scheme as well as the edge refinement and coarsening strategies these operations yield highly anisotropic grids in which the mesh movement significantly contributes to the stretching and realignment of the edges along unidirectional features of flow problems the results presented have been chosen to illustrate some important points first the method is gauged on problems with exact solutions demonstrating good agreement between the error estimate and the true error as well as an equidistribution of the error the cost effectiveness of grid adaptation is then addressed by determining the size of an anisotropic grid that would be equivalent to that of a given non adapted finer grid for the same error level the capture of sharp discontinuities through highly anisotropic grids is illustrated on a transonic flow flow in a gas turbine combustor demonstrates how automatically generated meshes can sometimes cause convergence difficulties and how mesh adaptation can cure these ills finally the flow over a wing nacelle pylon configuration is studied to further validate the solver mesh adaptation capabilities by comparing the numerical results against experiments

simple sufficient conditions for reachability of discrete time polynomial systems we consider reachability of discrete time polynomial systems the reachability of such systems can be interpreted as the surjectivity of the polynomial mappings defined by the systems for a polynomial mapping between suitable spaces of the same dimensions it has been shown that the injectivity of the mapping also implies the surjectivity by utilizing this fact we derive sufficient conditions for the reachability of the polynomial systems which essentially check the injectivity of the polynomial mappings

a finite element formulation of compressible flows using various sets of independent variables abstract this paper presents a finite element method for the simulation of compressible flows the navier stokes and euler equations are solved in the conservation form using various sets of independent variables a variational formulation is developed based upon a variant of the petrov galerkin method and uses a shock capturing operator an adaptive algorithm based on a particular residual norm is proposed several numerical examples are presented to demonstrate the performances of each set of variables in solving compressible high speed flows

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner

numerical assessment of error estimators for euler equations grid convergence studies are conducted to assess four error estimators for their asymptotic behavior explicit residual solution reconstruction richardson extrapolation and solution of the error equations their accuracy reliability and efficitivity to predict the true error are verified on the quasi one dimensional euler equations solved by a second order accurate finite volume method

petrov galerkin solutions of the incompressible navier stokes equations in primitive variables with adaptive remeshing the solution of the incompressible navier stokes equations in primitive variables is addressed in this paper a petrov galerkin formulation which automatically introduces streamline upwinding and allows equal order interpolation for all flow variables is presented the solution algorithm is segregated involving a series of updatings of the velocity and pressure fields error estimation and adaptive remeshing strategies for both steady and unsteady problems are demonstrated in some representative numerical examples

quality estimates and stretched meshes based on delaunay triangulations any other vertex is exploited for the automation of the grid generation process moreover delaunay grids have many interesting properties an extensive documentation of which can be found in ref 10 in the following we will first describe the different elements of frod the derivation of the background mesh as well as the vertex generation for the viscous and inviscid regions the latter half of this paper presents the quality measures that can be derived for the isotropic vertex generation part

commutative algebraic methods for controllability of discrete time polynomial systems abstractin this paper we consider controllability of discrete time polynomial systems first we present a forward accessibility local reachability condition that can be verified in finite time in contrast to conventional conditions second we give a backward accessibility local controllability condition for an invertible system and a condition to verify invertibility finally we derive sufficient conditions to test whether the forward accessible system is reachable and to test the backward accessible system is controllable

controllability of nonlinear discrete time systems a lie algebraic approach this paper presents a geometric study of controllability for discrete time nonlinear systems various accessibility properties are characterized in terms of lie algebras of vector fields some of the results obtained are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

a comparison of three error estimation techniques for finite volume solutions of compressible flows three techniques to obtain error estimates for finite volume solutions on unstructured grids are compared in this study the first estimation technique uses richardson extrapolation involving three flow solutions on different grids error estimates on these grids are computed simultaneously with the order of convergence the second technique is based on the difference between the computed solution and a higher order reconstruction obtained using the least squares method finally a third technique solves an error equation driven by source terms computed from the flux jump at cell interfaces the flows solved as test cases are governed by the two dimensional euler equations and the discretization employs roe s flux difference splitting scheme comparisons with exact errors allow the efficiency of each error estimation technique to be assessed for various types of flows

adaptive remeshing for three dimensional compressible flow computations an adaptive mesh procedure for computing steady state solutions of the compressible euler equations in three dimensions is presented the method is an extension of previous work in two dimensions the approach requires the coupling of a surface triangulator an automatic tetrahedral mesh generator a finite element flow solver and an error estimation procedure an example involving flow at high mach number is included to demonstrate the numerical performance of the proposed approach the example shows that the use of this form of adaptivity in three dimensions offers the potential of even greater computational savings than those attained in the corresponding two dimensional implementation

metric tensors for anisotropic mesh generation it has been amply demonstrated that significant improvements in accuracy and efficiency can be gained when a properly chosen anisotropic mesh is used in the numerical solution for a large class of problems which exhibit anisotropic solution features in practice an anisotropic mesh is commonly generated as a quasi uniform mesh in the metric determined by a tensor specifying the shape size orientation of elements thus it is crucial to choose an appropriate metric tensor for anisotropic mesh generation and adaptation in this paper we develop a general formula for the metric tensor for use in any spatial dimension the formulation is based on error estimates for polynomial preserving interpolation on simiplicial elements numerical results in two dimensions are presented to demonstrate the ability of the metric tensor to produce anisotropic meshes with correct mesh concentration and good overall quality the procedure developed in this paper for defining the metric tensor can also be applied to other types of error estimates

adaptative remeshing for viscous incompressible flows this paper presents an adaptive finite element procedure for solving viscous incompressible flows the methodology is based on adaptive remeshing for steady state problems the navier stokes equations for an incompressible fluid are solved in primitive variables by an uzawa algorithm using a highly accurate element the efficiency and convergence rate of the adaptive strategy are evaluated by solving problems with known analytical solutions finally the methodology is applied to the flow over a backward facing step and predictions are compared with experimental measurements the use of the proposed adaptive procedure is shown to lead to improved accuracy of the finite element predictions nomenclature c a constant e error in the solution h element size dissipation energy n number of elements in the mesh p pressure 5 step and fence height u velocity vector u v velocity components x y coordinates v gradient operator 6 element size predicted by adaptation module e strain rate tensor 1a v u v ut a stress tensor 2 e similarity variable in a boundary layer t relative error on a mesh h absolute viscosity of the fluid v kinematic viscosity of the fluid

adaptive quadrilateral and triangular finite element scheme for compressible flows the development of an adaptive mesh refinement procedure for analyzing high speed compressible flows using the finite element method is described this new adaptation procedure which uses both quadrilateral and triangular elements was implemented with two explicit finite element algorithms the two step taylor galerkin and the multistep galerkin runge kutta schemes a von neumann stability analysis and a rotating cosine hill problem demonstrate the instability of the taylor galerkin scheme when coupled with the adaptation procedure for the same adaptive refinement scheme the galerkin runge kutta procedure yields stable solutions within its explicit stability limit the utility of this new adaptation procedure for the prediction of compressible flow features is illustrated for inviscid problems involving strong shock interactions at hypersonic speeds

3d transient fixed point mesh adaptation for time dependent problems application to cfd simulations this paper deals with the adaptation of unstructured meshes in three dimensions for transient problems with an emphasis on cfd simulations the classical mesh adaptation scheme appears inappropriate when dealing with such problems hence another approach based on a new mesh adaptation algorithm and a metric intersection in time procedure suitable for capturing and track such phenomena is proposed more precisely the classical approach is generalized by inserting a new specific loop in the main adaptation loop in order to solve a transient fixed point problem for the mesh solution couple to perform the anisotropic metric intersection operation we apply the simultaneous reduction of the corresponding quadratic form regarding the adaptation scheme an anisotropic geometric error estimate based on a bound of the interpolation error is proposed the resulting computational metric is then defined using the hessian of the solution the mesh adaptation stage surface and volume is based on the generation by global remeshing of a unit mesh with respect to the prescribed metric a 2d model problem is used to illustrate the difficulties encountered then 2d and 3d complexes and representative examples are presented to demonstrate the efficiency of this method

an a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes a new a posteriori residual error estimator is defined and rigorously analysed for anisotropic tetrahedral finite element meshes all considerations carry over to anisotropic triangular meshes with minor changes only the lower error bound is obtained by means of bubble functions and the corresponding anisotropic inverse inequalities in order to prove the upper error bound it is vital that an anisotropic mesh corresponds to the anisotropic function under consideration to measure this correspondence a so called matching function is defined and its discussion shows it to be a useful tool with its help anisotropic interpolation estimates and subsequently the upper error bound are proven additionally it is pointed out how to treat robin boundary conditions in a posteriori error analysis on isotropic and anisotropic meshes a numerical example supports the anisotropic error analysis

electromagnetics via the taylor galerkin finite element method on unstructured grids traditional techniques for computing electromagnetic solutions in the time domain rely on finite differences these so called fdtd finite difference time domain methods are usually defined only on regular lattices of points and can be too restrictive for geometrically demanding problems great geometric flexibility can be achieved by abandoning the regular latticework of sample points and adopting an unstructured grid an unstructured grid allows one to place the grid points anywhere one chooses so that curved boundaries can be fit with ease and local regions in which the field gradients are steep can be selectively resolved with a fine mesh in this paper we present a technique for solving maxwell s equations on an unstructured grid based on the taylor galerkin finite element method we present several numerical examples which reveal the fundamental accuracy and adaptability of the method although our examples are in two dimensions the techniques and results generalize readily to 3d

adaptivity techniques for compressible inviscid flows abstract to enhance the resolution of numerically simulated flowfields grid adaptivity is vitally important further to afford complete flexibility in the spatial discretisation of the flow domain both structured unstructured and combinations of grid types are likely to be required hence the development of grid adaptivity techniques for general grids is important this paper discusses adaptivity achieved through point enrichment point derefinement and point movement applied on general grids a flexible data structure is described together with suitable strategies for adaptively refining a computational grid applications are presented of adaptive grid refinement for two dimensional compressible flow simulation

an optimization based framework for anisotropic simplex mesh adaptation we present a general framework for anisotropic h adaptation of simplex meshes given a discretization and any element wise localizable error estimate our adaptive method iterates toward a mesh that minimizes error for a given degrees of freedom utilizing mesh metric duality we consider a continuous optimization problem of the riemannian metric tensor field that provides an anisotropic description of element sizes first our method performs a series of local solves to survey the behavior of the local error function this information is then synthesized using an affine invariant tensor manipulation framework to reconstruct an approximate gradient of the error function with respect to the metric tensor field finally we perform gradient descent in the metric space to drive the mesh toward optimality the method is first demonstrated to produce optimal anisotropic meshes minimizing the l 2 projection error for a pair of canonical problems containing a singularity and a singular perturbation the effectiveness of the framework is then demonstrated in the context of output based adaptation for the advection diffusion equation using a high order discontinuous galerkin discretization and the dual weighted residual dwr error estimate the method presented provides a unified framework for optimizing both the element size and anisotropy distribution using an a posteriori error estimate and enables efficient adaptation of anisotropic simplex meshes for high order discretizations

on the adaptive finite element method of steady state rolling contact for hyperelasticity in finite deformations in this paper we present an adaptive finite element method for steady state rolling contact in finite deformations along with a residual based a posteriori error estimator for rolling contact problem with coulomb friction a general formulation of rolling contact geometry is derived from the point of view of differential geometry solvability conditions for the rolling contact problems are discussed we use newton s method to solve variational equations derived from a penalty regularization of the finite element approximation of the rolling contact problem we provide a numerical example to illustrate the method

closed form stiffness matrices and error estimators for plane hierarchic triangular elements closed form expressions for the stiffness matrix and a simple error estimator and error indicator are derived for plane straight sided triangular finite elements in elasticity problems the calculation of the error estimator is performed on an element by element basis and is found to be very accurate and efficient in general the solutions for benchmark problems using the error indicators for selective refinement of the regions show accelerated convergence when compared to the convergence rate of solutions using uniform mesh refinement evaluation of the stiffness matrices and error estimators using explicit formulations is found to be several times faster than numerical integration

delaunay triangulation in computational fluid dynamics abstract a method which utilises the delaunay criterion is described by which computational grids consisting of assemblies of triangles or tetrahedra can be constructed an algorithm is briefly outlined to construct the triangulation and its dual the voronoi diagram issues related to how to construct boundary conforming grids from such a triangulation are addressed and details are presented of how grid points within the domain can be generated automatically the point generation algorithm utilises either the given boundary point distribution or for grid adaption a background mesh computational aspects of constructing the triangulation in both 2 and 3 dimensions are covered examples of meshes and flow computations for a range of aerospace geometries are presented

on error estimates and adaptivity in elastoplastic solids applications to the numerical simulation of strain localization in classical and cosserat continua the a posteriori error estimates based on the post processing approach are introduced for elastoplastic solids the standard energy norm error estimate established for linear elliptic problems is generalized here to account for the presence of internal variables through the norm associated with the complementary free energy this is known to represent a natural metric for the class of elastoplastic problems of evolution in addition the intrinsic dissipation functional is utilized as a basis for a complementary a posteriori error estimates a posteriori error estimates and adaptive refinement techniques are applied to the finite element analysis of a strain localization problem as a model problem the constitutive equations describing a generalization of standard j2 elastoplasticity within the cosserat continuum are used to overcome serious limitations exhibited by classical continuum models in the post instability region the proposed a posteriori error estimates are appropriately modified to account for the cosserat continuum model and linked with adaptive techniques in order to simulate strain localization problems superior behaviour of the cosserat continuum model in comparison to the classical continuum model is demonstrated through the finite element simulation of the localization in a plane strain tensile test for an elastopiastic softening material resulting in convergent solutions with an h refinement and almost uniform error distribution in all considered error norms

on the finiteness of accessibility test for nonlinear discrete time systems it is shown that for two large subclasses of discrete time nonlinear systems analytic systems defined on a compact state space and rational systems the minimum length r for input sequences ca

compressible flowfield solutions with unstructured grids generated by delaunay triangulation a method is described that constructs three dimensional unstructured tetrahedral meshes using the delaunay triangulation criterion the approach includes an automatic point creation technique and ensures that given an initial surface triangulation which bounds a domain a valid boundary conforming assembly of tetrahedra is produced the efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities the grids generated are used with two finite element algorithms to simulate inviscid transonic compressible flows flow solutions for aerospace configurations are presented and computed results compared with experimental data

dead beat controllability of polynomial systems symbolic computation approaches state and output dead beat controllability tests for a very large class of polynomial systems with rational coefficients may be based on the quantifier elimination by partial cylindrical algebraic decomposition qepcad symbolic computation program the method is unified for a very large class of systems and can handle one or two sided control constraints families of minimum time state output dead beat controllers are obtained the computational complexity of the test is prohibitive for general polynomial systems but by constraining the structure of the system we may beat the curse of complexity a computationally less expensive algebraic test for output dead beat controllability for a class of odd polynomial systems is presented necessary and sufficient conditions are given they are still very difficult to check therefore a number of easier to check sufficient conditions are also provided the latter are based on the grobner basis method and qepcad it is shown on a subclass of odd polynomial systems how it is possible to further reduce the computational complexity by exploiting the structure of the system

adaptive analysis of thin shells using facet elements an adaptive mesh refinement amr procedure is used in static thin shell analysis using triangular facet shell elements the procedure described herein uses the h version of adaptive refinement based on an error estimate determined by using the best guess values of bending moments and membrane forces obtained from a previous solution it includes the use of a relaxation factor to achieve better convergence some examples are presented to illustrate this method the results obtained are compared with those of uniform mesh refinement umr

observability at an initial state for polynomial systems we consider observability at an initial state for polynomial systems when testing for local observability for nonlinear systems the observability rank condition based on the inverse function theorem is commonly used however the rank condition is a sufficient condition and we cannot test for global observability using the rank condition in this paper first we derive necessary and sufficient conditions for global observability at an initial state for continuous time polynomial systems then necessary and sufficient conditions for local observability are derived from one of the global observability conditions using the localization of a polynomial ring using the same procedure we derive both global and local observability conditions for discrete time polynomial systems each condition is characterized by a finite set of equations since polynomial rings are noetherian finally examples demonstrate the proposed criteria for testing for observability

a new approach to the development of automatic quadrilateral mesh generation a methodology for the automatic mesh generation of quadrilateral elements is proposed the methodology is based on the facts that i a region can always be subdivided entirely into quadrilaterals if the polygon which forms the boundary of the region has an even number of sides ii a quadrilateral can be formed by two triangles which share a common side by taking advantage of the techniques developed in an existing automatic triangular mesh generator quadrilateral meshes can be generated according to the distribution of user specified element size over the domain of interest in particular an automatic quadrilateral mesh generator based on the advancing front technique for triangular mesh generation1 is described techniques to improve the quality of the generated quadrilateral meshes are introduced the robustness and versatility of the mesh generator are demonstrated by a variety of examples

an adaptive finite element approach for frictionless contact problems the derivation of an a posteriori error estimator for frictionless contact problems under the hypotheses of linear elastic behaviour and infinitesimal deformation is presented the approximated solution of this problem is obtained by using the finite element method a penalization or augmented lagrangian technique is used to deal with the unilateral boundary condition over the contact boundary an a posteriori error estimator suitable for adaptive mesh refinement in this problem is proposed together with its mathematical justification up to the present time this mathematical proof is restricted to the penalization approach several numerical results are reported in order to corroborate the applicability of this estimator and to compare it with other a posteriori error estimators copyright 2001 john wiley sons ltd

adaptive finite element methods in computational mechanics we present a general approach to adaptivity for finite element methods and give applications to linear elasticity non linear elasto plasticity and nonlinear conservation laws including numerical results

a linear algebraic framework for the analysis of discrete time nonlinear systems a linear algebraic framework for the analysis of synthesis type problems for discrete time nonlinear systems is introduced this is an extension of a similar tool for continuous time systems that established important connections between many algorithms associated with right invertibility left invertibility and dynamic decoupling as well as between these algorithms and an approach based upon differential algebra a similar payoff is seen to be possible in the discrete time setting

a new functional for variational mesh generation and adaptation based on equidistribution and alignment conditions abstract a new functional is presented for variational mesh generation and adaptation it is formulated based on combining the equidistribution and alignment conditions into a single condition with only one dimensionless parameter the functional is shown to be coercive but not convex a solution procedure using a discrete moving mesh partial differential equation is employed it is shown that the element volumes and altitudes of a mesh trajectory of the mesh equation associated with the new functional are bounded away from zero and the mesh trajectory stays nonsingular if it is so initially numerical examples demonstrate that the new functional performs comparably as an existing one that is also based on the equidistribution and alignment conditions and known to work well but contains an additional parameter

finite element euler computations in three dimensions an explicit finite element solution procedure for the three dimensional euler equations is presented the solution domain is automatically meshed using a tetrahedral mesh generator which is an extension of our previous two dimensional work several examples are included to illustrate the performance of the generator and solver an adaptive mesh regeneration procedure is used for the first time in three dimensions

interval criteria for oscillation of second order nonlinear differential equations by employing the generalized riccati technique and the integral averaging technique new interval oscillation criteria are established for second order nonlinear differential equations

an automatic adaptive meshing technique for delaunay triangulations abstract a new algorithm is described for adaptivity of delaunay triangulations it distinguishes between regions of mesh according to whether they are to be refined unaltered or coarsened the method automatically identifies nodes of the mesh which are candidates for deletion for a region to be coarsened a node deletion process is proposed and it is proved that the resulting triangulation is delaunay after coarsening the mesh retains a high quality for two reasons the first is because a set of nodes have been used to obtain the coarse mesh which are equi distant apart in some sense defined by the original mesh the second is because the triangulation is delaunay the mesh refinement procedure sub divides elements into a number of similar elements in the regions to be refined two dimensional examples demonstrate the quality of the mesh after coarsening refinement

adaptive mesh generation for viscous flows using delaunay triangulation abstract a method for generating an unstructured triangular mesh in two dimensions suitable for computing high reynolds number flows over arbitrary configurations is presented the method is based on a delaunay triangulation which is perfored in a locally stretched space in order to obtain very high aspect ratio tiangles in the boundary layer and wake regions it is shown how the method can be coupled with an unstructured navier stokes solver to produce a solution adaptive mesh generation procedure for viscous flows

local observability of nonlinear systems a necessary and sufficient condition for local observability of analytic systems is presented for smooth systems this condition is only sufficient but it is still weaker than the hermann krener rank condition it is expressed with the language of ideals of germs of analytic or smooth functions and real radicals of such ideals the condition may be practically checked in many cases

regridding surface triangulations an advancing front surface gridding technique that operates on discretely defined surfaces i e triangulations is presented different aspects that are required to make the procedure reliable for complex geometries are discussed notable among these are a the recovery of surface features and discrete surface patches from the discrete data b filtering based on point and side normals to remove undesirable data close to cusps and corners c the proper choice of host faces for ridges and d fast interpolation procedures suitable for complex geometries post generation surface recovery or repositioning techniques are discussed several examples ranging from academic to industrial demonstrate the utility of the proposed procedure forab initiosurface meshing from discrete data such as those encountered when the surface description is already given as discrete the improvement of existing surface triangulations as well as remeshing applications during runs exhibiting significant change of domain

adjoint based airfoil optimization with adaptive isogeometric discontinuous galerkin method abstract in this work an adjoint based airfoil shape optimization algorithm is developed based on the adaptive isogeometric discontinuous galerkin method for compressible euler equations to investigate the significance of each design variable of airfoil b spline parameterization we first parameterize the airfoil by b spline curve approximation with some control points viewed as design variables and build the b spline representation of the flow field with the curve to apply the goal oriented h adaptive isogeometric dg method for flow solution then we compute and employ the discrete adjoint solutions for both multi target error estimation in adaptive mesh refinement with the isogeometric nature not only all the geometrical cells but also the numerical basis functions can be analytically expressed by the design variables indicating that the numerical solutions and objective could be differentiable with respect to those variables consequently the gradient is totally computed in an accurate approach and the sensitivity analysis is thus improved by reducing the spatial discretization error and introducing the analytical expression of derivative to reveal the key parameters for optimization in an intuitive and efficient manner although the sqp optimization algorithm is adopted in the paper the given accurate gradient can be applied to any gradient based optimization algorithm the proposed algorithm is demonstrated on rae2822 airfoil with inviscid transonic flow where the shape is optimized to minimize the drag coefficient at a constrained lift and airfoil area the numerical results show that the drag is much more sensitive to the design variables near the tailing edge at the beginning but sensitivity is reduced when optimal

comparison of mesh adaptation using the adjoint methodology and truncation error estimates mesh adaptation based on error estimation has become a key technique to improve th eaccuracy o fcomputational fluid dynamics computations the adjoint based approach for error estimation is one of the most promising techniques for computational fluid dynamics applications nevertheless the level of implementation of this technique in the aeronautical industrial environment is still low because it is a computationally expensive method in the present investigation a new mesh refinement method based on estimation of truncation error is presented in the context of finite volume discretization the estimation method uses auxiliary coarser meshes to estimate the local truncation error which can be used for driving an adaptation algorithm the method is demonstrated in the context of two dimensional naca0012 and three dimensional onera m6 wing inviscid flows and the results are compared against the adjoint based approach and physical sensors based on features of the flow field

arbitrary lagrangian eulerian finite element analysis of strain localization in transient problems non local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint the non locality prevents strain localization with zero global dissipation of energy and consequently finite element calculations converge upon mesh refinements to non zero width localization zones one of the major drawbacks of these models is that the element size needed in order to capture the localization zone must be smaller than the internal length hence the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity this paper deals with the application of the arbitrary lagrangian eulerian ale formulation well known in hydrodynamics and fluid structure interaction problems to transient strain localization in a non local damageable material it is shown that the ale formulation which is employed in large boundary motion problems can also be well suited for non linear transient analysis of softening materials where localization bands appear the remeshing strategy is based on the equidistribution of an indicator that quantifies the interelement jump of a selected state variable two well known one dimensional examples illustrate the capabilities of this technique the first one deals with localization due to a propagating wave in a bar and the second one studies the wave propagation in a hollow sphere

error estimates and adaptive refinement for plate bending problems the zienkiewicz zhu error estimator is shown to be effective in problems of plate flexure when used in conjunction with triangular elements and an adaptive mesh generator allowing a prescribed size of elements to be developed very fast adaptive convergence for results of specified accuracy is achieved

arbitrary order edge elements for electromagnetic scattering simulations using hybrid meshes and a pml the use of arbitrary order edge elements for the simulation of two dimensional electromagnetic scattering problems on hybrid meshes of triangles and quadrilaterals is described single frequency incident waves generated by a source in the far field are considered and the solution is determined in the frequency domain for numerical simulation the solution domain is truncated at a finite distance from the perfectly conducting scatterer and the non reflecting boundary condition at the truncated boundary is imposed by the use of a perfectly matched layer pml several examples are included to demonstrate the performance of the proposed procedure copyright 2002 john wiley sons ltd

controllability of structured polynomial systems two algorithms based on the grobner basis method which facilitate the controllability analysis for a class of polynomial systems are presented the authors combine these algorithms with some results on output dead beat controllability in order to obtain sufficient as well as necessary conditions for complete and state dead beat controllability for a surprisingly large class of polynomial systems our results are generically applicable to the class of polynomial systems in strict feedback form

shape optimization in frictionless contact problems a finite element approach for shape optimization in two dimensional 2 d frictionless contact problems is presented in this work the goal is to find the shape that gives a constant distribution of stresses along the contact boundary the whole formulation including mathematical model for the unilateral problem sensitivity analysis and geometry definition is treated in a continuous form independently of the discretization in finite elements shape optimization is performed by direct modification of geometry through b spline curves and an automatic mesh generator is used at each new configuration to provide the finite element input data for numerical analysis and sensitivity computations using augmented lagrangian techniques to solve the contact problem and an interior point mathematical programming algorithm for shape optimization we obtain several results reported at the end of the article

unsteady flow simulation using unstructured meshes transient flows involving moving boundaries are more difficult to simulate as the geometry of the computational domain changes with time regardless of the changes occurring in the solution the mesh must be modified during the computation in order to accommodate the changes in the geometry although the literature on this subject describes a number of different approaches for handling this type of problem the approach followed in this paper is to use unstructured mesh methods we consider initially the simulation of inviscid two dimensional transient flows involving moving bodies employing an extension of adaptivity procedures which have been successfully used for steady state problems with the error estimation procedure coupled to an automatic triangular mesh generator this approach is extended to produce a three dimensional capability using tetrahedral meshes a number of examples are included to illustrate the numerical performance of these methods

algebraic criteria of global observability of polynomial systems global observability of continuous time polynomial systems is studied an algebraic necessary and sufficient condition of global observability is proved it is expressed with the aid of real radicals of ideals in the ring of polynomials and is based on the real theorem of zeros from real algebraic geometry

hp version discontinuous galerkin methods for hyperbolic conservation laws abstract the development of hp version discontinuous galerkin methods for hyperbolic conservation laws is presented in this work a priori error estimates are derived for a model class of linear hyperbolic conservation laws these estimates are obtained using a new mesh dependent norm that reflects the dependence of the approximate solution on the local element size and the local order of approximation the results generalize and extend previous results on mesh dependent norms to hp version discontinuous galerkin methods a posteriori error estimates which provide bounds on the actual error are also developed in this work numerical experiments verify the a priori estimates and demonstrate the effectiveness of the a posteriori estimates in providing reliable estimates of the actual error in the numerical solution

adaptive mesh generation for fluid mechanics problems in this study we give an in depth investigation of the adaptive procedures for compressible and incompressible flow problems many tests have been carried out with different error indicators for different problems these refinement procedures show that the interpolation error indicators are adequate to predict an accurate solution comparison between the gradient and curvature based error indicators show that the former yields better performance in most situations however we found that the latter indicators predict better motion in the recirculatory and unstable regions than the gradient based method many test cases have been presented for both compressible and incompressible flow problems in the later part of the paper we suggest a simple way of combining the curvature gradient indicators of different key variables and present an appropriate problem where it is applicable a wide coverage of relevant literature has also been presented in this paper copyright 2000 john wiley sons ltd

adaptive remeshing for the k epsilon model of turbulence an adaptive nite element method for solving incompressible turbulentows using the k model of turbulence is presented solutions are obtained in primitive variables using a highly accurate quadratic nite element on unstructured grids turbulence is modeled using the k model of turbulence two error estimators are presented that take into account in a rigorous way the relative importance of the errors in velocity pressure turbulence variables and eddy viscosity the ef ciency and convergence rate of the methodology are evaluated by solving problemswith known analytical solutions themethod isthen applied to turbulent free shearowsand predictions are compared to measurements nomenclature cl c1 c2 k model constants e error f body force h element size k element in the mesh k turbulent kinetic energy n outward unit vector p u production of turbulence p pressure u velocity vector