a purely lagrangian method for computing linearly perturbed flows in spherical geometry in many physical applications one wishes to control the development of multi dimensional instabilities around a one dimensional 1d complex flow for predicting the growth rates of these perturbations a general numerical approach is viable which consists in solving simultaneously the one dimensional equations and their linearized form for three dimensional perturbations in clarisse et al j m clarisse s jaouen p a raviart a godunov type method in lagrangian coordinates for computing linearly perturbed planar symmetric flows of gas dynamics j comp phys 198 2004 80 105 a class of godunov type schemes for planar symmetric flows of gas dynamics has been proposed pursuing this effort we extend these results to spherically symmetric flows a new method to derive the lagrangian perturbation equations based on the canonical form of systems of conservation laws with zero entropy flux b despres lagrangian systems of conservation laws invariance properties of lagrangian systems of conservation laws approximate riemann solvers and the entropy condition numer math 89 2001 99 134 b despres c mazeran lagrangian gas dynamics in two dimensions and lagrangian systems arch rational mech anal 178 2005 327 372 is also described it leads to many advantages first of all many physical problems we are interested in enter this formalism gas dynamics two temperature plasma equations ideal magnetohydrodynamics etc whatever is the geometry secondly a class of numerical entropic schemes is available for the basic flow 11 last linearizing and devising numerical schemes for the perturbed flow is straightforward the numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that due to its simplicity and its low computational cost the linear perturbations code lpc is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime

discontinuous galerkin methods for incompressible and nearly incompressible elasticity by nitsche s method we propose and analyze a discontinuous finite element method for nearly incompressible linear elasticity on triangular meshes we show optimal error estimates that are uniform with respect to poisson s ratio the method is thus locking free we also introduce an equivalent mixed formulation allowing for completely incompressible elasticity problems numerical results are presented

positive invariant sets for fault tolerant multisensor control schemes this article deals with fault tolerant multisensor control schemes for systems with linear dynamics positive invariance is a common analysis and control design tool for systems affected by bounded constraints and disturbances this article revisits the construction of e approximations of minimal robust positive invariant sets for linear systems upon contractive set iterations the cases of switching between different sets of disturbances and the inclusion of a predefined region of the state space are treated in detail all these results are used in multisensor control schemes which have to deal with specific problems originated by the switching between different estimators and by the presence of faults in some of the sensors the construction of positive invariant sets for different operating regimes provides in this context effective fault detection information within the same framework global stability of the switching strategies can be assured if the invariant sets topology allows the exclusive se

a high order godunov type scheme for shock interactions in ideal magnetohydrodynamics a high order godunov type scheme is developed for the shock interactions in ideal magnetohydrodynamics mhd the scheme is based on a nonlinear riemann solver and follows the basic procedure in the piecewise parabolic method the scheme takes into account all the discontinuities in ideal mhd and is in a strict conservation form the scheme is applied to numerical examples which include shock tube problems in ideal mhd and various interactions between strong mhd shocks all the waves involved in the corresponding riemann problems are resolved and are correctly displayed in the simulation results the correctness of the scheme is shown by the comparison between the simulation results and the solutions of the riemann problems the robustness of the scheme is demonstrated through the numerical examples it is shown that the scheme offers the principle advantages of a high order godunov type scheme robust operation in the presence of very strong waves thin shock fronts and thin contact and slip surface discontinuities

controlled invariance and feedback laws we consider controlled invariance for cones translated cones polyhedra and various special polyhedral structures for any polyhedron if controlled invariance occurs then all and nothing but the admissible controls can be obtained by an inequative feedback controller for each special polyhedral structure we compare this feedback controller against piecewise affine linear and affine feedback controllers

non uniform convergence of finite volume schemes for riemann problems of ideal magnetohydrodynamics this paper presents riemann test problems for ideal magnetohydrodynamics mhd finite volume schemes the test problems place emphasis on the hyperbolic irregularities of the ideal mhd system namely the occurrence of intermediate shocks and non unique solutions we investigate numerical solutions for the test problems obtained by several commonly used methods roe hlle central scheme all methods turned out to show a non uniform convergence behavior which may be paraphrased as pseudo convergence initially the methods show convergence towards a wrong solution with irregular wave patterns only after heavy grid refinement the methods switch to converge to the true solution this behavior is most pronounced whenever the solution should be unique but its phase space trajectory lies in the vicinity of that of a non unique solution we show detailed grid convergence studies and empirical error analysis the results may be related to similar results for a 2 2 model system and to time dependent investigations of other authors the non uniform convergence is expected to be present for any diffusive finite volume method and question the reliability of coarse grid ideal mhd solutions also in higher space dimensions

parameter range reduction from partial data in systems of differential algebraic equations abstract this paper presents an algorithm for parameter range reduction from partial data in systems of differential algebraic equations interval arithmetic and linear multistep discretizations are used to prune regions of parameter space that are inconsistent with available time series data methods of splitting parameter space to ensure further progress are discussed the algorithm outputs a reduced range and an approximation for each parameter value these outputs are shown to have beneficial effect as input to traditional parameter estimation schemes the range reduction algorithm is tested on three systems with partial data sets

roe matrices for ideal mhd and systematic construction of roe matrices for systems of conservation laws in this paper the construction of a roe s scheme for the conservative system of ideal magnetohydrodynamics mhd is presented as this method relies on the computation of a roe matrix the problem is to find a matrixa ul ur which satisfies the following properties it is required to be consistent with the jacobian of the fluxf to have real eigenvalues a complete set of eigenvectors and to satisfy the relation f a ul ur u whereulandurare two admissible states and utheir difference for the ideal mhd system using eulerian coordinates a roe matrix is obtained without any hypothesis on the specific heat ratio especially its construction relies on an original expression of the magnetic pressure jump moreover a roe matrix is computed for lagrangian ideal mhd by extending the results of munz who obtained such a matrix for the system of lagrangian gas dynamics so this second matrix involves arithmetic averages unlike the eulerian one which contains classical roe averages like in eulerian gas dynamics in this paper a systematic construction of lagrangian roe matrices in terms of eulerian roe matrices for a general system of conservation laws is also presented this result applied to the above eulerian and lagrangian matrices for ideal mhd gives two new matrices for this system in the same way by applying this construction to the gas dynamics equations new roe matrices are also obtained all these matrices allow the construction of roe type schemes some numerical examples on the shock tube problem show the applicability of this method

an entropic solver for ideal lagrangian magnetohydrodynamics in this paper we adapt to the ideal 1d lagrangian mhd equations a class of numerical schemes of order one in time and space presented in an earlier paper and applied to the gas dynamics system they use some properties of systems of conservation laws with zero entropy flux which describe fluid models invariant by galilean transformation and reversible for regular solutions these numerical schemes satisfy an entropy inequality under cfl conditions in the last section we describe a particular scheme for the mhd equations and show with some numerical applications its robustness and accuracy the generalization to full eulerian multidimensional mhd will be the subject of a forthcoming paper

providing a basin of attraction to a target region of polynomial systems by computation of lyapunov like functions in this paper we present a method for computing a basin of attraction to a target region for polynomial ordinary differential equations this basin of attraction is ensured by a lyapunov like polynomial function that we compute using an interval based branch and relax algorithm this algorithm relaxes the necessary conditions on the coefficients of the lyapunov like function to a system of linear interval inequalities that can then be solved exactly it iteratively refines these relaxations in order to ensure that whenever a nondegenerate solution exists it will eventually be found by the algorithm application of an implementation to a range of benchmark problems shows the usefulness of the approach

a multiwave approximate riemann solver for ideal mhd based on relaxation i theoretical framework we present a relaxation system for ideal magnetohydrodynamics mhd that is an extension of the suliciu relaxation system for the euler equations of gas dynamics from it one can derive approximate riemann solvers with three or seven waves that generalize the hllc solver for gas dynamics under some subcharacteristic conditions the solvers satisfy discrete entropy inequalities and preserve positivity of density and internal energy the subcharacteristic conditions are nonlinear constraints on the relaxation parameters relating them to the initial states and the intermediate states of the approximate riemann solver itself the 7 wave version of the solver is able to resolve exactly all material and alfven isolated contact discontinuities practical considerations and numerical results will be provided in another paper

survey of interval algorithms for ordinary differential equations interval algorithms compute an interval valued function in which the solution to a system of ordinary differential equations is guaranteed to lie interval algorithms use differential inequalities finite difference approximations with remainders taylor series defect corrections or contractive iterations

korn s inequalities for piecewise h 1 vector fields korn s inequalities for piecewise h 1 vector fields are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

mixed finite element formulations of strain gradient elasticity problems theories on intrinsic or material length scales find applications in the modeling of size dependent phenomena in elasticity length scales enter the constitutive equations through the elastic strain energy function which in this case depends not only on the strain tensor but also on gradients of the rotation and strain tensors in the present paper the strain gradient elasticity theories developed by mindlin and co workers in the 1960s are treated in detail in such theories when the problem is formulated in terms of displacements the governing partial differential equation is of fourth order if traditional finite elements are used for the numerical solution of such problems then c 1 displacement continuity is required an alternative mixed finite element formulation is developed in which both the displacement and the displacement gradients are used as independent unknowns and their relationship is enforced in an integralsense a variational formulation is developed which can be used for both linear and non linear strain gradient elasticity theories the resulting finite elements require only c 0 continuity and are simple to formulate the proposed technique is applied to a number of problems and comparisons with available exact solutions are made 2002 elsevier science b v all rights reserved

causal state feedback parameterizations in robust model predictive control in this paper we investigate the problem of nonlinearity and non convexity typically associated with linear state feedback parameterizations in the robust model predictive control rmpc for uncertain systems in particular we propose two tractable approaches to compute an rmpc controller consisting of both a causal state feedback gain and a control perturbation component for linear discrete time systems involving bounded disturbances and norm bounded structured model uncertainties along with hard constraints on the input and state both the state feedback gain and the control perturbation are explicitly considered as decision variables in the online optimization while avoiding nonlinearity and non convexity in the formulation the proposed rmpc controller computed through lmi optimizations is responsible for steering the uncertain system state to a terminal invariant set numerical examples from the literature demonstrate the advantages of the proposed scheme

two robust nonconforming hbox h 2 elements for linear strain gradient elasticity we propose two finite elements to approximate a boundary value problem arising from strain gradient elasticity which is a high order perturbation of the linearized elastic system our elements are hbox h 2 nonconforming while hbox h 1 conforming we show both elements converge in the energy norm uniformly with respect to the perturbation parameter

validated solutions of initial value problems for ordinary differential equations compared to standard numerical methods for initial value problems ivps for ordinary differential equations odes validated methods for ivps for odes have two important advantages if they return a solution to a problem then 1 the problem is guaranteed to have a unique solution and 2 an enclosure of the true solution is produced the authors survey taylor series methods for validated solutions of ivps for odes describe several such methods in a common framework and identify areas for future research

continuous time analysis eigenstructure assignment and h sub 2 synthesis with enhanced linear matrix inequalities lmi characterizations this note describes a new framework for the analysis and synthesis of control systems which constitutes a genuine continuous time extension of results that are only available in discrete time in contrast to earlier results the proposed methods involve a specific transformation on the lyapunov variables and a reciprocal variant of the projection lemma in addition to the classical linearizing transformations on the controller data for a wide range of problems including robust analysis and synthesis multichannel h sub 2 stateand output feedback syntheses the approach leads to potentially less conservative linear matrix inequality lmi characterizations this comes from the fact that the technical restriction of using a single lyapunov function is to some extent ruled out in this new approach moreover the approach offers new potentials for problems that cannot be handled using earlier techniques an important instance is the eigenstructure assignment problem blended with lyapunov type constraints which is given a simple and tractable formulation

feedback control of linear discrete time systems under state and control constraints in this paper the problem of stabilizing linear discrete time systems under state and control linear constraints is studied based on the concept of positive invariance existence conditions of linear state feedback control laws respecting both the constraints are established these conditions are then translated into an algorithm of linear programming

bracketing the solutions of an ordinary differential equation with uncertain initial conditions in this paper we present a new method for bracketing i e characterizing from inside and from outside all solutions of an ordinary differential equation in the case where the initial time is inside an interval and the initial state is inside a box the principle of the approach is to cast the problem into bracketing the largest positive invariant set which is included inside a given set x although there exists an efficient algorithm to solve this problem when x is bounded we need to adapt it to deal with cases where x is unbounded

entropy satisfying flux vector splittings and kinetic bgk models we establish forward and backward relations between entropy satisfying bgk relaxation models such as those introduced previously by the author and the first order flux vector splitting numerical methods for general systems of conservation laws classically to a kinetic bgk model that is compatible with some family of entropies we can associate an entropy flux vector splitting we prove that the converse is true any entropy flux vector splitting can be interpreted by a kinetic model and we obtain an explicit characterization of entropy satisfying flux vector splitting schemes we deduce a new proof of discrete entropy inequalities under a sharp cfl condition that generalizes the monotonicity criterion in the scalar case in particular this gives a stability condition for numerical kinetic methods with noncompact velocity support a new interpretation of general kinetic schemes is also provided via approximate riemann solvers we deduce the construction of finite velocity relaxation systems for gas dynamics and obtain a hllc scheme for which we are able to prove positiveness of density and internal energy and discrete entropy inequalities

an observation on korn s inequality for nonconforming finite element methods by utilizing a simple observation on traces of rigid motions we are able to strengthen a result of brenner 2004 on korn s inequality for nonconforming finite element methods the approach here is tightly connected to the theory developed in brenner s work our motivation for the analysis was the desire to show that a robust darcy stokes element satisfies korn s inequality and to achieve this the stronger result seems necessary

a mathcal c 0 interior penalty method for a fourth order elliptic singular perturbation problem in this paper we develop a mathcal c 0 interior penalty method for a fourth order singular perturbation elliptic problem in two dimensions on polygonal domains using some a posteriori error analysis techniques we are able to show that the method converges in the energy norm uniformly with respect to the perturbation parameter under minimal regularity assumptions in addition we analyze the convergence of the numerical solution to the unperturbed second order problem finally we perform some numerical experiments that back up the theoretical results

optimized robust control invariance for linear discrete time systems theoretical foundations this paper introduces the concept of optimized robust control invariance for discrete time linear time invariant systems subject to additive and bounded state disturbances a novel characterization of two families of robust control invariant sets is given the existence of a constraint admissible member of these families can be checked by solving a single and tractable convex programming problem in the generic linear convex case and a standard linear quadratic program when the constraints are polyhedral or polytopic the solution of the same optimization problem yields the corresponding feedback control law that is in general set valued a procedure for selection of a point valued nonlinear control law is provided

brief nonlinear model predictive control with polytopic invariant sets ellipsoidal invariant sets have been widely used as target sets in model predictive control mpc these sets can be computed by constructing appropriate linear difference inclusions together with additional constraints to ensure that the ellipsoid lies within a given inclusion polytope the choice of inclusion polytope has a significant effect on the size of the target ellipsoid but the optimal inclusion polytope cannot in general be computed systematically this paper shows that use of polytopic invariant sets overcomes this difficulty allowing larger stabilizable sets without loss of performance in the interests of online efficiency consideration is focused on interpolation based mpc

on the gap between the quadratic integer programming problem and its semidefinite relaxation consider the semidefinite relaxation sdr of the quadratic integer program qip where q is a given symmetric matrix and d is diagonal we consider the sdr gap we establish the uniqueness of the sdr solution and prove that if and only if r n 1max xtvvtx x 1 1 n 1 where v is an orthogonal matrix whose columns span the r dimensional null space of d q and where d is the unique sdr solution we also give a test for establishing whether that involves 2r 1 function evaluations in the case that r 1 we derive an upper bound on which is tighter than thus we show that breaching the sdr gap for the qip problem is as difficult as the solution of a qip with the rank of the cost function matrix equal to the dimension of the null space of d q this reduced rank qip problem has been recently shown to be solvable in polynomial time for fixed r

nonconforming finite element methods for the equations of linear elasticity in the adaptation of nonconforming finite element methods to the equations of elasticity with traction boundary conditions the main difficulty in the analysis is to prove that an appropriate discrete version of korn s second inequality is valid such a result is shown to hold for nonconforming piecewise quadratic and cubic finite elements and to be false for nonconforming piecewise linears optimal order error estimates uniform for poisson ratio v e 0 1 2 are then derived for the corresponding p2 and p3 methods this contrasts with the use of c finite elements where there is a deterioration in the convergence rate as v 1 2 for piecewise polynomials of degree 3 modifications of the continuous methods and the nonconforming linear method which also give uniform optimal order error estimates are discussed

robust solutions to uncertain semidefinite programs in this paper we consider semidefinite programs sdps whose data depend on some unknown but bounded perturbation parameters we seek robust solutions to such programs that is solutions which minimize the worst case objective while satisfying the constraints for every possible value of parameters within the given bounds assuming the data matrices are rational functions of the perturbation parameters we show how to formulate sufficient conditions for a robust solution to exist as sdps when the perturbation is full our conditions are necessary and sufficient in this case we provide sufficient conditions which guarantee that the robust solution is unique and continuous holder stable with respect to the unperturbed problem s data the approach can thus be used to regularize ill conditioned sdps we illustrate our results with examples taken from linear programming maximum norm minimization polynomial interpolation and integer programming

a one step 7 stage hermite birkhoff taylor ode solver of order 11 a one step 7 stage hermite birkhoff taylor method of order 11 denoted by hbt 11 7 is constructed for solving nonstiff first order initial value problems y f t y y t 0 y 0 the method adds the derivatives y to y 6 used in taylor methods to a 7 stage runge kutta method of order 6 forcing an expansion of the numerical solution to agree with a taylor expansion of the true solution to order 11 leads to taylor and runge kutta type order conditions these conditions are reorganized into vandermonde type linear systems whose solutions are the coefficients of the method the new method has a larger scaled interval of absolute stability than the dormand prince dp87 and a larger unscaled interval of absolute stability than the taylor method t11 of order 11 hbt 11 7 is superior to dp87 and t11 in solving several problems often used to test higher order ode solvers on the basis of the number of steps cpu time and maximum global error numerical results show the benefit of adding high order derivatives to runge kutta methods

a positivity preserving lagrangian discontinuous galerkin method for ideal magnetohydrodynamics equations in one dimension abstract in this paper we propose a conservative lagrangian discontinuous galerkin dg scheme for solving the ideal compressible magnetohydrodynamics mhd equations in one dimensional this scheme can preserve positivity of physically positive variables such as density and thermal pressure we first develop a lagrangian hlld approximate riemann solver which can keep positivity preserving property under some appropriate signal speeds with this solver a first order positivity preserving lagrangian dg scheme can be constructed then we design a high order positivity preserving and conservative lagrangian dg scheme by using the strong stability preserving ssp high order time discretizations and the positivity preserving scaling limiter we adopt tvb minmod limiter with the local characteristic fields for the ideal mhd system to control spurious oscillations around the shock wave some numerical examples are presented to demonstrate the accuracy and positivity preserving property of our scheme

low complexity polytopic invariant sets for linear systems subject to norm bounded uncertainty we propose a novel algorithm to compute low complexity polytopic robust control invariant rci sets along with the corresponding state feedback gain for linear discrete time systems subject to norm bounded uncertainty additive disturbances and state input constraints using a slack variable approach we propose new results to transform the original nonlinear problem into a convex lmi problem whilst introducing only minor conservatism in the formulation through numerical examples we illustrate that the proposed algorithm can yield improved maximal minimal volume rci set approximations in comparison with the schemes given in the literature

modelling of localisation and scale effect in thick walled cylinders with gradient elastoplasticity we model the progressive localisation of deformation which causes failure around thick walled cylinders under external radial pressure the study is based on a second gradient elastoplastic model developed to regularise the ill posedness caused by material strain softening behaviour the stress increment is related to both the strain increment and its laplacian the gradient terms introduce an internal length scale to the material allowing robust modelling of its post peak behaviour the numerical implementation is based on a c 1 finite element displacement formulation mesh insensitivity in terms of load displacement and failure mechanism is demonstrated the internal length in the constitutive equations enables modelling of the scale effect in thick walled cylinders according to which the load required to induce failure appears to be much larger for small holes than for large holes

one step 5 stage hermite birkhoff taylor ode solver of order 12 a one step 5 stage hermite birkhoff taylor method hbt 12 5 of order 12 is constructed for solving nonstiff systems of differential equations y f t y y t 0 y 0 where email protected r n the method uses derivatives y to y 9 as in taylor methods combined with a 5 stage runge kutta method forcing an expansion of the numerical solution to agree with a taylor expansion of the true solution to order 12 leads to taylor and runge kutta type order conditions which are reorganized into vandermonde type linear systems whose solutions are the coefficients of the method hbt 12 5 has a larger interval of absolute stability than dormand prince dp 8 7 13m and taylor method t12 of order 12 the new method has also a smaller norm of principal error term than t12 it is superior to dp 8 7 13m and t12 on the basis the number of steps cpu time and maximum global error on common test problems the formulae of hbt 12 5 are listed in an appendix

on efficient computation of low complexity controlled invariant sets for uncertain linear systems a method is presented for determining invariant low complexity polytopic sets and associated linear feedback laws for linear systems with polytopic uncertainty conditions based on the relationship between 2 and norms are used to define an initial invariant low complexity polytope as the solution of a semi definite program the problem of computing a maximal controlled invariant low complexity polytopic set is then formulated as a bilinearly constrained problem and a relaxation of this problem is derived as an iterative sequence of convex programs the proposed method scales linearly with the state dimension which allows the possibility of determining low complexity robust controlled invariant sets for high order systems

analysis of error control strategies for continuous runge kutta methods there has been considerable recent progress in the analysis and development of interpolation schemes that can be associated with discrete runge kutta methods with the availability of these schemes it can now be asked that a numerical method provide a continuous approximation to the solution thispaper rather than view such a continuous method as an interpolant superimposed on a standard discrete method considers how the interpolant and its associated defect can be effectively used in the underlying error and stepsize control mechanism in particular four error control strategies are considered that can be used in methods based on runge kutta formula pairs with interpolants an asymptotic and a nonasymptotic analysis of each strategy are presented it is shown that a strategy based on direct defect control can provide significant advantages over existing strategies with only a modest increase in cost

a survey of the s lemma in this survey we review the many faces of the s lemma a result about the correctness of the s procedure the basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization convex geometry and linear algebra as well these were all active research areas but as there was little interaction between researchers in these different areas their results remained mainly isolated here we give a unified analysis of the theory by providing three different proofs for the s lemma and revealing hidden connections with various areas of mathematics we prove some new duality results and present applications from control theory error estimation and computational geometry

a robust finite element method for darcy stokes flow finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed the system is approximately a linear stokes problem when the perturbation parameter is large while it degenerates to a mixed formulation of poisson s equation as the perturbation parameter tends to zero it is established basically by numerical experiments that most of the proposed finite element methods for stokes problem or the mixed poisson s system are not well behaved uniformly in the perturbation parameter this is used as the motivation for introducing a new robust finite element which exhibits this property

shock capturing approach and nonevolutionary solutions in magnetohydrodynamics shock capturing methods have become an effective tool for the solution of hyperbolic partial differential equations both upwind and symmetric tvd schemes in the framework of the shock capturing approach are thoroughly investigated and applied with great success to a number of complicated multidimensional gasdynamic problems the extension of these schemes to magnetohydrodynamic mhd equations is not a simple task first the exact solution of the mhd riemann problem is too multivariant to be used in regular calculations on the other hand the extensions of roe s approximate riemann problem solvers for mhd equations in general case are nonunique and need further investigation that is why some simplified approaches should be constructed in this work the second order of accuracy in time and space high resolution lax friedrichs type scheme is suggested that gives a drastic simplification of the numerical algorithm comparing to the precise characteristic splitting of jacobian matrices the necessity is shown to solve the full set of mhd equations for modeling of multishocked flows even when the problem is axisymmetric to obtain evolutionary solutions for the numerical example the mhd riemann problem is used with the initial data consisting of two constant states lying to the right and to the left from the centerline of the computational domain if the problem is solved as purely coplanar a slow compound wave appears in the self similar solution obtained by any shock capturing scheme if the full set of mhd equations is used and a small uniform tangential disturbance is added to the magnetic field vector a rotational jump splits from the compound wave and it degrades into a slow shock the reconstruction process of the nonevolutionary compound wave into evolutionary shocks is investigated presented results should be taken into account in the development of shock capturing methods for mhd flows

finite element formulations of strain gradient theory for microstructures and the c0 1 patch test based on finite element formulations for the strain gradient theory of microstructures a convergence criterion for the c0 1 patch test is introduced and a new approach to devise strain gradient finite elements that can pass the c0 1 patch test is proposed the displacement functions of several plane triangular elements which satisfy the c0 continuity and weak c1 continuity conditions are evaluated by the c0 1 patch test the difference between the proposed c0 1 patch test and the c0 constant stress and c1 constant curvature patch tests is elucidated an 18 dof plane strain gradient triangular element rct9 rt9 which passes the c0 1 patch test and has no spurious zero energy modes is proposed numerical examples are employed to examine the performance of the proposed element by carrying out the c0 1 patch test and eigenvalue test the proposed element is found to be without spurious zero energy modes and it possesses higher accuracy compared with other strain gradient elements copyright 2004 john wiley sons ltd

an interval approach to compute invariant sets this paper proposes an original interval based method to compute an outer approximation of all invariant sets such as limit cycles of a continuous time nonlinear dynamic system which are included inside a prior set of the state space contrary to all other existing approaches our method has the following properties first it is guaranteed a solution cannot be lost second it is applicable to a large class of systems without any specific assumption such as the knowledge of a lyapunov function or any partial linearity and third there is no need to integrate the system

invariant approximations of the minimal robust positively invariant set this note provides results on approximating the minimal robust positively invariant mrpi set also known as the 0 reachable set of an asymptotically stable discrete time linear time invariant system it is assumed that the disturbance is bounded persistent and acts additively on the state and that the constraints on the disturbance are polyhedral results are given that allow for the computation of a robust positively invariant outer approximation of the mrpi set conditions are also given that allow one to a priori specify the accuracy of this approximation

atomft solving odes and daes using taylor series abstract taylor series methods compute a solution to an initial value problem in ordinary differential equations by expanding each component of the solution in a long taylor series the series terms are generated recursively using the techniques of automatic differentiation the atomft system includes a translator to transform statements of the system of odes into a fortran 77 object program that is compiled linked with the atomft runtime library and run to solve the problem we review the use of the atomft system for nonstiff and stiff odes the propagation of global errors and applications to differential algebraic equations arising from certain control problems to boundary value problems to numerical quadrature and to delay problems

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

a robust nonconforming h 2 element finite element methods for some elliptic fourth order singular perturbation problems are discussed we show that if such problems are discretized by the nonconforming morley method in a regime close to second order elliptic equations then the error deteriorates in fact a counterexample is given to show that the morley method diverges for the reduced second order equation as an alternative to the morley element we propose to use a nonconforming h 2 element which is h 1 conforming we show that the new finite element method converges in the energy norm uniformly in the perturbation parameter