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

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 the spectral expansion of hyperbolic eisenstein series in this article we determine the spectral expansion meromorphic continuation and location of poles with identifiable singularities for the scalar valued hyperbolic eisenstein series similar to the form valued hyperbolic eisenstein series studied in kudla and millson invent math 54 193 211 1979 the scalar valued hyperbolic eisenstein series is defined for each primitive hyperbolic conjugacy class within the uniformizing group associated to any finite volume hyperbolic riemann surface going beyond the results in kudla and millson invent math 54 193 211 1979 and risager int math res not 41 2125 2146 2004 we establish a precise spectral expansion for the hyperbolic eisenstein series for any finite volume hyperbolic riemann surface by first proving that the hyperbolic eisenstein series is in l2 our other results such as meromorphic continuation and determination of singularities are derived from the spectral expansion

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

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

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

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

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

analytic torsion for surfaces with cusps i compact perturbation theorem and anomaly formula we define the analytic torsion associated with a riemann surface endowed with a metric having poincare type singularities in the neighborhood of a finite number of points and a hermitian vector bundle with at most logarithmic singularities at those points coming from the metric on the negative power of the canonical line bundle twisted by the divisor of the points then we provide a relation between this analytic torsion and the ray singer analytic torsion of the compactified surface from this relation we then establish the anomaly formula which describes how the analytic torsion changes under the change of the metric on the surface and on the vector bundle

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

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

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

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 burghelea friedlander kappeler gluing formula for zeta determinants on a warped product manifold and a product manifold the burghelea friedlander kappeler bfk gluing formula for the regularized zeta determinants of laplacians contains a constant which is expressed by the constant term in the asymptotic expansion of the regularized zeta determinants of a one parameter family of the dirichlet to neumann operators when the dimension of a cutting hypersurface is odd or the metric is a product one near a cutting hypersurface this constant is well known in this paper we discuss this constant in two cases one is when a warped product metric is given near a cutting hypersurface and the other is when a manifold is a product manifold especially in the first case we use the result of fucci and kirsten commun math phys 317 635 665 2013 in which the regularized zeta determinant of the laplacian defined on a warped product manifold is computed

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

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

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

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

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

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

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

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

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

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

deriving ultrametric tree structures from proximity data confounded by differential stimulus familiarity this paper presents a new procedure called treefam for estimating ultrametric tree structures from proximity data confounded by differential stimulus familiarity the objective of the proposed treefam procedure is to quantitatively filter out the effects of stimulus unfamiliarity in the estimation of an ultrametric tree a conditional alternating maximum likelihood procedure is formulated to simultaneously estimate an ultrametric tree under the unobserved condition of complete stimulus familiarity and subject specific parameters capturing the adjustments due to differential unfamiliarity we demonstrate the performance of the treefam procedure under a variety of alternative conditions via a modest monte carlo experimental study an empirical application provides evidence that the treefam outperforms traditional models that ignore the effects of unfamiliarity in terms of superior tree recovery and overall goodness of fit

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

on the asymptotics of determinant of laplacian at the principal boundary of the principal stratum of the moduli space of abelian differentials let x be a translation surface of genus g 1 with 2g 2 conical points of angle 4 and let be two homologous saddle connections of length s joining two conical points of x and bounding two surfaces s and s with boundaries s and s gluing the opposite sides of the boundary of each surface s s one gets two closed translation surfaces x x of genera g g g g g let and be the friedrichs extensions of the laplacians corresponding to the flat conical metrics on x x and x respectively we study the asymptotical behavior of the modified i e with zero modes excluded zeta regularized determinant det as and shrink we find the asymptotics

asymptotics of the spectrum and the selberg zeta function on the space of riemann surfaces letz s r be the selberg zeta function of a compact riemann surfacer we study the behavior ofz s r asr tends to infinity in the moduli space of stable curves the main result is an estimate forz s r valid fors in a neighborhood depending only on the genus ofs 1 our analysis gives an alternate proof of the belavin knizhnik double pole result 5

extremals of determinants of laplacians on etudie le determinant associe au laplacien en fonction de la metrique sur une surface donnee et en particulier ses valeurs extremes quand la metrique est bien restreinte

superconvergence of finite element approximations for the stokes problem by projection methods this paper derives a general superconvergence result for finite element approximations of the stokes problem by using projection methods proposed and analyzed recently by wang j math study 33 2000 pp 229 243 for the standard galerkin method the superconvergence result is based on some regularity assumption for the stokes problem and is applicable to any finite element method with regular but nonuniform partitions the method is proved to give a convergent scheme for certain finite element spaces which fail to satisfy the well known uniform inf sup condition of brezzi and babuska

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

surfaces with boundary their uniformizations determinants of laplacians and isospectrality let be a compact surface of type g n n 0 obtained by re moving n disjoint disks from a closed surface of genus g assuming 0 while osgood phillips and sarnak o p s3 showed the properness when g 0

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

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 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

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 nonspatial methodology for the analysis of two way proximity data incorporating the distance density hypothesis this paper presents a nonspatial operationalization of the krumhansl 1978 1982 distancedensity model of similarity this model assumes that the similarity between two objectsi andj is a function of both the interpoint distance betweeni andj and the density of other stimulus points in the regions surroundingi andj we review this conceptual model and associated empirical evidence for such a specification a nonspatial tree fitting methodology is described which is sufficiently flexible to fit a number of competing hypotheses of similarity formation a sequential unconstrained minimization algorithm is technically presented together with various program options three applications are provided which demonstrate the flexibility of the methodology finally extensions to spatial models three way analyses and hybrid models are discussed

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

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

convergence of the normalized spectral counting function on degenerating hyperbolic riemann surfaces of finite volume abstract in this paper we study spectral asymptotics of degenerating families of hyperbolic riemann surfaces either compact or non compact but always of finite volume we prove that the second integral of the spectral counting function has an asymptotic expansion out to o l where l is the degeneration parameter the first term in the expansion is a diverging term which depends solely on the degeneration parameter and the counting parameters and the second term is the second integral of the spectral counting function of the limit surface

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

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

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

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

superconvergence in finite element methods and meshes that are locally symmetric with respect to a point consider a second order elliptic boundary value problem in any number of space dimensions with locally smooth coefficients and solution consider also its numerical approximation by standard conforming finite element methods with for example fixed degree piecewise polynomials on a quasi uniform mesh family the h method it will be shown that if the finite element function spaces are locally symmetric about a point x 0 with respect to the antipodal map x to x 0 x x 0 then superconvergence ensues at xo under mild conditions on what happens outside a neighborhood of x 0 for piecewise polynomials of even degree superconvergence occurs in function values for piecewise polynomials of odd degree it occurs in derivatives