experiments with implicit upwind methods for the euler equations abstract a number of implicit integration schemes for the one dimensional euler equations with conservative upwind spatial differencing are tested on a problem of steady discontinuous flow fastest convergence quadratic for the first order backward euler scheme is obtained with the upwind switching provided by van leer s differentiable split fluxes which easily linearize in time with roe s nondifferentiable split flux differences the iterations may get trapped in a limit cycle this also happens in a second order scheme with split fluxes if the matrix coefficients arising in the implicit time linearization are not properly centered in space the use of second order terms computed from split fluxes degrades the accuracy of the solution especially if these are subjected to a limiter for the sake of monotonicity preservation second order terms computed from the characteristic variables perform best

an interactive fuzzy satisficing method for multiobjective 0 1 programming problems with fuzzy numbers through genetic algorithms with double strings abstract in this paper by considering the experts vague or fuzzy understanding of the nature of the parameters in the problem formulation process multiobjective 0 1 programming problems involving fuzzy numbers are formulated using the a level sets of fuzzy numbers the corresponding nonfuzzy programming problem is introduced the fuzzy goals of the decision maker dm for the objective functions are quantified by eliciting the corresponding linear membership functions through the introduction of an extended pareto optimality concept if the dm specifies the degree and the reference membership values the corresponding extended pareto optimal solution can be obtained by solving the augmented minimax problems through genetic algorithms with double strings then an interactive fuzzy satisficing method for deriving a satisficing solution for the dm efficiently from an extended pareto optimal solution set is presented an illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method

accurate three dimensional lid driven cavity flow a chebyshev collocation method in space is introduced which allows an accurate calculation of three dimensional lid driven cavity flows the time integration is carried out by an adams bashforth backward euler scheme the accuracy of the method relies on the representation of the solution as a superposition of stationary local asymptotic solutions and a residual flow field this way the most severe discontinuities in the boundary conditions which arise along the lines where moving and stationary walls meet are taken care of analytically and thus do not spoil the numerical part of the solution calculations are carried out for no slip boundary conditions at the cavity end walls as well as for periodic end wall conditions in general the spatial accuracy is better than fifth order for rigid end wall conditions the accuracy is reduced near the end walls to o n 3 2 but recovers in the bulk tabulated data are provided for the most interesting flow properties

genetic algorithms with double strings for 0 1 programming problems abstract in this paper genetic algorithms with double strings for 0 1 knapsack problems are first revisited together with some modifications and computational experiments then the genetic algorithms with double strings for 0 1 knapsack problems are extended to deal with more general 0 1 programming problems involving both positive and negative coefficients in the constraints especially new decoding algorithms for double strings using reference solutions both without and with the reference solution updating procedure are proposed so that each of individuals is decoded to the corresponding feasible solution for the general 0 1 programming problems the efficiency and effectiveness of the proposed methods are investigated by comparing them with a branch and bound method with respect to the accuracy of an approximate solution and the processing time through a number of numerical experiments

discontinuous skeletal gradient discretisation methods on polytopal meshes in this work we develop arbitrary order discontinuous skeletal gradient discretisations dsgd on general polytopal meshes discontinuous skeletal refers to the fact that the globally coupled unknowns are broken polynomial on the mesh skeleton the key ingredient is a high order gradient reconstruction composed of two terms i a consistent contribution obtained mimicking an integration by parts formula inside each element and ii a stabilising term for which sufficient design conditions are provided an example of stabilisation that satisfies the design conditions is proposed based on a local lifting of high order residuals on a raviart thomas nedelec subspace we prove that the novel dsgds satisfy coercivity consistency limit conformity and compactness requirements that ensure convergence for a variety of elliptic and parabolic problems links with hybrid high order non conforming mimetic finite difference and non conforming virtual element methods are also studied numerical examples complete the exposition

on the absolute stability of multivariable non linear systems using a block tridiagonal state space representation this paper proposes a block tridiagonal state space representation to establish alternative algebraic sufficient conditions for the absolute stability of multivariable non linear systems the systems considered are described by a transfer function matrix given by a left matrix fraction description with multiple non linear feedback elements satisfying the positive infinite sector condition new matrix algorithms are presented in order to construct the block tridiagonal representation of the system the relationship of these absolute stability conditions to passivity properties is discussed

an implicit high order hybridizable discontinuous galerkin method for the incompressible navier stokes equations we present an implicit high order hybridizable discontinuous galerkin method for the steady state and time dependent incompressible navier stokes equations the method is devised by using the discontinuous galerkin discretization for a velocity gradient pressure velocity formulation of the incompressible navier stokes equations with a special choice of the numerical traces the method possesses several unique features which distinguish itself from other discontinuous galerkin methods first it reduces the globally coupled unknowns to the approximate trace of the velocity and the mean of the pressure on element boundaries thereby leading to a significant reduction in the degrees of freedom moreover if the augmented lagrangian method is used to solve the linearized system the globally coupled unknowns become the approximate trace of the velocity only second it provides for smooth viscous dominated problems approximations of the velocity pressure and velocity gradient which converge with the optimal order of k 1 in the l2 norm when polynomials of degree k 0 are used for all components of the approximate solution and third it displays superconvergence properties that allow us to use the above mentioned optimal convergence properties to define an element by element postprocessing scheme to compute a new and better approximate velocity indeed this new approximation is exactly divergence free h div conforming and converges with order k 2 for k 1 and with order 1 for k 0 in the l2 norm moreover a novel and systematic way is proposed for imposing boundary conditions for the stress viscous stress vorticity and pressure which are not naturally associated with the weak formulation of the method this can be done on different parts of the boundary and does not result in the degradation of the optimal order of convergence properties of the method extensive numerical results are presented to demonstrate the convergence and accuracy properties of the method for a wide range of reynolds numbers and for various polynomial degrees

a new staggered dg method for the brinkman problem robust in the darcy and stokes limits abstract in this paper we propose a novel staggered discontinuous galerkin method for the brinkman problem on general polygonal meshes the proposed method is robust in the stokes and darcy limits in addition hanging nodes can be automatically incorporated in the construction of the method which are desirable features in practical applications there are three unknowns involved in our formulation namely velocity gradient velocity and pressure unlike the original staggered dg formulation proposed for the stokes equations in kim et al 2013 we relax the tangential continuity of velocity and enforce different staggered continuity properties for the three unknowns which is tailored to yield an optimal l 2 error estimates for velocity gradient velocity and pressure independent of the viscosity coefficient moreover by choosing suitable projection superconvergence can be proved for l 2 error of velocity finally several numerical results illustrating the good performances of the proposed method and confirming the theoretical findings are presented

a staggered semi implicit discontinuous galerkin method for the two dimensional incompressible navier stokes equations in this paper we propose a new spatially high order accurate semi implicit discontinuous galerkin dg method for the solution of the two dimensional incompressible navier stokes equations on staggered unstructured curved meshes while the discrete pressure is defined on the primal grid the discrete velocity vector field is defined on an edge based dual grid the flexibility of high order dg methods on curved unstructured meshes allows to discretize even complex physical domains on rather coarse grids formal substitution of the discrete momentum equation into the discrete continuity equation yields one sparse linear equation system with four non zero blocks per element for only one scalar unknown namely the pressure the method is computationally efficient since the resulting system is not only very sparse but also symmetric and positive definite for appropriate boundary conditions furthermore all the volume and surface integrals needed by the scheme presented in this paper depend only on the geometry and the polynomial degree of the basis and test functions and can therefore be precomputed and stored in a preprocessor stage which leads to savings in terms of computational effort for the time evolution part in this way also the extension to a fully curved isoparametric approach becomes natural and affects only the preprocessing step the method is validated for polynomial degrees up to p 3 by solving some typical numerical test problems and comparing the numerical results with available analytical solutions or other numerical and experimental reference data

a hybrid high order method for the incompressible navier stokes problem robust for large irrotational body forces abstract we develop a novel hybrid high order method for the incompressible navier stokes problem robust for large irrotational body forces the key ingredients of the method are discrete versions of the body force and convective contributions in the momentum equation formulated in terms of a globally divergence free velocity reconstruction two key properties are mimicked at the discrete level namely the invariance of the velocity with respect to irrotational body forces and the non dissipativity of the convective term a full convergence analysis is carried out showing optimal orders of convergence under a smallness condition involving only the solenoidal part of the body force the performance of the method is illustrated by a complete panel of numerical tests including comparisons that highlight the benefits with respect to more standard formulations

a pressure correction scheme for convection dominated incompressible flows with discontinuous velocity and continuous pressure in this work we present a pressure correction scheme for the incompressible navier stokes equations combining a discontinuous galerkin approximation for the velocity and a standard continuous galerkin approximation for the pressure the main interest of pressure correction algorithms is the reduced computational cost compared to monolithic strategies in this work we show how a proper discretization of the decoupled momentum equation can render this method suitable to simulate high reynolds regimes the proposed spatial velocity pressure approximation is lbb stable for equal polynomial orders and it allows adaptive p refinement for velocity and global p refinement for pressure the method is validated against a large set of classical two and three dimensional test cases covering a wide range of reynolds numbers in which it proves effective both in terms of accuracy and computational cost

a sufficient condition for the stability of matrix polynomials a sufficient condition is presented for the stability of the matrix polynomials based on algebraic properties of the matrix coefficients the stability condition is derived from the lyapunov theory by a multivariable feedback system that is associated to the matrix polynomial illustrative examples are given a block schwarz form related to the matrix polynomial is obtained directly from the given realization algorithm

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

an arbitrary order scheme on generic meshes for miscible displacements in porous media we design analyze and implement an arbitrary order scheme applicable to generic meshes for a coupled elliptic parabolic pde system describing miscible displacement in porous media the discretiza

fuzzy programming for multiobjective 0 1 programming problems through revised genetic algorithms abstract recently genetic algorithms gas a new learning paradigm that models a natural evolution mechanism have received a great deal of attention regarding their potential as optimization techniques for solving combinatorial optimization problems in this paper we focus on multiobjective 0 1 programming problems as a generalization of the traditional single objective ones by considering the imprecise nature of human judgements we assume that the decision maker may have fuzzy goal for each of the objective functions after eliciting the linear membership functions through the interaction with the decision maker we adopt the fuzzy decision of bellman and zadeh or minimum operator for combining them in order to investigate the applicability of the conventional gas for the solution of the formulated problems a lot of numerical simulations are performed by assuming several genetic operators then instead of using the penalty function for treating the constraints we propose three types of revised gas which generate only feasible solutions illustrative numerical examples demonstrate both feasibility and efficiency of the proposed methods

operation planning of district heating and cooling plants through genetic algorithms for nonlinear 0 1 programming abstract in recent years the operation planning of district heating and cooling plants has been arousing interest as a result of development of cooling load prediction methods for district heating and cooling systems in this paper we formulate an operation planning problem of a district heating and cooling plant as a nonlinear 0 1 programming problem realizing that there does not exist an efficient exact solution method and the problem involves hundreds of variables we propose an approximate solution method using genetic algorithms for the formulated nonlinear 0 1 programming problem furthermore we investigate the feasibility and effectiveness of the proposed method for an operation planning problem of an actual district heating and cooling plant

the nonconforming virtual element method for the stokes equations we present the nonconforming virtual element method vem for the numerical approximation of velocity and pressure in the steady stokes problem the pressure is approximated using discontinuous piecewise polynomials while each component of the velocity is approximated using the nonconforming virtual element space on each mesh element the local virtual space contains the space of polynomials of up to a given degree plus suitable nonpolynomial functions the virtual element functions are implicitly defined as the solution of local poisson problems with polynomial neumann boundary conditions as typical in vem approaches the explicit evaluation of the non polynomial functions is not required this approach makes it possible to construct nonconforming virtual spaces for any polynomial degree regardless of the parity for two and three dimensional problems and for meshes with very general polygonal and polyhedral elements we show that the nonconforming vem is inf sup stable and establish optimal a pri

a discontinuous skeletal method for the viscosity dependent stokes problem we devise and analyze arbitrary order nonconforming methods for the discretization of the viscosity dependent stokes equations on simplicial meshes we keep track explicitly of the viscosity and aim at pressure robust schemes that can deal with the practically relevant case of body forces with large curl free part in a way that the discrete velocity error is not spoiled by large pressures the method is inspired from the recent hybrid high order hho methods for linear elasticity after elimination of the auxiliary variables by static condensation the linear system to be solved involves only discrete face based velocities which are polynomials of degree k ge 0 and cell wise constant pressures our main result is a pressure independent energy error estimate on the velocity of order k 1 the main ingredient to achieve pressure independence is the use of a divergence preserving velocity reconstruction operator in the discretization of the body forces we also prove an l 2 pressure estimate of order k 1 and an l 2 velocity estimate of order k 2 the latter under elliptic regularity the local mass and momentum conservation properties of the discretization are also established finally two and three dimensional numerical results are presented to support the analysis

hybridizable discontinuous galerkin projection methods for navier stokes and boussinesq equations schemes for the incompressible navier stokes and boussinesq equations are formulated and derived combining the novel hybridizable discontinuous galerkin hdg method a projection method and implicit explicit runge kutta imex rk time integration schemes we employ an incremental pressure correction and develop the corresponding hdg finite element discretization including consistent edge space fluxes for the velocity predictor and pressure correction we then derive the proper forms of the element local and hdg edge space final corrections for both velocity and pressure including the hdg rotational correction we also find and explain a consistency relation between the hdg stability parameters of the pressure correction and velocity predictor we discuss and illustrate the effects of the time splitting error we then detail how to incorporate the hdg projection method time split within standard imex rk time stepping schemes our high order hdg projection schemes are implemented for arbitrary mixed element unstructured grids with both straight sided and curved meshes in particular we provide a quadrature free integration method for a nodal basis that is consistent with the hdg method to prevent numerical oscillations we develop a selective nodal limiting approach its applications show that it can stabilize high order schemes while retaining high order accuracy in regions where the solution is sufficiently smooth we perform spatial and temporal convergence studies to evaluate the properties of our integration and selective limiting schemes and to verify that our solvers are properly formulated and implemented to complete these studies and to illustrate a range of properties for our new schemes we employ an unsteady tracer advection benchmark a manufactured solution for the steady diffusion and stokes equations and a standard lock exchange boussinesq problem

virtual elements for the navier stokes problem on polygonal meshes a family of virtual element methods for the two dimensional navier stokes equations is proposed and analyzed the schemes provide a discrete velocity field which is pointwise divergence free a ri

staggered discontinuous galerkin methods for the helmholtz equation with large wave number abstract in this paper we investigate staggered discontinuous galerkin method for the helmholtz equation with large wave number on general polygonal meshes the method is highly flexible by allowing rough grids such as the trapezoidal grids and highly distorted grids and at the same time is numerical flux free furthermore it allows hanging nodes which can be simply treated as additional vertices by exploiting a modified duality argument the stability and convergence can be proved under the condition that h c 0 1 1 m 1 where m is the polynomial order is the wave number h is the mesh size and c 0 is a positive constant independent of h error estimates for both the scalar and vector variables in l 2 norm are established several numerical experiments are tested to verify our theoretical results and to present the capability of our method for capturing singular solutions

a nonconforming high order method for the biot problem on general meshes in this work we introduce a novel algorithm for the biot problem based on a hybrid high order discretization of the mechanics and a symmetric weighted interior penalty discretization of the flow the method has several assets including in particular the support of general polyhedral meshes and arbitrary space approximation order our analysis delivers stability and error estimates that hold also when the specific storage coefficient vanishes and shows that the constants have only a mild dependence on the heterogeneity of the permeability coefficient numerical tests demonstrating the performance of the method are provided

a discontinuous skeletal method for advection diffusion reaction on general meshes we design and analyze an approximation method for advection diffusion reaction equa tions where the generalized degrees of freedom are polynomials of order k 0 at mesh faces the method hinges on local discrete reconstruction operators for the diffusive and advective derivatives and a weak enforcement of boundary conditions fairly general meshes with poly topal and nonmatching cells are supported arbitrary polynomial orders can be considered including the case k 0 which is closely related to mimetic finite difference mixed hybrid finite volume methods the error analysis covers the full range of peclet numbers including the delicate case of local degeneracy where diffusion vanishes on a strict subset of the domain computational costs remain moderate since the use of face unknowns leads to a compact stencil with reduced communications numerical results are presented

a discontinuous galerkin method with nonoverlapping domain decomposition for the stokes and navier stokes problems a family of discontinuous galerkin finite element methods is formulated and analyzed for stokes and navier stokes problems an inf sup condition is established as well as optimal energy estimates for the velocity and l 2 estimates for the pressure in addition it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces

analysis of an sdg method for the incompressible navier stokes equations in this paper we analyze a staggered discontinuous galerkin sdg method for the incompressible navier stokes equations the method is based on a novel splitting of the nonlinear convection term and results in a skew symmetric discretization of it as a result the sdg discretization has a better conservation property and numerical stability property the aim of this paper is to develop a mathematical theory for this method in particular we will show that the sdg method is well posed and has an optimal rate of convergence a superconvergence result will also be shown

a hybrid high order method for the incompressible navier stokes equations based on temam s device abstract in this work we propose a novel hybrid high order method for the incompressible navier stokes equations based on a formulation of the convective term including temam s device for stability the proposed method has several advantageous features it supports arbitrary approximation orders on general meshes including polyhedral elements and non matching interfaces it is inf sup stable it is locally conservative it supports both the weak and strong enforcement of velocity boundary conditions it is amenable to efficient computer implementations where a large subset of the unknowns is eliminated by solving local problems inside each element particular care is devoted to the design of the convective trilinear form which mimicks at the discrete level the non dissipation property of the continuous one the possibility to add a convective stabilisation term is also contemplated and a formulation covering various classical options is discussed the proposed method is theoretically analysed and an energy error estimate in h k 1 with h denoting the meshsize is proved under the usual data smallness assumption a thorough numerical validation on two and three dimensional test cases is provided both to confirm the theoretical convergence rates and to assess the method in more physical configurations including in particular the well known two and three dimensional lid driven cavity problems

a hybrid high order locking free method for linear elasticity on general meshes abstract we devise an arbitrary order locking free method for linear elasticity the method relies on a pure displacement primal formulation and leads to a symmetric positive definite system matrix with compact stencil the degrees of freedom are vector valued polynomials of arbitrary order k 1 on the mesh faces so that in three space dimensions the lowest order scheme only requires 9 degrees of freedom per mesh face the method can be deployed on general polyhedral meshes the key idea is to reconstruct the symmetric gradient and divergence inside each mesh cell in terms of the degrees of freedom by solving inexpensive local problems the discrete problem is assembled cell wise using these operators and a high order stabilization bilinear form locking free error estimates are derived for the energy norm and for the l 2 norm of the displacement with optimal convergence rates of order k 1 and k 2 respectively for smooth solutions on general meshes the theoretical results are confirmed numerically and the cpu cost is evaluated on both standard and polygonal meshes

a priori and a posteriori error analysis of a mixed scheme for the brinkman problem this paper deals with the analysis of new mixed finite element methods for the brinkman equations formulated in terms of velocity vorticity and pressure employing the babuska brezzi theory it is proved that the resulting continuous and discrete variational formulations are well posed in particular we show that raviart thomas elements of order k ge 0 k 0 for the approximation of the velocity field piecewise continuous polynomials of degree k 1 k 1 for the vorticity and piecewise polynomials of degree k for the pressure yield unique solvability of the discrete problem on the other hand we also show that families of finite elements based on brezzi douglas marini elements of order k 1 k 1 for the approximation of velocity piecewise continuous polynomials of degree k 2 k 2 for the vorticity and piecewise polynomials of degree k for the pressure ensure the well posedness of the associated galerkin scheme we note that these families provide exactly divergence free approximations of the velocity field we establish a priori error estimates in the natural norms with constants independent of the viscosity and we carry out the reliability and efficiency analysis of a residual based a posteriori error estimator finally we report several numerical experiments illustrating the behaviour of the proposed schemes and confirming our theoretical results on unstructured meshes additional examples of cases not covered by our theory are also presented

transformations of a class of multivariable control systems to block companion forms similarity block transformations are developed to transform a class of linear time invariant mimo state equations in arbitrary coordinates into block companion forms so that the classical lines of thought for siso systems can be extended to mimo systems

an artificial compressibility flux for the discontinuous galerkin solution of the incompressible navier stokes equations discontinuous galerkin dg methods have proved to be well suited for the construction of robust high order numerical schemes on unstructured and possibly nonconforming grids for a variety of problems their application to the incompressible navier stokes ins equations has also been recently considered although the subject is far from being fully explored in this work we propose a new approach for the dg numerical solution of the ins equations written in conservation form the inviscid numerical fluxes both in the continuity and in the momentum equation are computed using the values of velocity and pressure provided by the exact solution of the riemann problem associated with a local artificial compressibility perturbation of the equations unlike in most of the existing methods artificial compressibility is here introduced only at the interface flux level therefore resulting in a consistent discretization of the ins equations irrespectively of the amount of artificial compressibility introduced the discretization of the viscous term follows the well established dg scheme named br2 the performance and the accuracy of the method are demonstrated by computing the kovasznay flow and the two dimensional lid driven cavity flow for a wide range of reynolds numbers and for various degrees of polynomial approximation

a locally conservative ldg method for the incompressible navier stokes equations in this paper a new local discontinuous galerkin method for the incompressible stationary navier stokes equations is proposed and analyzed four important features render this method unique its stability its local conservativity its high order accuracy and the exact satisfaction of the incompressibility constraint although the method uses completely discontinuous approximations a globally divergence free approximate velocity in h div is obtained by simple element by element post processing optimal error estimates are proven and an iterative procedure used to compute the approximate solution is shown to converge this procedure is nothing but a discrete version of the classical fixed point iteration used to obtain existence and uniqueness of solutions to the incompressible navier stokes equations by solving a sequence of oseen problems numerical results are shown which verify the theoretical rates of convergence they also confirm the independence of the number of fixed point iterations with respect to the discretization parameters finally they show that the method works well for a wide range of reynolds numbers

a high order mimetic method on unstructured polyhedral meshes for the diffusion equation abstract we present a new family of mimetic finite difference schemes for solving elliptic partial differential equations in the primal form on unstructured polyhedral meshes these mimetic discretizations are built to satisfy local consistency and stability conditions the consistency condition is an exactness property i e the mimetic schemes are exact when the solution is a polynomial of an assigned degree the stability condition ensures the well posedness of the method the degrees of freedom are the solution moments on mesh faces and inside mesh cells higher order schemes are built using higher order moments the developed schemes are verified numerically on diffusion problems with constant and spatially variable possibly discontinuous tensorial coefficients

a hybrid high order discretisation of the brinkman problem robust in the darcy and stokes limits abstract in this work we develop and analyse a novel hybrid high order discretisation of the brinkman problem the method hinges on hybrid discrete velocity unknowns at faces and elements and on discontinuous pressures based on the discrete unknowns we reconstruct inside each element a stokes velocity one degree higher than face unknowns and a darcy velocity in the raviart thomas nedelec space these reconstructed velocities are respectively used to formulate the discrete versions of the stokes and darcy terms in the momentum equation along with suitably designed penalty contributions the proposed construction is tailored to yield optimal error estimates that are robust throughout the entire spectrum of local stokes or darcy dominated regimes as identified by a dimensionless number which can be interpreted as a friction coefficient the singular limit corresponding to the darcy equation is also fully supported by the method numerical examples corroborate the theoretical results this paper also contains two contributions whose interest goes beyond the specific method and application treated in this work an investigation of the dependence of the constant in the second korn inequality on star shaped domains and its application to the study of the approximation properties of the strain projector in general sobolev seminorms

discrete functional analysis tools for discontinuous galerkin methods with application to the incompressible navier stokes equations two discrete functional analysis tools are established for spaces of piecewise polynomial functions on general meshes i a discrete counterpart of the continuous sobolev embeddings in both hilbertian and non hilbertian settings ii a compactness result for bounded sequences in a suitable discontinuous galerkin norm together with a weak convergence property for some discrete gradients the proofs rely on techniques inspired by the finite volume literature which differ from those commonly used in finite element analysis the discrete functional analysis tools are used to prove the convergence of discontinuous galerkin approximations of the steady incompressible navier stokes equations two discrete convective trilinear forms are proposed a non conservative one relying on temam s device to control the kinetic energy balance and a conservative one based on a nonstandard modification of the pressure

an interactive fuzzy satisficing method for general multiobjective 0 1 programming problems through genetic algorithms with double strings based on a reference solution in this paper focusing on general multiobjective 0 1 programming problems involving positive and negative coefficients we propose an interactive fuzzy satisficing method by extending our previous genetic algorithms with double strings for multiobjective multidimensional 0 1 knapsack problems in the extended genetic algorithms a new decoding algorithm for individuals represented by double strings which maps each individual to a feasible solution is proposed through the introduction of backtracking and individual modification after examining the feasibility and efficiency of the extended genetic algorithms with double strings using a lot of 0 1 programming problems involving positive and negative coefficients an illustrative numerical example demonstrated the feasibility and efficiency of the proposed interactive fuzzy satisficing method