a staggered grid lagrangian eulerian remap code for 3 d mhd simulations abstract in this paper an approach to multidimensional magnetohydrodynamics mhd which correctly handles shocks but does not use an approximate riemann solver is proposed this approach is simple and is based on control volume averaging with a staggered grid the method builds on the older and often overlooked technique of on each step taking a fully 3 d lagrangian step and then conservatively remapping onto the original grid at the remap step gradient limiters are applied so that the scheme is monotonicity preserving for euler s equations this technique combined with an appropriately staggered grid and wilkins artificial viscosity can give results comparable to those from approximate riemann solvers we show how this can be extended to include a magnetic field maintaining the divergence free condition and pressure positivity and then present numerical test results where possible a comparison with other shock capturing techniques is presented and the advantages and disadvantages of the proposed scheme are clearly explained

central finite volume schemes on nonuniform grids and applications we propose a new one dimensional unstaggered central scheme on nonuniform grids for the numerical solution of homogeneous hyperbolic systems of conservation laws with applications in two phase flows and in hydrodynamics with and without gravitational effect the numerical base scheme is a generalization of the original lax friedrichs scheme and an extension of the nessyahu and tadmor central scheme to the case of nonuniform irregular grids the main feature that characterizes the proposed scheme is its simplicity and versatility in fact the developed scheme evolves a piecewise linear numerical solution defined at the cell centers of a nonuniform grid and avoids the resolution of the riemann problems arising at the cell interfaces thanks to a layer of staggered cells used intermediately spurious oscillations are avoided using a slopes limiting procedure the developed scheme is then validated and used to solve classical problems arising in gas solid two phase flow problems the proposed scheme is then extended to the case of non homogenous hyperbolic systems with a source term in particular to the case of euler equations with a gravitational source term the obtained numerical results are in perfect agreement with corresponding ones appearing in the recent literature thus confirming the efficiency and potential of the proposed method to handle both homogeneous and non homogeneous hyperbolic systems

sequential optimal truss generator for frequency ranges abstract the concept of an ordered set of optimum designs is introduced here and all the design variables and behavioral variables belonging to the optimum designs are represented by successive piecewise taylor series a most natural direct and efficient way of generating or sweeping out all the optimum designs sequentially in the set is devised the procedure is started with the eigenvalue analysis on the truss defined by the set of all the minimum cross sectional areas neither any further eigenvalue analysis nor application of any optimization technique is required in the proposed procedure it is demonstrated that the proposed method is efficient not only for an ordered set of optimum designs of a large truss associated with the single lowest eigenvector but also for that associated with multiple lowest eigenvectors

improved fct algorithm for shock hydrodynamics the new ydfct algorithm is presented for the numerical solution of hydrodynamic flow problems with steep gradients this algorithm is an explicit finite difference scheme based on the flux corrected transport technique and it is an improvement of the etbfct and the xdfct algorithms the erosion of sharp edges the phase distortion of curved profiles and the terracing effect and velocity oscillations are eliminated or significantly reduced these improvements are obtained by following action of the limiter at edges more detailed linear numerical analysis of the difference scheme and considering the velocity gradient in the diffusion and antidiffusion coefficients properties of the new algorithm are also demonstrated by the solution of three test problems

developability conditions for prestress optimization of a curved surface developability conditions are presented for prestressed curved surfaces to be reduced to plane sheets by relaxing the stresses those conditions are applied to an optimization problem for minimizing the deviation of stresses from the target values two formulations based on the displacements defined by the local and global coordinates of finite elements are presented it is shown that the numbers of constraints by those formulations are same if triangular elements are used and there is an upper bound in the number of the elements in a cutting sheet performances of the two formulations are compared in the numerical examples and the local formulation is shown to lead to more accurate estimation of stresses that are actually generated by connecting and stretching the plane sheets

robust inventory management an optimal control approach we formulate and solve static and dynamic models of inventory management that lie at the intersection of robust optimization and optimal control theory our objective is to minimize cumulative ordering holding and shortage costs over a horizon 0 t where the variable is a nonnegative ordering rate function q t 2 0 t the demand rate function d t is unknown and is only assumed to belong to an uncertainty set d t l2 0 t a 1 t 0td t dt b a d t b t 0 t this set is motivated by the strong law of large numbers for stochastic processes limt 1 t 0td t dt where is the mean drift we analyze a static model where the ordering rate function must be fully specified at time zero and three dynamic variants where re optimizations are allowed during the planning horizon 0 t at prespecified review epochs in the dynamic models at review epoch 0 t the past demand on 0 is observable in the first dynamic model we ignore this information and define a variant of that i

provably near optimal sampling based policies for stochastic inventory control models in this paper we consider two fundamental inventory models the single period newsvendor problem and its multiperiod extension but under the assumption that the explicit demand distributions are not known and that the only information available is a set of independent samples drawn from the true distributions under the assumption that the demand distributions are given explicitly these models are well studied and relatively straightforward to solve however in most real life scenarios the true demand distributions are not available or they are too complex to work with thus a sampling driven algorithmic framework is very attractive both in practice and in theory we shall describe how to compute sampling based policies that is policies that are computed based only on observed samples of the demands without any access to or assumptions on the true demand distributions moreover we establish bounds on the number of samples required to guarantee that with high probability the expected cost of the sampling based policies is arbitrarily close i e with arbitrarily small relative error compared to the expected cost of the optimal policies which have full access to the demand distributions the bounds that we develop are general easy to compute and do not depend at all on the specific demand distributions

sensitivity of optimum solutions of problem parameters solution of the optimum sensitivity problem yields the values of derivatives of the optimal objective function and design variables with respect to those physical quantities which were kept constant as problem parameters during optimization examples of these sensitivity derivatives might include derivatives of cross section al area and structural mass with respect to allowable stress and derivatives of fuel consumed and wing aspect ratio with respect to aircraft range derivation of the sensitivity equations that yield the sensitivity derivatives directly which avoids the costly and inaccurate perturb and reoptimize approach is discussed and solvability of the equations is examined the equations apply to optimum solutions obtained by direct search methods as well as those generated by procedures of the sequential unconstrained minimization technique sumt class applications are discussed for the use of the sensitivity derivatives in extrapolation of the optimal objective function and design variable values for incremented parameters optimization with multiple objectives and decomposition of large optimization problems several aspects of these applications and verification of the sensitivity equations are presented through numerical examples

efficient calculation of optimum design sensitivity two methods for obtaining the sensitivity of an optimized design to changes in problem parameters are presented the first order method uses gradient information to estimate the required sensitivity the second order method uses second derivatives of the design objective and constraint functions to provide a quadratic approximation to the new design which results from changing the specified parameter it is shown that the sensitivity of the optimized design may be discontinuous with respect to the new parameter this discontinuity is accounted for in the present methods these methods are compared to a previous approach based on the kuhn tucker necessary conditions for optimality it is shown that the present methods provide the appropriate sensitivity information in an efficient manner the methods are demonstrated by a structural synthesis example

an adaptive distribution free algorithm for the newsvendor problem with censored demands with applications to inventory and distribution we consider the problem of optimizing inventories for problems where the demand distribution is unknown and where it does not necessarily follow a standard form such as the normal we address problems where the process of deciding the inventory and then realizing the demand occurs repeatedly the only information we use is the amount of inventory left over rather than attempting to estimate the demand distribution we directly estimate the value function using a technique called the concave adaptive value estimation cave algorithm cave constructs a sequence of concave piecewise linear approximations using sample gradients of the recourse function at different points in the domain since it is a sampling based method cave does not require knowledge of the underlying sample distribution the result is a nonlinear approximation that is more responsive than traditional linear stochastic quasi gradient methods and more flexible than analytical techniques that require distribution information in addition we demonstrate near optimal behavior of the cave approximation in experiments involving two different types of stochastic programs the newsvendor stochastic inventory problem and two stage distribution problems

a new optimized fct algorithm for shock wave problems abstract the new xdfct algorithm is presented for the solution of hydrodynamic flow problems with steep gradients this algorithm is an explicit finite difference scheme based on the fluxcorrected transport technique and it is a modification of existing etbfct algorithm the use of different diffusive and antidiffusive fluxes enables us to use twice the time step with similar accuracy this is shown by linear numerical analysis and verified by solution of three test problems

notes on the eigensystem of magnetohydrodynamics the eigenstructure of the equations governing one dimensional ideal magnetohy drodynamics is examined motivated by the wish to exploit it for construction of high resolution computational algorithms the results are given in simple forms that avoid indeterminacy or degeneracy whenever possible the unavoidable indeterminacy near the magnetosonic or triple umbilic state is analysed and shown to cause no difficulty in evaluating a numerical flux function the structure of wave paths close to this singularity is obtained and simple expressions are presented for the structure coefficients that govern wave steepening

critical sets in parametric optimization we deal with one parameter families of optimization problems in finite dimensions the constraints are both of equality and inequality type the concept of a generalized critical point g c point is introduced in particular every local minimum kuhn tucker point and point of fritz john type is a g c point under fairly weak even generic conditions we study the set consisting of all g c points due to the parameter the set is pieced together from one dimensional manifolds the points of can be divided into five characteristic types the subset of nondegenerate critical points first type is open and dense in nondegenerate means strict complementarity nondegeneracy of the corresponding quadratic form and linear independence of the gradients of binding constraints a nondegenerate critical point is completely characterized by means of four indices the change of these indices along is presented finally the kuhn tucker subset of is studied in more detail in particular in connection with the failure of the mangasarian fromowitz constraint qualification

fully distribution free profit maximization the inventory management case we study profit maximization in inventory control problems where demands are unknown neither probabilistic distributions nor sets are available to characterize the unknown demand parameters therefore we adopt an online optimization perspective for our analysis the usual competitive ratio is not well defined for the problems we analyze consequently we introduce a new worst case metric that is suitable we consider two inventory management frameworks 1 perishable products with lost sales and 2 durable products with backlogged demand we consider both finite and infinite planning horizons we design best possible online procurement strategies for all cases

on godunov type methods near low densities abstract when the energy of a flow is largely kinetic many conservative differencing schemes may fail by predicting non physical states with negative density or internal energy we describe as positively conservative the subclass of schemes that by contrast always generate physical solutions from physical data and show that the godunov method is positively conservative it is also shown that no scheme whose interface flux derives from a linearised riemann solution can be positively conservative classes of data that will bring about the failure of such schemes are described however the harten lax van leer hlle scheme is positively conservative under certain conditions on the numerical wavespeeds and this observation allows the linearised schemes to be rescued by modifying the wavespeeds employed

robust solutions of optimization problems affected by uncertain probabilities in this paper we focus on robust linear optimization problems with uncertainty regions defined by divergences for example chi squared hellinger kullback leibler we show how uncertainty regions based on divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector such problems frequently occur in for example optimization problems in inventory control or finance that involve terms containing moments of random variables expected utility etc we show that the robust counterpart of a linear optimization problem with divergence uncertainty is tractable for most of the choices of typically considered in the literature we extend the results to problems that are nonlinear in the optimization variables several applications including an asset pricing example and a numerical multi item newsvendor example illustrate the relevance of the proposed approach this paper was accepted by gerard p cachon optimization

a staggered mesh algorithm using high order godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations the equations of magnetohydrodynamics mhd have been formulated as a hyperbolic system of conservation laws in that form it becomes possible to use higher order godunov schemes for their solution this results in a robust and accurate solution strategy however the magnetic field also satisfies a constraint that requires its divergence to be zero at all times this is a property that cannot be guaranteed in the zone centered discretizations that are favored in godunov schemes without involving a divergence cleaning step in this paper we present a staggered mesh strategy which directly uses the properly upwinded fluxes that are provided by a godunov scheme the process of directly using the upwinded fluxes relies on a duality that exists between the fluxes obtained from a higher order godunov scheme and the electric fields in a plasma by exploiting this duality we have been able to construct a higher order godunov scheme that ensures that the magnetic field remains divergence free up to the computer s round off error we have even presented a variant of the basic algorithm that uses multidimensional features in the flow to design an upwinded strategy that aligns itself with the predominant upwinded direction in the flow we have devised several stringent test problems to show that the scheme works robustly and accurately in all situations in doing so we have shown that a scheme that involves a collocation of magnetic field variables that is different from the one traditionally favored in the design of higher order godunov schemes can nevertheless offer the same robust and accurate performance of higher order godunov schemes provided the properly upwinded fluxes from the godunov methodology are used in the scheme s construction

from cost sharing mechanisms to online selection problems we consider a general class of online optimization problems called online selection problems where customers arrive sequentially and one has to decide upon arrival whether to accept or reject each customer if a customer is rejected then a rejection cost is incurred the accepted customers are served with minimum possible cost either online or after all customers have arrived the goal is to minimize the total production costs for the accepted customers plus the rejection costs for the rejected customers these selection problems are related to online variants of offline prize collecting combinatorial optimization problems that have been widely studied in the computer science literature in this paper we provide a general framework to develop online algorithms for this class of selection problems in essence the algorithmic framework leverages any cost sharing mechanism with certain properties into a poly logarithmic competitive online algorithm for the respective problem the competitive ratios ar

a direct application of higher order parametric programming techniques to structural optimization computational methods based on a sequence of parametric programming problems are presented for solving constrained optimization problems cop without any parameter an auxiliary parametric programming problem appp is formulated in order to solve cop the procedure is started with an arbitrary initial solution which is the trivial solution of appp corresponding to the initial value of the parameter then the optimal solution for the final value of the parameter which is the optimal solution of cop is estimated by taylor s expansion with respect to the parameter where higher order terms are incorporated it is shown that the incorporation of the higher order terms indeed leads to a faster convergence of the solution as an extension of the method a general algorithm is presented for optimum design problems with state variable constraints which are implicit functions of the design variables logarithmic penalty functions are incorporated and the weight coefficients for the penalty terms are updated continuously the derivatives of the state variables with respect to the parameter and their sensitivity coefficients are expressed explicitly in terms of those of the design variables finally a method of simultaneous analysis and optimization is developed for trusses with geometrical non linearity

flux corrected transport techniques for multidimensional compressible magnetohydrodynamics a prescription is given for conservatively integrating generalized hydromagnetic equations using flux corrected transport fct techniques by placing the magnetic field components at the interface locations of the finite difference grid the field is kept divergence free to within machine roundoff error the use of fct techniques allows an integration scheme of high accuracy to be employed while the numerical ripples associated with large dispersion errors are avoided the method is particularly well suited for problems involving magnetohydrodynamic shocks and other discontinuities

regret in the newsvendor model with partial information traditional stochastic inventory models assume full knowledge of the demand probability distribution however in practice it is often difficult to completely characterize the demand distribution especially in fast changing markets in this paper we study the newsvendor problem with partial information about the demand distribution e g mean variance symmetry unimodality in particular we derive the order quantities that minimize the newsvendor s maximum regret of not acting optimally most of our solutions are tractable which makes them attractive for practical application our analysis also generates insights into the choice of the demand distribution as an input to the newsvendor model in particular the distributions that maximize the entropy perform well under the regret criterion our approach can be extended to a variety of problems that require a robust but not conservative solution

the behavior of flux difference splitting schemes near slowly moving shock waves abstract an investigation of the behavior of shock capturing schemes which compute the numerical flux from a solution of riemann s problem is performed the schemes of godunov roe and osher are examined for a one dimensional model problem consisting of a nearly stationary shock both scalar and systems of equations are examined it is found that for slow shocks there is a significant error generated when solving systems of equations while the scalar results are well behaved this error consists of a long wavelength noise in the downstream running wave families that is not effectively damped by the dissipation of the scheme the source of this error is shown and the implications for the performance of these schemes are considered this error may contribute to the slow convergence to steady state reported by many researchers

shape stress trade off design of membrane structures for specified sequence of boundary shapes a new method is presented for parametrically generating optimal shapes and stresses of a membrane structure supported by a frame the problem considered here is a so called trade off design problem where the weighted sum of the deviations of the initial stress and the shape from the desired distribution is to be minimized the membrane is discretized by using the finite element method and optimal shapes are expanded with respect to a parameter defining the shape of the boundary frame an approximate method is presented without exact calculation of the hessian of the stresses with respect to the nodal coordinates the explicit developability conditions derived by the authors are used to guarantee the curved surface to be reduced to a set of plane cutting patterns after removing the pretensioning force in the examples trade off designs are found for an hp type membrane structure and the efficiency of the proposed method is discussed

central finite volume schemes with constrained transport divergence treatment for three dimensional ideal mhd we present three dimensional central finite volume methods for solving systems of hyperbolic equations based on the lax friedrichs and nessyahu tadmor one dimensional central finite difference schemes the numerical methods we propose involve an original and a staggered grid in order to avoid the resolution of the riemann problems at the cell interfaces the cells of the original grid are cartesian cubes with faces parallel to the axes while those of the staggered grid are either cartesian or diamond shaped we apply these methods and solve some ideal magnetohydrodynamics problems to satisfy the solenoidal property of the magnetic field in the numerical solution we present an adaptation of evans and hawley s constrained transport method for central schemes which we call ctcs the ctcs method is easy to implement it deals directly with the computed solution and does not require any additional staggering for the magnetic field components furthermore it preserves the second order accuracy of the base scheme even without the application of the ctcs procedure our numerical base schemes do not break down and may even in some cases deliver reasonable results the diamond dual cell scheme has a slight advantage for shocks and contact discontinuities our numerical results are in good agreement with corresponding results appearing in the recent literature

comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems two versions of flux corrected transport and two versions of total variation diminishing schemes are tested for several one and two dimensional hydrodynamic and magnetohydrodynamic problems two of the schemes ydfct and tvdlf are tested extensively for the first time the results give an insight into the limitations of the methods their relative strengths and weaknesses some subtle points of the algorithms and the effects of selecting different options for certain methods are emphasised

well balanced unstaggered central schemes for one and two dimensional shallow water equation systems abstract we propose a new well balanced unstaggered central finite volume scheme for hyperbolic balance laws with geometrical source terms in particular we construct a new one and two dimensional finite volume method for the numerical solution of shallow water equations on flat variable bottom topographies the proposed scheme evolves a non oscillatory numerical solution on a single grid avoids the time consuming process of solving riemann problems arising at the cell interfaces and is second order accurate both in space and time furthermore the numerical scheme follows a well balanced discretization that first discretizes the geometrical source term according to the discretization of the flux terms and then mimics the surface gradient method and discretizes the water height according to the discretization of the water level the resulting scheme exactly satisfies the c property at the discrete level the proposed scheme is then applied and classical one and two dimensional shallow water equation problems with flat or variable bottom topographies are successfully solved the obtained numerical results are in good agreement with corresponding ones appearing in the recent literature thus confirming the potential and efficiency of the proposed method

an adaptive algorithm for finding the optimal base stock policy in lost sales inventory systems with censored demand we consider a periodic review single location single product inventory system with lost sales and positive replenishment lead times it is well known that the optimal policy does not possess a simple structure motivated by recent results showing that base stock policies perform well in these systems we study the problem of finding the best base stock policy in such a system in contrast to the classical inventory literature we assume that the manager does not know the demand distribution a priori but must make the replenishment decision in each period based only on the past sales censored demand data we develop a nonparametric adaptive algorithm that generates a sequence of order up to levels whose running average of the inventory holding and lost sales penalty cost converges to the cost of the optimal base stock policy and we establish the cubic root convergence rate of the algorithm our analysis is based on recent advances in stochastic online convex optimization and on the uniform ergodicity of markov chains associated with bases stock policies

closed form solutions for robust inventory management we propose and analyze robust optimization models of an inventory management problem where cumulative purchase inventory and shortage costs over n periods are minimized for correlated nonidentically distributed demand we assume that the means and covariance matrix of stochastic demand are known the distributions are not needed we derive closed form ordering quantities for both symmetric and asymmetric uncertainty sets under capacitated inventory constraints in both static and dynamic settings the behaviors of our robust strategies differ qualitatively depending on the symmetry of the uncertainty set for instance considering our simplest static problem 1 if the uncertainty set is symmetric then there is positive ordering in all periods whereas 2 if the set is asymmetric then there is a set of periods in the middle of the planning horizon with zero orders we also link the symmetry of the uncertainty set to the symmetry of the demand distribution finally we present encouraging computati

limiting and divergence cleaning for continuous finite element discretizations of the mhd equations abstract this work introduces a new type of constrained algebraic stabilization for continuous piecewise linear finite element approximations to the equations of ideal magnetohydrodynamics mhd at the first step of the proposed flux corrected transport fct algorithm the galerkin element matrices are modified by adding graph viscosity proportional to the fastest characteristic wave speed at the second step limited antidiffusive corrections are applied and divergence cleaning is performed for the magnetic field the limiting procedure developed for this stage is designed to enforce local maximum principles as well as positivity preservation for the density and thermodynamic pressure additionally it adjusts the magnetic field in a way which penalizes divergence errors without violating conservation laws or positivity constraints numerical studies for 2d test problems are performed to demonstrate the ability of the proposed algorithms to accomplish this task in applications to ideal mhd benchmarks

sensitivity analysis of discrete structural systems methods for calculating sensitivity derivatives for discrete structural systems are surveyed primarily covering literature published during the past two decades methods are described for calculating derivatives of static displacements and stresses eigenvalues and eigenvectors transient structural response and derivatives of optimum structural designs with respect to problem parameters the survey is focused on publications developed in nonstructural fields such as electronics controls and physical chemistry which are directly applicable to structural problems most notable among the nonstructural based methods are the adjoint variable technique from control theory and the green s function and fast methods from physical chemistry

scalar hyperbolic pde simulations and coupling strategies we report on grid adaptive multi dimensional simulations for hyperbolic pdes with a deliberate focus on the analytically tractable scalar case motivated by recent efforts towards multi physics simulation strategies we investigate a variety of coupling strategies for numerically solving hyperbolic partial differential equations pdes we use adaptive mesh refinement in combination with shock capturing spatio temporal discretizations and first present accuracy and validation tests on both smooth and shock dominated evolutions to investigate the feasibility of coupling means for multi physics simulations we then introduce new reference tests where spatially different flux prescriptions require coupling strategies across the domains where local advection burgers or nonconvex behavior is imposed for these nonlinear single scalar equations we can illustrate and analytically explain the evolutions obtained when handling cases where fluxes differ in spatially non overlapping regions we discuss both conservative and non conservative ways of coupling across the region boundaries when coupling scalar conservation laws where the characteristic speeds change discontinuously across the regional boundaries these two strategies yield differing but mathematically sound solution behaviors their relevance for multi physics simulations where one couples systems of hyperbolic pdes is discussed

a high resolution tvd finite volume scheme for the euler equations in conservation form abstract a finite volume numerical algorithm using nonuniformly distributed skewed quadrilateral cells is developed to solve the euler equations in conservation form fluxes across the cell boundaries are computed using the total variation diminishing tvd methodology developed by harten proof of the tvd property for nonuniform grid systems and a truncation error analysis are presented along with a discussion of the treatment of boundary conditions four test cases are given to examine the efficacy of the present scheme using a system of skewed and nonuniform cells the excellent agreement of the numerical results with exact solutions and carefully designed experiments demonstrates the ability of the present scheme to accurately resolve complicated wave developments and interactions using highly nonuniform multiblock zonal cell distributions

central finite volume methods with constrained transport divergence treatment for ideal mhd two and three dimensional finite volume extensions of the lax friedrichs lf and nessyahu tadmor one dimensional difference schemes were previously presented and successfully applied to several problems for nonlinear hyperbolic systems and in particular to typical test cases for both inviscid and viscous compressible flows these central schemes by pass the resolution at the cell interfaces of the riemann problems thanks to the use of the staggered lf scheme which serves as the base scheme on which high order finite volume methods can be constructed using van leer s muscl type limited reconstruction principle for this purpose two dual grids are used at alternate time steps these methods are extended here to several problems in one and multi dimensional ideal compressible magnetohydrodynamics using a modified version of the first author s central methods with oblique diamond shaped dual cells in two dimensions the system has eight equations and solving the corresponding riemann problem is an elaborate and time consuming process central methods lead to significant computing time reductions and the numerical experiments presented here suggest the accuracy is quite satisfactory in order to satisfy the physical constraint b 0 we have constructed a strategy ctcs inspired from the constrained transport method of evans and hawley the validity of our base scheme and our ctcs approach is clearly confirmed by the results

a nonparametric asymptotic analysis of inventory planning with censored demand we study stochastic inventory planning with lost sales and instantaneous replenishment where contrary to the classical inventory theory knowledge of the demand distribution is not available furthermore we observe only the sales quantity in each period and lost sales are unobservable that is demand data are censored the manager must make an ordering decision in each period based only on historical sales data excess inventory is either perishable or carried over to the next period in this setting we propose nonparametric adaptive policies that generate ordering decisions over time we show that the t period average expected cost of our policy differs from the benchmark newsvendor cost the minimum expected cost that would have incurred if the manager had known the underlying demand distribution by at most o 1 t0 5

an fct finite element scheme for ideal mhd equations in 1d and 2d abstract this paper presents an implicit finite element fe scheme for solving the equations of ideal magnetohydrodynamics in 1d and 2d the continuous galerkin approximation is constrained using a flux corrected transport fct algorithm the underlying low order scheme is constructed using a rusanov type artificial viscosity operator based on scalar dissipation proportional to the fast wave speed the accuracy of the low order solution can be improved using a shock detector which makes it possible to prelimit the added viscosity in a monotonicity preserving iterative manner at the fct correction step the changes of conserved quantities are limited in a way which guarantees positivity preservation for the density and thermal pressure divergence free magnetic fields are extracted using projections of the fct predictor into staggered finite element spaces forming exact sequences in the 2d case the magnetic field is projected into the space of raviart thomas finite elements numerical studies for standard test problems are performed to verify the ability of the proposed algorithms to enforce relevant constraints in applications to ideal mhd flows