stability and error estimates of local discontinuous galerkin methods with implicit explicit time marching for advection diffusion problems the main purpose of this paper is to analyze the stability and error estimates of the local discontinuous galerkin ldg methods coupled with carefully chosen implicit explicit imex runge kutta time discretization up to third order accuracy for solving one dimensional linear advection diffusion equations in the time discretization the advection term is treated explicitly and the diffusion term implicitly there are three highlights of this work the first is that we establish an important relationship between the gradient and interface jump of the numerical solution with the independent numerical solution of the gradient in the ldg methods the second is that by aid of the aforementioned relationship and the energy method we show that the imex ldg schemes are unconditionally stable for the linear problems in the sense that the time step tau is only required to be upper bounded by a constant which depends on the ratio of the diffusion and the square of the advection coefficients and is independent

local discontinuous galerkin numerical solutions of non newtonian incompressible flows modeled by p navier stokes equations we present a local discontinuous galerkin ldg method for solving non newtonian incompressible flow problems the problems are modeled by p type navier stokes equations the extra stress tensor follows a p power rule p ns the aim of this paper is to present an efficient way for discretizing the governing equations by an ldg method choosing both equal and mixed order local polynomial space for velocity and pressure the velocity gradient is introduced as an auxiliary variable and the p ns system is decomposed into a first order system including the projection of the nonlinear stress tensor components to the local discontinuous space every equation resulting from the splitting of the extra stress tensor is discretized under the dg element by element technique in the divergence constraint equation an artificial compressibility term time derivative of the pressure with a small parameter is added and the first order terms are expressed in a divergence form and are discretized by utilizing the lax friedrichs numerical fluxes an upwind wave analysis is applied on the outflow boundary for constructing artificial outflow boundary conditions for the time discretization s stage diagonally implicit runge kutta schemes are applied numerical experiments on problems with known exact solutions are performed for verifying the expected convergence rates of the method benchmark problems are considered in order to check the performance of the method for solving flow problems described by p ns systems

on 2d elliptic discontinuous galerkin methods we discuss the discretization using discontinuous galerkin dg formulation of an elliptic poisson problem two commonly used dg schemes are investigated the original average flux proposed by bassi and rebay j comput phys 1997 131 267 and the local discontinuous galerkin ldg siam j numer anal 1998 35 2440 2463 scheme in this paper we expand on previous expositions discontinuous galerkin methods theory computation and applications springer berlin 2000 135 146 siam j sci comput 2002 24 2 524 547 int j numer meth engng 2003 58 2 1119 1148 by adopting a matrix based notation with a view to highlighting the steps required in a numerical implementation of the dg method through consideration of standard c0 type expansion bases as opposed to elementally orthogonal expansions with the matrix formulation we are able to apply static condensation techniques to improve efficiency of the direct solver when high order expansions are adopted the use of c0 type expansions also permits the direct enforcement of dirichlet boundary conditions through a lifting approach where the ldg flux does not require further stabilization in our construction we also adopt a formulation of the continuous dg fluxes that permits a more general interpretation of their numerical implementation in particular it allows us to determine the conditions under which the ldg method provides a near local stencil finally a study of the conditioning and the size of the null space of the matrix systems resulting from the dg discretization of the elliptic problem is undertaken copyright 2005 john wiley sons ltd

a computational strategy for thermo poroelastic structures with a time space interface coupling this paper deals with a computational strategy suitable for the simulation of multiphysics problems based on the large time increment latin method the simulation of such problems must encounter the possible different time and space scales which usually arise with the different physics herein we focus on using different time and space discretizations for each physics by introducing an interface with its own discretization the feasibility of both a time and space couplings is exemplified on a nonlinear 3 physics strongly coupled problem the thermal fluid structure interaction in a thermo poroelastic structure

exponential convergence of mixed hp dgfem for stokes flow in polygons we analyze mixed hp discontinuous galerkin finite element methods dgfem for stokes flow in polygonal domains in conjunction with geometrically refined quadrilateral meshes and linearly increasing approximation orders we prove that the hp dgfem leads to exponential rates of convergence for piecewise analytic solutions exhibiting singularities near corners

a galerkin interface stabilisation method for the advection diffusion and incompressible navier stokes equations abstract a stabilised galerkin finite element method for the advection diffusion and incompressible navier stokes equations is presented which inherits features of both discontinuous and continuous galerkin methods the problem of interest is posed element wise with weakly imposed dirichlet boundary conditions the dirichlet boundary condition is supplied by a function on element boundaries which is determined such that weak continuity of the flux is assured the approach allows the natural incorporation of upwinding at element boundaries which is typical of discontinuous galerkin methods while retaining the same number of global degrees of freedom as for a continuous galerkin method the formulation also stabilises mixed incompressible problems which use equal order interpolations for linear elements only minor modifications are required to existing continuous finite element codes and the link to other stabilised methods is elaborated the method is supported by a range of numerical examples which demonstrate stability with minimal numerical dissipation

analysis of a discontinuous galerkin method for the biot s consolidation problem in this paper a fully discrete stabilized discontinuous galerkin method is proposed to solve the biot s consolidation problem the existence and uniqueness of the finite element solution are obtained the stability of the fully discrete solution is discussed the corresponding error estimates for the approximation of displacement and pressure in a mesh dependent norm are obtained the error estimate for the approximation of pressure in l 2 norm is also obtained

new finite element methods in computational fluid dynamics by h div elements in this paper the authors present two formulations for the stokes problem which make use of the existing h rm div elements of the raviart thomas type originally developed for the second order elliptic problems in addition two new h rm div elements are constructed and analyzed particularly for the new formulations optimal order error estimates are established for the corresponding finite element solutions in various sobolev norms the finite element solutions feature a full satisfaction of the continuity equation when existing raviart thomas type elements are employed in the numerical scheme

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 low order locking free hybrid discontinuous galerkin element formulation for large deformations abstract in this work a hybrid discontinuous galerkin dg quadrilateral element formulation is presented as usual in hybrid formulations the interior of the elements is treated separately from the skeleton which represents the element boundaries these are kinematically decoupled i e displacement jumps can occur between the skeleton and the interior of the elements the global degrees of freedom dofs are defined on the skeleton as the displacements at the corners which allows the implementation into existing finite element codes as usual in hybrid dg formulations the degrees of freedom in the interior are condensed out on the element level leading to the same number of global degrees of freedom as for continuous bilinear elements instead of using conventional shape functions in the interior the deformation gradient f is assumed constant within the element furthermore f is connected to the skeleton degrees of freedom via the weak form this leads to a very simple formulation and implementation the element is tested for several computational examples from the literature special choices of the penalty parameter are investigated which are partially derived analytically it is found that the element is free of volumetric and shear locking moreover the convergence is similar to that of other well known locking free finite element formulations

on the stability of projection methods for the incompressible navier stokes equations based on high order discontinuous galerkin discretizations abstract the present paper deals with the numerical solution of the incompressible navier stokes equations using high order discontinuous galerkin dg methods for discretization in space for dg methods applied to the dual splitting projection method instabilities have recently been reported that occur for small time step sizes since the critical time step size depends on the viscosity and the spatial resolution these instabilities limit the robustness of the navier stokes solver in case of complex engineering applications characterized by coarse spatial resolutions and small viscosities by means of numerical investigation we give evidence that these instabilities are related to the discontinuous galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure integration by parts of these terms with a suitable definition of boundary conditions is required in order to obtain a stable and robust method since the intermediate velocity field does not fulfill the boundary conditions prescribed for the velocity a consistent boundary condition is derived from the convective step of the dual splitting scheme to ensure high order accuracy with respect to the temporal discretization this new formulation is stable in the limit of small time steps for both equal order and mixed order polynomial approximations although the dual splitting scheme itself includes inf sup stabilizing contributions we demonstrate that spurious pressure oscillations appear for equal order polynomials and small time steps highlighting the necessity to consider inf sup stability explicitly

coupled discontinuous and continuous galerkin finite element methods for the depth integrated shallow water equations abstract in this paper we investigate a new approach for the two dimensional fully non linear depth averaged shallow water equations by coupling continuous and discontinuous galerkin methods we apply a discontinuous galerkin method to the primitive continuity and momentum equations and couple this to a continuous method discretizing the so called wave continuity and momentum equation herein we present the formulation and derive an a priori error estimate and demonstrate some preliminary numerical results this work represents the culmination of a series of papers exploring coupled methods for the shallow water equations

on the estimation of technical inefficiency in the stochastic frontier production function model abstract the error term in the stochastic frontier model is of the form v u where v is a normal error term representing pure randomness and u is a non negative error term representing technical inefficiency the entire v u is easily estimated for each observation but a previously unsolved problem is how to separate it into its two components v and u this paper suggests a solution to this problem by considering the expected value of u conditional on v u an explicit formula is given for the half normal and exponential cases

discontinuous continuous galerkin methods for coupling the primitive and wave continuity equations of shallow water in this paper we investigate a new approach for the numerical solution of the two dimensional depth integrated shallow water equations based on coupling discontinuous and continuous galerkin methods in this approach we couple a discontinuous galerkin method applied to the primitive continuity equation coupled to a continuous galerkin method applied to the so called wave continuity equation the formulation is derived and a priori error estimates are given preliminary numerical results for a simple model of flow in a channel are presented 2003 elsevier b v all rights reserved

average intersection and pivoting densities for the purposes of quantifying efficiency of more than one codimension piecewise linear continuation algorithms higher dimensional analogues of the average directional density are defined and studied two such are explicitly considered the average intersection density which measures the local density of intersections of an implicitly defined piecewise linear manifold with complementing faces of a decomposition of euclidean space and average pivoting density which considers the number of pivots such an intersection entails general results are established which relate the densities to geometric properties of the decomposition explicit closed formulae are presented for the most interesting case of the freudenthal kuhn triangulation and asymptotic expressions are developed

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 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

numerical analysis of the unconditionally stable discontinuous galerkin schemes for the nonstationary conduction convection problem abstract this work aims at employing the discontinuous galerkin dg methods for solving the nonstationary conduction convection model which is motivated by advantages of dg methods the discontinuous element pair p k p k 1 p k in the space discretization and backward euler scheme in time are applied as well as an explicit upwind scheme based on picard iteration is introduced for the coupled term existence and uniqueness of the approximation solutions are proved along with preserving the unconditional stability of the numerical schemes the priori error estimates for velocity pressure and temperature are also derived numerical tests are provided to verify the theoretical analysis and to indicate the efficiency of the dg methods in simulating practical problems

hybridizable discontinuous galerkin method hdg for stokes interface flow abstract in this paper we present a hybridizable discontinuous galerkin hdg method for solving the stokes interface problems with discontinuous viscosity and variable surface tension the jump condition of the stress tensor across the interface is naturally incorporated into the hdg formulation through a constraint on the numerical flux the most important feature of hdg method compared to other dg methods is that it reduces the number of globally coupled unknowns significantly when high order approximate polynomials are used for problems with polygonal interfaces it provides optimal convergence rates of order k 1 in l 2 norm for the velocity pressure and as well as the gradient of velocity furthermore a new approximate velocity can be obtained by an element by element postprocessing which converges with order k 2 in the l 2 norm for stokes interface problems with curved interfaces we use general curvilinear element to ensure the optimal convergence rates an error estimate is given for the approximation of the interface it indicates that curvilinear elements of degree 2 k 1 should be used for optimal convergence rate of order k 1

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

an embedded hybridized discontinuous galerkin finite element method for the stokes equations abstract we present and analyze a new embedded hybridized discontinuous galerkin finite element method for the stokes problem the method has the attractive properties of full hybridized methods namely an h div conforming velocity field pointwise satisfaction of the continuity equation and a priori error estimates for the velocity that are independent of the pressure the embedded hybridized formulation has advantages over a full hybridized formulation in that it has fewer global degrees of freedom for a given mesh and the algebraic structure of the resulting linear system is better suited to fast iterative solvers the analysis results are supported by a range of numerical examples that demonstrate rates of convergence and which show computational efficiency gains over a full hybridized formulation

a staggered discontinuous galerkin method for the stokes system discontinuous galerkin dg methods are a class of efficient tools for solving fluid flow problems there are in the literature many greatly successful dg methods in this paper a new staggered dg

an immersed discontinuous finite element method for stokes interface problems abstract we present a discontinuous immersed finite element ife method for stokes interface problems on cartesian meshes that do not require the mesh to be aligned with the interface as such the method allows unfitted meshes with elements cut by the interface and thus may contain more than one fluid on these unfitted meshes we construct an immersed q 1 q 0 finite element space according to the location of the interface and pertinent interface jump conditions the proposed q 1 q 0 ife shape functions have several desirable features such as the unisolvence and the partition of unity we present several numerical examples to demonstrate that the proposed ife spaces maintain the optimal approximation capability with respect to the polynomials used we also show that related discontinuous ife solutions of stokes interface problems maintain the optimal convergence rates in both l 2 and broken h 1 norms

a discontinuous galerkin method for the simulation of compressible gas gas and gas water two medium flows abstract in this paper we develop a new discontinuous galerkin method for the simulation of shocks and interfaces in compressible gas gas and gas water two medium flows by solving the based model the spatial discretization is carefully designed to possess the following features discrete conservation in terms of the total mass total momentum and total energy high order accuracy and consistency for smooth flows free of oscillations at an isolated material interface in order to handle potential discontinuities arising in the simulation a nonlinear limiter based on the weighted essentially non oscillatory weno strategy is employed to suppress numerical oscillations and to preserve high order of accuracy in regions of smooth flows the weno reconstruction is imposed on suitably selected quantities rather than the conserved ones in case for discontinuities with large pressure ratio low density and dramatic change of material property where unphysical variables may be encountered a posteriori solution correction on the subcell level is locally adopted to enhance the robustness a series of typical test cases for both one and two dimensional problems are provided to demonstrate the performance of the proposed method

superconvergence of h div finite element approximations for the stokes problem by l2 projection methods a general superconvergence result of h div finite element approximations for the stokes equations is established by using l 2 projection method regularity assumptions for the stokes problem with regular partitions is required numerical experiments are given to verify the theoretical results

energy stable and momentum conserving hybrid finite element method for the incompressible navier stokes equations a hybrid method for the incompressible navier stokes equations is presented the method inherits the attractive stabilizing mechanism of upwinded discontinuous galerkin methods when momentum advection becomes significant equal order interpolations can be used for the velocity and pressure fields and mass can be conserved locally using continuous lagrange multiplier spaces to enforce flux continuity across cell facets the number of global degrees of freedom is the same as for a continuous galerkin method on the same mesh different from our earlier investigations on the approach for the navier stokes equations the pressure field in this work is discontinuous across cell boundaries it is shown that this leads to very good local mass conservation and for an appropriate choice of finite element spaces momentum conservation also a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed even in the absence of a pointwise solenoidal velocity field mass conservation momentum conservation and global energy stability are proved for the time continuous case and for a fully discrete scheme the presented analysis results are supported by a range of numerical simulations

efficient construction of unified continuous and discontinuous galerkin formulations for the 3d euler equations a unified approach for the numerical solution of the 3d hyperbolic euler equations using high order methods namely continuous galerkin cg and discontinuous galerkin dg methods is presented first we examine how classical cg that uses a global storage scheme can be constructed within the dg framework using constraint imposition techniques commonly used in the finite element literature then we implement and test a simplified version in the non hydrostatic unified model of the atmosphere numa for the case of explicit time integration and a diagonal mass matrix constructing cg within the dg framework allows cg to benefit from the desirable properties of dg such as easier hp refinement better stability etc moreover this representation allows for regional mixing of cg and dg depending on the flow regime in an area the different flavors of cg and dg in the unified implementation are then tested for accuracy and performance using a suite of benchmark problems representative of cloud resolving scale meso scale and global scale atmospheric dynamics the value of our unified approach is that we are able to show how to carry both cg and dg methods within the same code and also offer a simple recipe for modifying an existing cg code to dg and vice versa

superconvergence of the local discontinuous galerkin method for elliptic problems on cartesian grids in this paper we present a superconvergence result for the local discontinuous galerkin ldg method for a model elliptic problem on cartesian grids we identify a special numerical flux for which the l2 norm of the gradient and the l2 norm of the potential are of orders k 1 2 and k 1 respectively when tensor product polynomials of degree at most k are used for arbitrary meshes this special ldg method gives only the orders of convergence of k and k 1 2 respectively we present a series of numerical examples which establish the sharpness of our theoretical results

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

nonparametric frontier estimation a robust approach most nonparametric methods for estimating production frontiers data envelopment analysis and free disposal hall fdh are based on envelopment techniques statistical inference based on these estimators is available but by construction they are very sensitive to extreme values or outliers we propose a nonparametric estimator which is more robust to these extreme values it is based on a concept of expected minimum input function or expected maximal output function we show how this function is related to the efficient frontier itself the resulting estimator is related to the fdh estimator but it will not envelop all the data the asymptotic theory is provided our approach includes the multiple input and multiple output cases c 2002 elsevier science s a all rights reserved

an a priori error analysis of the local discontinuous galerkin method for elliptic problems in this paper we present the first a priori error analysis for the local discontinuous galerkin ldg method for a model elliptic problem for arbitrary meshes with hanging nodes and elements of various shapes we show that for stabilization parameters of order one the l2 norm of the gradient and the l2 norm of the potential are of order k and k 1 2 respectively when polynomials of total degree at least k are used if stabilization parameters of order h 1 are taken the order of convergence of the potential increases to k 1 the optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains

hybridized globally divergence free ldg methods part i the stokes problem we devise and analyze a new local discontinuous galerkin ldg method for the stokes equations of incompressible fluid flow this optimally convergent method is obtained by using an ldg method to discretize a vorticity velocity formulation of the stokes equations and by applying a new hybridization to the resulting discretization one of the main features of the hybridized method is that it provides a globally divergence free approximate velocity without having to construct globally divergence free finite dimensional spaces only elementwise divergence free basis functions are used another important feature is that it has significantly less degrees of freedom than all other ldg methods in the current literature in particular the approximation to the pressure is only defined on the faces of the elements on the other hand we show that as expected the condition number of the schur complement matrix for this approximate pressure is of order h 2 in the mesh size h finally we present numerical experiments that confirm the sharpness of our theoretical a priori error estimates

the effects of exogenous variables in efficiency measurement a monte carlo study abstract a monte carlo study is conducted to compare the stochastic frontier method and the data envelopment analysis dea method in measuring efficiency in situations where firms are subject to the effects of factors which are beyond managerial control in making efficiency measurements and comparisons one must separate the effects of the environment the exogenous factors and the effects of the productive efficiency there are two basic approaches to account for the effects of exogenous variables 1 an one step procedure which includes the exogenous variables directly in estimating the efficiency measures and 2 a two step procedure which first estimates the relative gross efficiencies using inputs and outputs then analyzes the effects of the exogenous variables on the gross efficiency the results show that the magnitude of exogenous variables does not appear to have any significant effect on the performance of the one step stochastic frontier method as long as the exogenous variables are correctly identified and accounted for however the effects of exogenous variables are significant for the two step approach especially for the dea methods

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

a riemann problem based method for solving compressible and incompressible flows a riemann problem based method for solving two medium flow including compressible and incompressible regions is presented the material interface is advanced by front tracking method and the material interface boundary conditions are defined by modified ghost fluid method a coupled compressible and incompressible riemann problem constructed in the normal direction of the material interface is proposed to predict the interfacial states with the ghost fluid states the compressible and incompressible flows are solved by discontinuous galerkin method an incompressible discontinuous galerkin method with nonuniform time step is also deduced for shock wave formed in compressible flow the numerical errors for the ghost fluid method in earlier works are analyzed and discussed in the numerical examples it shows that the proposed method can provide reasonable results including shock wave location two medium flow including compressible and incompressible regions is investigated an incompressible discontinuous galerkin method with nonuniform time step is derived a coupled compressible and incompressible riemann problem is proposed reasonable results are obtained for strong shock wave formed in compressible flow

discontinuous legendre wavelet element method for elliptic partial differential equations abstract by incorporating the legendre multiwavelet into the discontinuous galerkin dg method this paper presents a novel approach for solving poisson s equation with dirichlet boundary which is known as the discontinuous legendre multiwavelet element dlwe method derive an adaptive algorithm for the method and estimate the approximating error of its numerical fluxes one striking advantage of our method is that the differential operator boundary conditions and numerical fluxes involved in the elementwise computation can be done with lower time cost numerical experiments demonstrate the validity of this method furthermore this paper generalizes the dlwe method to the general elliptic equations defined on a bounded domain and describes the possibilities of constructing optimal adaptive algorithm the proposed method and its generalizations are also applicable to some other kinds of partial differential equations

a high order discontinuous galerkin method for the unsteady incompressible navier stokes equations we present a high order discontinuous galerkin discretization of the unsteady incompressible navier stokes equations in convection dominated flows using triangular and tetrahedral meshes the scheme is based on a semi explicit temporal discretization with explicit treatment of the nonlinear term and implicit treatment of the stokes operator the nonlinear term is discretized in divergence form by using the local lax friedrichs fluxes thus local conservativity is inherent spatial discretization of the stokes operator has employed both equal order p k p k and mixed order p k p k 1 velocity and pressure approximations a second order approximate algebraic splitting is used to decouple the velocity and pressure calculations leading to an algebraic helmholtz equation for each component of the velocity and a consistent poisson equation for the pressure the consistent poisson operator is replaced by an equivalent in stability and convergence operator namely that arising from the interior penalty discretization of the standard poisson operator with appropriate boundary conditions this yields a simpler and more efficient method characterized by a compact stencil size we show the temporal and spatial behavior of the method by solving some popular benchmarking tests for an unsteady stokes problem second order temporal convergence is obtained while for the taylor vortex test problem on both semi structured and fully unstructured triangular meshes spectral convergence with respect to the polynomial degree k is obtained by studying the orr sommerfeld stability problem we demonstrate that the p k p k method yields a stable solution while the p k p k 1 formulation leads to unphysical instability the good performance of the method is further shown by simulating vortex shedding in flow past a square cylinder we conclude that the proposed discontinuous galerkin method with the p k p k formulation is an efficient scheme for accurate and stable solution of the unsteady navier stokes equations in convection dominated flows

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

a unifying theory of a posteriori error control for discontinuous galerkin fem a unified a posteriori error analysis is derived in extension of carstensen numer math 100 617 637 2005 and carstensen and hu j numer math 107 3 473 502 2007 for a wide range of discontinuous galerkin dg finite element methods fem applied to the laplace stokes and lame equations two abstract assumptions a1 and a2 guarantee the reliability of explicit residual based computable error estimators the edge jumps are recast via lifting operators to make arguments already established for nonconforming finite element methods available the resulting reliable error estimate is applied to 16 representative dg fems from the literature the estimate recovers known results as well as provides new bounds to a number of schemes

application of a combined continuous discontinuous galerkin finite element method for the solution of the girkmann problem abstract in january 2008 the international association of computational mechanics iacm invited the scientific community to solve the girkmann problem by finite element methods the challenge was to get certain quantities of interest in terms of the approximate solutions within 5 of accuracy of their exact counterparts for instance the goal could be to evaluate the bending moment or the shear force at the junction of the shell and the ring the purpose of the present paper is to solve an axisymmetric solid elastic model for this problem using a continuous finite element method in combination with discontinuous interface elements in the region of interest named as the dg fem method the numerical results of the p version of the dg fem method are presented and discussed the results are verified with respect to previous results published in the literature showing excellent consistent results

hp adaptive discontinuous galerkin methods for bifurcation phenomena in open flows we consider the application of high order hp version adaptive discontinuous galerkin finite element methods for the discretization of the bifurcation problem associated with the steady incompressible navier stokes equations based on exploiting the dual weighted residual approach reliable and efficient a posteriori estimates of the error in the computed critical reynolds number at which a steady pitchfork bifurcation occurs when the underlying physical system possesses either reflectional z 2 symmetry or rotational and reflectional o 2 symmetry are derived numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on hp adaptively refined computational meshes are presented for both two and three dimensional problems

preconditioning methods for local discontinuous galerkin discretizations a multilevel interior penalty method is used as an efficient preconditioner for the schur complement of the local discontinuous galerkin ldg discretization of a poisson problem the method is then used in a block triangular preconditioner of the ldg saddle point system the block preconditioner is of the same efficiency as the schur complement version finally the block preconditioner is extended to the discretization of the stokes problem by the ldg method again the preconditioned saddle point problem can be solved in about as many steps as the schur complement the influence of several parameters on the performance of these methods is investigated

a finite element method by patch reconstruction for the stokes problem using mixed formulations abstract in this paper we develop a patch reconstruction finite element method for the stokes problem the weak formulation of the interior penalty discontinuous galerkin is employed the proposed method has a great flexibility in velocity pressure space pairs whose stability properties are confirmed by the inf sup tests numerical examples show the applicability and efficiency of the proposed method

a discontinuous galerkin method for nonlinear shear flexible shells abstract in this paper a discontinuous galerkin method for a nonlinear shear flexible shell theory is proposed that is suitable for both thick and thin shell analysis the proposed method extends recent work on reissner mindlin plates to avoid locking without the use of projection operators such as mixed methods or reduced integration techniques instead the flexibility inherent to discontinuous galerkin methods in the choice of approximation spaces is exploited to satisfy the thin plate compatibility conditions a priori a benefit of this approach is that only generalized displacements appear as unknowns we take advantage of this to craft the method in terms of a discrete energy minimization principle thereby restoring the rayleigh ritz approach in addition to providing a straightforward and elegant derivation of the discrete equilibrium equations the variational character of the method could afford numerous advantages in terms of mesh adaptation and available solution techniques the proposed method is exercised on a set of benchmarks and example problems to assess its performance numerically and to test for shear and membrane locking

stability analysis and error estimates of local discontinuous galerkin methods with implicit explicit time marching for nonlinear convection diffusion problems the main purpose of this paper is to analyze the stability and error estimates of the local discontinuous galerkin ldg methods coupled with implicit explicit imex time discretization schemes for solving one dimensional convection diffusion equations with a nonlinear convection both runge kutta and multi step imex methods are considered by the aid of the energy method we show that the imex ldg schemes are unconditionally stable for the nonlinear problems in the sense that the time step is only required to be upper bounded by a positive constant which depends on the flow velocity and the diffusion coefficient but is independent of the mesh size h we also give optimal error estimates for the imex ldg schemes under the same temporal condition if a monotone numerical flux is adopted for the convection numerical experiments are given to verify our main results

discontinuous galerkin method for the fully dynamic biot s model abstract in this paper a fully discrete scheme of the fully dynamic biot s model problem is proposed which is constructed by using interior penalty discontinuous galerkin method for the spatial approximation and a tailor difference scheme to approximate the first and second order temporal derivative terms first of all we prove the existence and uniqueness of solutions of proposed fully discrete scheme in proper norms then based on the error equations a priori error estimates shall be derived for both primal variables displacement and pore pressure finally a series of numerical examples are given to examine the convergence results by using the proposed numerical scheme to solve the fully dynamic biot s model problem

adaptive discontinuous galerkin methods for eigenvalue problems arising in incompressible fluid flows in this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous galerkin finite element approximations of the hydrodynamic stability problem associated with the incompressible navier stokes equations particular attention is given to the reliable error estimation of the eigenvalue problem in channel and pipe geometries here computable a posteriori error bounds are derived based on employing the generalization of the standard dual weighted residual approach originally developed for the estimation of target functionals of the solution to eigenvalue stability problems the underlying analysis consists of constructing both a dual eigenvalue problem and a dual problem for the original base solution in this way errors stemming from both the numerical approximation of the original nonlinear flow problem and the underlying linear eigenvalue problem are correctly controlled numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented

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

a multiscale discontinuous galerkin method with the computational structure of a continuous galerkin method proliferation of degrees of freedom has plagued discontinuous galerkin methodology from its inception over 30 years ago this paper develops a new computational formulation that combines the advantages of discontinuous galerkin methods with the data structure of their continuous galerkin counterparts the new method uses local element wise problems to project a continuous finite element space into a given discontinuous space and then applies a discontinuous galerkin formulation the projection leads to parameterization of the discontinuous degrees of freedom by their continuous counterparts and has a variational multiscale interpretation this significantly reduces the computational burden and at the same time little or no degradation of the solution occurs in fact the new method produces improved solutions compared with the traditional discontinuous galerkin method in some situations

estimation and inference in two stage semi parametric models of production processes many papers have regressed non parametric estimates of productive efficiency on environmental variables in two stage procedures to account for exogenous factors that might affect firms performance none of these have described a coherent data generating process dgp moreover conventional approaches to inference employed in these papers are invalid due to complicated unknown serial correlation among the estimated efficiencies we first describe a sensible dgp for such models we propose single and double bootstrap procedures both permit valid inference and the double bootstrap procedure improves statistical efficiency in the second stage regression we examine the statistical performance of our estimators using monte carlo experiments

unobserved heterogeneity and endogeneity in nonparametric frontier estimation in production theory and eciency analysis rm eciencies are measured by their distances to a production frontier which is the geometrical locus of optimal combinations of inputs and outputs it is today recognized that in the presence of heterogenous conditions like environmental factors that influence the shape and the position of the frontier traditional measures of efficiency obtained in the space of inputs outputs have no sensible economic meaning this is because the benchmark frontier may not be attainable for a firm facing different heterogenous conditions using a nonparametric approach this can be corrected by using conditional frontiers and conditional efficiency scores developed in the literature in this paper we extend these concepts in the case where the heterogeneity is not observed we propose and analyze a model where the heterogeneity variable is linked to a particular input or output it is defined as the part of the input or the output independent from some instrumental variable through a nonseparable nonparametric model we discuss endogeneity issues involved in this model under certain regularity assumptions we show that the model is identified we propose nonparametric estimators of the conditional frontier and the conditional efficiency score and analyze their asymptotic properties when using fdh estimators we prove the asymptotic convergence to a weibull distribution whereas when using the robust order m estimators we obtain the asymptotic normality of the estimators the method is illustrated with some simulated and real data examples a monte carlo experiment shows how the procedure works for finite samples

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

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

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

environmental factors in frontier estimation a monte carlo analysis we compare three recently developed frontier estimators namely the conditional dea daraio and simar 2005 2007b the latent class sfa greene 2005 orea and kumbhakar 2004 and the stonezd approach johnson and kuosmanen 2011 by means of monte carlo simulation we focus on their ability to identify production frontiers and efficiency rankings in the presence of environmental factors our simulations match features of real life datasets and cover a wide range of scenarios with variations in sample size distribution of noise and inefficiency as well as in distributions intensity and number of environmental variables our results provide insight in the finite sample properties of the estimators while also identifying estimator specific characteristics overall the latent class approach is found to perform best although in many cases stonezd shows a similar performance performance of cdea is most often inferior

optimal bandwidth selection for conditional efficiency measures a data driven approach in productivity analysis an important issue is to detect how external environmental factors exogenous to the production process and not under the control of the producer might in uence the production process and the resulting efficiency of the rms most of the traditional approaches proposed in the literature have serious drawbacks an alternative approach is to describe the production process as being conditioned by a given value of the environmental variables cazals florens and simar 2002 daraio and simar 2005 this de nes conditional efficiency measures where the production set in the input output space may depend on the value of the external variables the statistical properties of nonparametric estimators of these conditional measures are now established jeong park and simar 2008 these involve the estimation of a nonstandard conditional distribution function which requires the speci cation of a smoothing parameter a bandwidth so far only the asymptotic optimal order of this bandwidth has been established this is of little interest for the practitioner in this paper we ll this gap and we propose a data driven technique for selecting this parameter in practice the approach based on a least squares cross validation procedure lscv provides an optimal bandwidth that minimizes an appropriate weighted integrated squared error ise the method is carefully described and exempli ed with some simulated data with univariate and multivariate environmental factors an application on real data performances of mutual funds illustrates how this new optimal method of bandwidth selection works in practice

a reconstructed discontinuous galerkin method for the compressible navier stokes equations on arbitrary grids a reconstruction based discontinuous galerkin rdg method is presented for the solution of the compressible navier stokes equations on arbitrary grids the rdg method originally developed for the compressible euler equations is extended to discretize viscous and heat fluxes in the navier stokes equations using a so called inter cell reconstruction where a smooth solution is locally reconstructed using a least squares method from the underlying discontinuous dg solution similar to the recovery based dg rdg methods this reconstructed dg method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional dg methods unlike rdg methods this rdg method does not need to judiciously choose a proper form of a recovered polynomial thus is simple flexible and robust and can be used on arbitrary grids the developed rdg method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy efficiency robustness and versatility the numerical results indicate that this rdg method is able to deliver the same accuracy as the well known bassi rebay ii scheme at a half of its computing costs for the discretization of the viscous fluxes in the navier stokes equations clearly demonstrating its superior performance over the existing dg methods for solving the compressible navier stokes equations

arbitrary high order discontinuous galerkin schemes based on the grp method for compressible euler equations combined with the discontinuous galerkin dg framework the generalized riemann problem grp method is applied to design a grp dg scheme with high order accuracy for compressible euler equations since numerical fluxes with second order accuracy in time are derived by the grp method the reconstruction steps for physical variables in the new scheme are halved compared with the traditional runge kutta discontinuous galerkin rk dg scheme the numerical results are also improved due to more introduced physical information several numerical examples verify the validity of the proposed schemes

equivalence of surface density and average directional density the average directional density criteria for evaluating tilings is shown to be equivalent to surface density and valid for random broken paths just as for straight paths

a hybridizable discontinuous galerkin method for stokes flow abstract in this paper we introduce a hybridizable discontinuous galerkin method for stokes flow the method is devised by using the discontinuous galerkin methodology to discretize a velocity pressure gradient formulation of the stokes system with appropriate choices of the numerical fluxes and by applying a hybridization technique to the resulting discretization one of the main features of this approach is that it reduces the globally coupled unknowns to the numerical trace of the velocity and the mean of the pressure on the element boundaries thereby leading to a significant reduction in the size of the resulting matrix moreover by using an augmented lagrangian method the globally coupled unknowns are further reduced to the numerical trace of the velocity only another important feature is that the approximations of the velocity pressure and gradient converge with the optimal order of k 1 in the l 2 norm when polynomials of degree k 0 are used to represent the approximate variables based on the optimal convergence of the hdg method we apply an element by element postprocessing scheme to obtain a new approximate velocity which converges with order k 2 in the l 2 norm for k 1 the postprocessing performed at the element level is less expensive than the solution procedure numerical results are provided to assess the performance of the method

optimal a priori error estimates for the hp version of the local discontinuous galerkin method for convection diffusion problems we study the convergence properties of the hp version of the local discontinuous galerkin finite element method for convection diffusion problems we consider a model problem in a one dimensional space domain we allow arbitrary meshes and polynomial degree distributions and obtain upper bounds for the energy norm of the error which are explicit in the mesh width h in the polynomial degree p and in the regularity of the exact solution we identify a special numerical flux for which the estimates are optimal in both h and p the theoretical results are confirmed in a series of numerical examples

local mass corrections for continuous pressure approximations of incompressible flow in this work we discuss a family of finite element discretizations for the incompressible stokes problem using continuous pressure approximations on simplicial meshes we show that after a simple and cheap correction the mass fluxes obtained by the considered schemes preserve local conservation on dual cells without reducing the convergence order this allows the direct coupling to vertex centered finite volume discretizations of transport equations further we can postprocess the mass fluxes independently for each dual box to obtain an elementwise conservative velocity approximation of optimal order that can be used in cell centered finite volume or discontinuous galerkin schemes numerical examples for stable and stabilized methods are given to support our theoretical findings moreover we demonstrate the coupling to vertex and cell centered finite volume methods for advective transport

discontinuous galerkin methods for friedrichs systems part iii multifield theories with partial coercivity this paper is the third and last part of a work attempting to give a unified analysis of discontinuous galerkin methods the purpose of this paper is to extend the framework that has been developed in part ii for two field friedrichs systems associated with second order pdes we now consider two field friedrichs systems with partial l 2 coercivity and three field friedrichs systems with an even weaker l 2 coercivity hypothesis in particular this work generalizes the discontinuous galerkin methods of part ii to compressible and incompressible linear continuum mechanics we also show how the stabilizing parameters of the method must be set when the two field friedrichs system is composed of terms that may be of different magnitude thus accounting for instance for advection diffusion equations at high peclet numbers

analysis of hdg methods for stokes flow in this paper we analyze a hybridizable discontinuous galerkin method for numerically solving the stokes equations the method uses polynomials of degree k for all the components of the approximate solution of the gradient velocity pressure formulation the novelty of the analysis is the use of a new projection tailored to the very structure of the numerical traces of the method it renders the analysis of the projection of the errors very concise and allows us to see that the projection of the error in the velocity superconverges as a consequence we prove that the approximations of the velocity gradient the velocity and the pressure converge with the optimal order of convergence of k 1 in l 2 for any k 0 moreover taking advantage of the superconvergence properties of the velocity we introduce a new element by element postprocessing to obtain a new velocity approximation which is exactly divergence free h div conforming and converges with order k 2 for k 1 and with order 1 for k 0 numerical experiments are presented which validate the theoretical results

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

an algorithm for piecewise linear approximation of an implicitly defined manifold a simplicial method is used to approximate the solution manifold to a system of nonlinear equations h x theta where h mathbb r n k to mathbb r n the method begins at a point x 0 in the solution set where the derivative dh x 0 is of full rank given any varepsilon 0 a piecewise linear manifold is constructed along which h x infty varepsilon an algorithm is presented to carry out this construction in an efficient fashion

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

the derivation of hybridizable discontinuous galerkin methods for stokes flow in this paper we introduce a new class of discontinuous galerkin methods for the stokes equations the main feature of these methods is that they can be implemented in an efficient way through a hybridization procedure which reduces the globally coupled unknowns to certain approximations on the element boundaries we present four ways of hybridizing the methods which differ by the choice of the globally coupled unknowns classical methods for the stokes equations can be thought of as limiting cases of these new methods

an a posteriori error analysis of an augmented discontinuous galerkin formulation for darcy flow in this paper we develop an a posteriori error analysis for an augmented discontinuous garlerkin formulation applied to the darcy flow more precisely we derive a reliable and efficient a posteriori error estimator which consists of residual terms finally we present several numerical experiments showing the robustness of the method and the theoretical properties of the estimator thus confirming the capability of the corresponding adaptive algorithms to localize the inner layers the singularities and or the large stress regions of the exact solution

cross validation and the estimation of conditional probability densities many practical problems especially some connected with forecasting require nonparametric estimation of conditional densities from mixed data for example given an explanatory data vector x for a prospective customer with components that could include the customer s salary occupation age sex marital status and address a company might wish to estimate the density of the expenditure y that could be made by that person basing the inference on observations of x y for previous clients choosing appropriate smoothing parameters for this problem can be tricky not in the least because plug in rules take a particularly complex form in the case of mixed data an obvious difficulty is that there exists no general formula for the optimal smoothing parameters more insidiously and more seriously it can be difficult to determine which components of x are relevant to the problem of conditional inference for example if the jth component of x is independent of y then that component is irrelevant to es

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

a robust numerical method for stokes equations based on divergence free h div finite element methods a computational method based on a divergence free h div approach is presented for the stokes equations in this article this method is designed to find velocity approximation in an exact divergence free subspace of the corresponding h div finite element space that is the continuity equation is strongly enforced a priori and the pressure is eliminated from the linear system in calculation a strength of this approach is that the saddle point problem for stokes equations is reduced to a symmetric positive definite problem in a subspace for which basis functions are readily available the resulting discrete system can then be solved by using existing sophisticated solvers the aim of this article is to demonstrate the efficiency and robustness of h div finite element methods for stokes equations the results not only confirm the existing theoretical results but also reveal additional advantages of the method in dealing with discontinuous boundary conditions

a discontinuous finite volume method for the stokes problems we develop a new discontinuous finite volume method for solving the stokes equations on both triangular and rectangular meshes an optimal error estimate for the approximation of velocity is obtained in a mesh dependent norm first order l 2 error estimates are derived for the approximations of both velocity and pressure

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