local discontinuous galerkin methods for the stokes system in this paper we introduce and analyze local discontinuous galerkin methods for the stokes system for a class of shape regular meshes with hanging nodes we derive a priori estimates for the l2 norm of the errors in the velocities and the pressure we show that optimal order estimates are obtained when polynomials of degree k are used for each component of the velocity and polynomials of degree k 1 for the pressure for any k ge1 we also consider the case in which all the unknowns are approximated with polynomials of degree k and show that although the orders of convergence remain the same the method is more efficient numerical experiments verifying these facts are displayed

on stabilized finite element methods based on the scott zhang projector circumventing the inf sup condition for the stokes problem abstract in this work we propose a stabilized finite element method that permits us to circumvent discrete inf sup conditions e g allowing equal order interpolation the type of method we propose belongs to the family of symmetric stabilization techniques which are based on the introduction of additional terms that penalize the difference between some quantities i e the pressure gradient in the stokes problem and their finite element projections the key feature of the formulation we propose is the definition of the projection to be used a non standard scott zhang projector that is well defined for l 1 functions the resulting method has some appealing features the projector is local and nested meshes or enriched spaces are not required

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

reasonable properties for the ordering of fuzzy quantities ii as a continuation of the first part related to the first and second class of ordering approaches this paper deals with the fulfilment of reasonable properties in the third class of ordering approaches to do so we briefly introduce fuzzy relations on which the third class of approaches is based then we recall some transitivity related concepts and an ordering procedure based on a acyclic fuzzy relation acyclicity is a very weak restriction on a fuzzy relation we prove that many fuzzy relations used for the comparison of fuzzy quantities satisfy some conditions stronger than acyclicity so we give a widely applicable formulation to derive a total ranking order from a fuzzy relation with our formulation we examine all the ordering indices in the third class with respect to the proposed axioms in part i

an hp adaptive mixed discontinuous galerkin fem for nearly incompressible linear elasticity we develop the a posteriori error estimation of mixed hp version discontinuous galerkin finite element methods for nearly incompressible elasticity problems in two space dimensions computable upper and lower bounds on the error measured in terms of a natural mesh dependent energy norm are derived the bounds are explicit in the local mesh sizes and approximation orders and are independent of the locking parameter a series of numerical experiments are presented which demonstrate the performance of the proposed error estimator within an automatic hp adaptive refinement procedure

approaches to multistage one shot decision making abstract in this research multistage one shot decision making under uncertainty is studied in such a decision problem a decision maker has one and only one chance to make a decision at each stage with possibilistic information based on the one shot decision theory approaches to multistage one shot decision making are proposed in the proposed approach a decision maker chooses one state amongst all the states according to his her attitude about satisfaction and possibility at each stage the payoff at each stage is associated with the focus points at the succeeding stages based on the selected states focus points the sequence of optimal decisions is determined by dynamic programming the proposed method is a fundamental alternative for multistage decision making under uncertainty because it is scenario based instead of lottery based as in the other existing methods the one shot optimal stopping problem is analyzed where a decision maker has only one chance to determine stopping or continuing at each stage the theoretical results have been obtained

the determination of the imaginary abelian number fields with class number one in this paper we determine all the imaginary abelian number fields with class number one there exist exactly 172 imaginary abelian number fields with class number one the maximal conductor of these fields is 10921 67 163 which is the conductor of the biquadratic number field q vc 6 1 63

the theory of fuzzy stochastic processes abstract in this paper we deal with the general theory of fuzzy stochastic processes we give the suitable definitions of fuzzy random function fuzzy stochastic process and their fall shadow distribution functions the concepts of separability and measurability of a fuzzy random function are introduced and some properties of these new concepts are derived we investigate the continuity of fuzzy sample function of a fuzzy stochastic process

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

a symmetric method for weakly imposing dirichlet boundary conditions in embedded finite element meshes summary in this paper we propose a way to weakly prescribe dirichlet boundary conditions in embedded finite element meshes the key feature of the method is that the algorithmic parameter of the formulation which allows to ensure stability is independent of the numerical approximation relatively small and can be fixed a priori moreover the formulation is symmetric for symmetric problems an additional element discontinuous stress field is used to enforce the boundary conditions in the poisson problem additional terms are required in order to guarantee stability in the convection diffusion equation and the stokes problem the proposed method is then easily extended to the transient navier stokes equations copyright 2012 john wiley sons ltd

stabilized discontinuous finite element approximations for stokes equations in this paper we derive two stabilized discontinuous finite element formulations symmetric and nonsymmetric for the stokes equations and the equations of the linear elasticity for almost incompressible materials these methods are derived via stabilization of a saddle point system where the continuity of the normal and tangential components of the velocity displacements are imposed in a weak sense via lagrange multipliers for both methods almost all reasonable pair of discontinuous finite element spaces can be used to approximate the velocity and the pressure optimal error estimate for the approximation of both the velocity of the symmetric formulation and pressure in l2 norm are obtained as well as one in a mesh dependent norm for the velocity in both symmetric and nonsymmetric formulations

the dpg method for the stokes problem we discuss well posedness and convergence theory for the dpg method applied to a general system of linear partial differential equations pdes and specialize the results to the classical stokes problem the stokes problem is an iconic troublemaker for standard bubnov galerkin methods if discretizations are not carefully designed they may exhibit non convergence or locking by contrast dpg does not require us to treat the stokes problem in any special manner we illustrate and confirm our theoretical convergence estimates with numerical experiments

discontinuous galerkin methods for the stokes equations with nonlinear damping term on general meshes abstract this paper presents the interior penalty discontinuous galerkin ipdg methods to solve the stationary stokes equations with nonlinear damping term the ipdg discrete schemes are established on general meshes the corresponding consistency and stabilization of those schemes are proved subsequently we analyze the existence boundedness and uniqueness of the discrete solutions then the optimal error estimates are derived in the l 2 norm and h 1 like dg norm for the velocity variable and l 2 norm for the pressure variable respectively finally some numerical experiments in two dimensional are reported to demonstrate the theoretical results and show the robustness of our discrete schemes

variational multiscale error estimators for solid mechanics adaptive simulations an orthogonal subgrid scale approach abstract in this work we present a general error estimator for the finite element solution of solid mechanics problems based on the variational multiscale method the main idea is to consider a rich model for the subgrid scales as an error estimator the subscales are considered to belong to a space orthogonal to the finite element space orthogonal subgrid scales and we take into account their contribution both in the element interiors and on the element boundaries subscales on the element boundaries a simple analysis shows that the upper bound for the obtained error estimator is sharper than in other error estimators based on the variational multiscale method numerical examples show that the proposed error estimator is an accurate approximation for the energy norm error and can be used both in simple linear constitutive models and in more complex non linear cases

a finite element formulation for the stokes problem allowing equal velocity pressure interpolation abstract in this paper we study a variational formulation of the stokes problem that accommodates the use of equal velocity pressure finite element interpolations the motivation of this method relies on the analysis of a class of fractional step methods for the navier stokes equations for which it is known that equal interpolations yield good numerical results the reason for this turns out to be the difference between two discrete laplacian operators computed in a different manner the formulation of the stokes problem considered here aims to reproduce this effect from the analysis of the finite element approximation of the problem we obtain stability and optimal error estimates using velocity pressure interpolations satisfying a compatibility condition much weaker than the inf sup condition of the standard formulation in particular this condition is fulfilled by the most common equal order interpolations

a geometric multigrid preconditioning strategy for dpg system matrices abstract the discontinuous petrov galerkin dpg methodology of demkowicz and gopalakrishnan 2010 2011 guarantees the optimality of the solution in an energy norm and provides several features facilitating adaptive schemes a key question that has not yet been answered in general though there are some results for poisson e g is how best to precondition the dpg system matrix so that iterative solvers may be used to allow solution of large scale problems in this paper we detail a strategy for preconditioning the dpg system matrix using geometric multigrid which we have implemented as part of camellia roberts 2014 2016 and demonstrate through numerical experiments its effectiveness in the context of several variational formulations we observe that in some of our experiments the behavior of the preconditioner is closely tied to the discrete test space enrichment we include experiments involving adaptive meshes with hanging nodes for lid driven cavity flow demonstrating that the preconditioners can be applied in the context of challenging problems we also include a scalability study demonstrating that the approach and our implementation scales well to many mpi ranks

superconvergence of h div finite element approximations for the stokes problem by local l 2 projection methods in this paper a general superconvergence result of h div finite element approximations for the stokes equations is established by using the local l 2 projection method local regularity assumptions for the stokes problem on regular partitions are required in order to derive superconvergence conclusions several numerical experiments are given to verify the theoretical results

stabilised vs stable mixed methods for incompressible flow abstract the accuracy of low order mixed finite element methods for the incompressible navier stokes equations is investigated in this work some numerical experiments suggest that the lowest order stabilised p 1 p 0 method linear velocity constant pressure is more efficient than the alternative a priori stable non conforming crouzeix raviart p 1 p 0 approach the relative accuracy of stabilised p 1 p 0 and p 1 p 1 linear velocity continuous linear pressure is assessed herein

a limit theorem in some dynamic fuzzy systems abstract in this paper using a fuzzy relation we define a dynamic fuzzy system with a compact state space by introducing a contraction property we study the limit of a sequence of fuzzy states and obtain a theorem for the existence and uniqueness of the solution of a fuzzy relational equation as an application we deal with a dynamic fuzzy system with a terminal fuzzy gain and give some characterizations for the fuzzy expected gain a numerical example is given to comprehend our idea in this paper

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

time dependent subscales in the stabilized finite element approximation of incompressible flow problems abstract in this paper we analyze a stabilized finite element approximation for the incompressible navier stokes equations based on the subgrid scale concept the essential point is that we explore the properties of the discrete formulation that results allowing the subgrid scales to depend on time this apparently natural idea avoids several inconsistencies of previous formulations and also opens the door to generalizations

continuous interior penalty finite element method for oseen s equations in this paper we present an extension of the continuous interior penalty method of douglas and dupont interior penalty procedures for elliptic and parabolic galerkin methods in computing methods in applied sciences lecture notes in phys 58 springer verlag berlin 1976 pp 207 216 to oseen s equations the method consists of a stabilized galerkin formulation using equal order interpolation for pressure and velocity to counter instabilities due to the pressure velocity coupling or due to a high local reynolds number we add a stabilization term giving l2 control of the jump of the gradient over element faces edges in two dimensions to the standard galerkin formulation boundary conditions are imposed in a weak sense using a consistent penalty formulation due to nitsche we prove energy type a priori error estimates independent of the local reynolds number and give some numerical examples recovering the theoretical results

a combined nodal continuous discontinuous finite element formulation for the maxwell problem abstract continuous galerkin formulations are appealing due to their low computational cost whereas discontinuous galerkin formulation facilitate adaptative mesh refinement and are more accurate in regions with jumps of physical parameters since many electromagnetic problems involve materials with different physical properties this last point is very important for this reason in this article we have developed a combined cg dg formulation for maxwell s problem that allows arbitrary finite element spaces with functions continuous in patches of finite elements and discontinuous on the interfaces of these patches in particular the second formulation we propose comes from a novel continuous galerkin formulation that reduces the amount of stabilization introduced in the numerical system in all cases we have performed stability and convergence analyses of the methods the outcome of this work is a new approach that keeps the low cpu cost of recent nodal continuous formulations with the ability to deal with coefficient jumps and adaptivity of discontinuous ones all these methods have been tested using a problem with singular solution and another one with different materials in order to prove that in fact the resulting formulations can properly deal with these problems

ranking and defuzzification methods based on area compensation abstract we present some interesting properties related to the area compensation procedure to compare fuzzy numbers it has been proved that this method produces more than a fuzzy interval order it induces a ranking of fuzzy numbers some further results are given about the transitivity property and about computational aspects extensions to non normal fuzzy numbers and fuzzy quantities are also proposed

cyclotomic function fields with ideal class number one abstract we list all imaginary cyclotomic extensions f q x m x f q x with ideal class number equal to one apart from the zero genus ones there are 17 solutions up to f q x isomorphism 13 of them are defined over f 3 and the 4 remainings are defined over f 4

divisor class number one problem for abelian extensions over rational function fields in this paper we determine all the abelian extensions of rational function fields which have divisor class number one we also determine all the imaginary abelian extensions with relative divisor class number one

optimal stopping problems in a stochastic and fuzzy system in a stochastic and fuzzy environment two kinds of stopping models are discussed and compared the optimal fuzzy stopping times are given under the assumptions of monotonicity and regularity for stopping rules also we find that fuzzy stopping times are favored in a comparison between fuzzy and classical stopping models

a posteriori error estimates for a discontinuous galerkin approximation of second order elliptic problems several a posteriori error estimators are introduced and analyzed for a discontinuous galerkin formulation of a model second order elliptic problem in addition to residual type estimators we introduce some estimators that are couched in the ideas and techniques of domain decomposition results of numerical experiments are presented

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 spalart allmaras turbulence model implementation in a discontinuous galerkin solver for incompressible flows in this paper the artificial compressibility flux discontinuous galerkin dg method for the solution of the incompressible navier stokes equations has been extended to deal with the reynolds averaged navier stokes rans equations coupled with the spalart allmaras sa turbulence model dg implementations of the rans and sa equations for compressible flows have already been reported in the literature including the description of limiting or stabilization techniques adopted in order to prevent the turbulent viscosity email protected from becoming negative in this paper we introduce an sa model implementation that deals with negative email protected values by modifying the source and diffusion terms in the sa model equation only when the working variable or one of the model closure functions become negative this results in an efficient high order implementation where either stabilization terms or even additional equations are avoided we remark that the proposed implementation is not dg specific and it is well suited for any numerical discretization of the rans sa governing equations the reliability robustness and accuracy of the proposed implementation have been assessed by computing several high reynolds number turbulent test cases the flow over a flat plate re 10 7 the flow past a backward facing step re 37400 and the flow around a naca 0012 airfoil at different angles of attack a 0 o 10 o 15 o and reynolds numbers re 2 88x10 6 6x10 6

unified stabilized finite element formulations for the stokes and the darcy problems in this paper we propose stabilized finite element methods for both stokes and darcy s problems that accommodate any interpolation of velocities and pressures apart from the interest of this fact the important issue is that we are able to deal with both problems at the same time in a completely unified manner in spite of the fact that the functional setting is different concerning the stabilization formulation we discuss the effect of the choice of the length scale appearing in the expression of the stabilization parameters both in what refers to stability and to accuracy this choice is shown to be crucial in the case of darcy s problem as an additional feature of this work we treat two types of stabilized formulations showing that they have a very similar behavior

fuzzy stopping problems in continuous time fuzzy stochastic systems in a continuous time fuzzy stochastic system a stopping model with fuzzy stopping times is presented the optimal fuzzy stopping times are given under an assumption of regularity for stopping rules also the optimal fuzzy reward is characterized as a unique solution of an optimality equation under a differentiability condition an example in the markov models is discussed

a reconstructed discontinuous galerkin method for incompressible flows on arbitrary grids abstract the discontinuous galerkin dg methods have attained increasing popularity for solving the incompressible navier stokes ins equations in recent years however the dg methods have their own weakness due to the high computational costs and storage requirements in this work we develop a high order hybrid reconstructed dg rdg method for solving the ins equations on arbitrary grids to be specific the inviscid term of the ins equations is discretized by applying the third order hybrid rdg p 1 p 2 method with a simplified artificial compressibility flux while the viscous term of the ins equations is discretized by using the simple direct dg ddg method a number of incompressible flow problems in both steady and unsteady forms for a variety flow conditions are computed to numerically assess the performance of the hybrid rdg p 1 p 2 method which confirm its ability to achieve the optimal third order of accuracy at a significantly reduced computational costs furthermore a detailed comparison of a variety of different reconstructed strategies is performed and presented numerical results demonstrate that the hybrid rdg p 1 p 2 method outperforms the rdg p 1 p 2 method based on either the original least squares reconstruction or the green gauss reconstruction for solving the ins equations

on the design of discontinuous galerkin methods for elliptic problems based on hybrid formulations abstract the objective of this paper is to present a new framework for the design of discontinuous galerkin dg methods for elliptic problems the idea is to start from a hybrid formulation of the problem involving as unknowns the main field in the interior of the element domains and its fluxes and traces on the element boundaries rather than working with this three field formulation fluxes are modeled using finite difference expressions and then the traces are determined by imposing continuity of fluxes although other strategies could be devised this procedure is applied to four elliptic problems namely the convection diffusion equation in the diffusion dominated regime the stokes problem the darcy problem and the maxwell problem we justify some well known dg methods with some modifications that in fact allow to improve the performance of the original methods particularly when the physical properties are discontinuous

penalty factor free discontinuous galerkin methods for 2 dim stokes problems this paper presents two new finite element methods for two dimensional stokes problems these methods are developed by relaxing the constraints of the crouzeix raviart nonconforming p 1 finite elements penalty terms are introduced to compensate for lack of continuity or the divergence free property however there is no need for choosing penalty factors and the formulations are symmetric these new methods are easy to implement and avoid solving saddle point linear systems numerical experiments are presented to illustrate the proved optimal error estimates

stabilized finite element approximation of transient incompressible flows using orthogonal subscales abstract in this paper we present a stabilized finite element method to solve the transient navier stokes equations based on the decomposition of the unknowns into resolvable and subgrid scales the latter are approximately accounted for so as to end up with a stable finite element problem which in particular allows to deal with convection dominated flows and the use of equal velocity pressure interpolations three main issues are addressed the first is a method to estimate the behavior of the stabilization parameters based on a fourier analysis of the problem for the subscales secondly the way to deal with transient problems discretized using a finite difference scheme is discussed finally the treatment of the nonlinear term is also analyzed a very important feature of this work is that the subgrid scales are taken as orthogonal to the finite element space in the transient case this simplifies considerably the numerical scheme

an approach to stopping problems of a dynamic fuzzy system we formulate a stopping problem for dynamic fuzzy systems concerning with fuzzy decision environment it could be regarded as a natural fuzzification of non fuzzy stopping problem with a deterministic dynamic system the validity of the approach by cuts of fuzzy sets will be discussed in constructing one step look ahead policy of an optimal fuzzy stopping time a numerical example is given to illustrate the theoretical results and to show a merit to use fuzzy stopping times in dynamic fuzzy systems

multiphysics discontinuous galerkin method for a poroelasticity model abstract in this paper we develop and analyze a multiphysics discontinuous galerkin method for a poroelasticity model which describes the dynamics of poro elastic materials under an applied mechanical force on the boundary and we prove that the multiphysics discontinuous galerkin method is absolutely stable for all positive mesh size h also we propose a time stepping algorithm which decouples the reformulated poroelasticity model at each time step into two sub problems one of which is a generalized stokes problem for the displacement vector field along with a pseudo pressure and the other is a diffusion problem for the pseudo pressure field and we give the optimal order error estimates in the energy norm finally we give the numerical examples to verify the theoretical results

the superconvergent patch recovery and a posteriori error estimates part 2 error estimates and adaptivity in this second part of the paper the issue of a posteriori error estimation is discussed in particular we derive a theorem showing the dependence of the effectivity index for the zienkiewicz zhu error estimator on the convergence rate of the recovered solution this shows that with superconvergent recovery the effectivity index tends asymptotically to unity the superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the zienkiewicz zhu error estimator to demonstrate accurate estimation of the exact error attainable numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient stress error estimation several examples of the performance of the error estimator in adaptive mesh refinement are also presented

the local discontinuous galerkin method for the oseen equations we introduce and analyze the local discontinuous galerkin method for the oseen equations of incompressible fluid flow for a class of shape regular meshes with hanging nodes we derive optimal a priori estimates for the errors in the velocity and the pressure in l 2 and negative order norms numerical experiments are presented which verify these theoretical results and show that the method performs well for a wide range of reynolds numbers

coupling of continuous and discontinuous galerkin methods for transport problems in this paper we formulate a coupled discontinuous continuous galerkin method for the numerical solution of convection diffusion transport equations where convection may be dominant one motivation for this approach is to use a discontinuous method where the solution is rough e g in regions of high gradients and use a continuous method where the solution is smooth in this approach the domain is decomposed into two regions and appropriate transmission conditions are applied at the interface between regions in one region a local discontinuous galerkin method is applied and in the other region a standard continuous galerkin method is employed stability and a priori error estimates for the coupled method are derived and numerical results in one space dimension are given for smooth problems and problems with sharp fronts 2002 elsevier science b v all rights reserved

an adaptive fixed mesh ale method for free surface flows in this work we present a fixed mesh ale method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain this mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required some of the main ingredients of the formulation are the use of an arbitrary lagrangian eulerian formulation for computing temporal derivatives the use of stabilization terms for stabilizing convection stabilizing the lack of compatibility between velocity and pressure interpolation spaces and stabilizing the ill conditioning introduced by the cuts on the background finite element mesh and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved the method is tested in several numerical examples the expected convergence rates both in space and time are observed smooth solution fields for both velocity and pressure are obtained as a result of the contribution of the stabilization terms finally a good agreement between the numerical results and the reference experimental data is obtained

adaptive finite element simulation of incompressible flows by hybrid continuous discontinuous galerkin formulations in this work we design hybrid continuous discontinuous finite element spaces that permit discontinuities on nonmatching element interfaces of nonconforming meshes then we develop an equal order stabilized finite element formulation for incompressible flows over these hybrid spaces which combines the element interior stabilization of supg type continuous galerkin formulations and the jump stabilization of discontinuous galerkin formulations optimal stability and convergence results are obtained for the adaptive setting we use a standard error estimator and marking strategy numerical experiments show the optimal accuracy of the hybrid algorithm for both uniformly and adaptively refined nonconforming meshes the outcome of this work is a finite element formulation that can naturally be used on nonconforming meshes as discontinuous galerkin formulations while keeping the much lower cpu cost of continuous galerkin formulations

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

mixed hp dgfem for incompressible flows we consider several mixed discontinuous galerkin approximations of the stokes problem and propose an abstract framework for their analysis using this framework we derive a priori error estimates for hp approximations on tensor product meshes we also prove a new stability estimate for the discrete divergence bilinear form