an analysis of the time integration algorithms for the finite element solutions of incompressible navier stokes equations based on a stabilised formulation abstract this work is concerned with the analysis of time integration procedures for the stabilised finite element formulation of unsteady incompressible fluid flows governed by the navier stokes equations the stabilisation technique is combined with several different implicit time integration procedures including both finite difference and finite element schemes particular attention is given to the generalised method and the linear discontinuous in time finite element scheme the time integration schemes are first applied to two model problems represented by a first order differential equation in time and the one dimensional advection diffusion equation and subjected to a detailed mathematical analysis based on the fourier series expansion in order to establish the accuracy and efficiency of the time integration schemes for the navier stokes equations a detailed computational study is performed of two standard numerical examples unsteady flow around a cylinder and flow across a backward facing step it is concluded that the semi discrete generalised method provides a viable alternative to the more sophisticated and expensive space time methods for simulations of unsteady flows of incompressible fluids governed by the navier stokes equations

stability of the fractional step t scheme for the nonstationary navier stokes equations stability and convergence analysis of the fractional step theta scheme for the navier stokes equations coupled with the finite element approximations is presented the solutions of the underlying stokes and burgers problems are described in detail the asymptotic solution obtained by the numerical stabilization is compared with the analytical solution of the lid driven cavity problem

an analysis of the prothero robinson example for constructing new dirk and row methods this note analyses the order reduction phenomenon of diagonally implicit runge kutta methods dirk methods and rosenbrock wanner methods row methods applied on the prothero robinson example new order conditions to reduce order reduction are derived and a new third order dirk and row method is created the new schemes are applied to the prothero robinson example and on the semi discretised incompressible navier stokes equations numerical examples show that the new methods have better convergence properties than comparable methods

implicit time discretization schemes for mixed least squares finite element formulations abstract this work is an extension of the ideas in averweg et al 2019 with the focus on a detailed investigation of implicit time discretization schemes to model instationary fluid flow based on the incompressible navier stokes equations and linear elastodynamic structural behavior the variational approaches for fluid and solid mechanics are based on a mixed least squares finite element method the l 2 norm minimization of the residuals of the constructed first order systems of the governing differential equations is based on two field stress velocity sv functionals for the time discretization of the sv fluid formulation four different types of implicit integration schemes are investigated namely the houbolt method the crank nicolson method and two explicit singly diagonally implicit runge kutta methods esdirk the sv formulation for the solid is discretized applying the houbolt method the presented time integration schemes are validated investigating an unsteady fluid flow and an elastodynamic structural benchmark since both fluid and solid sv formulations are discretized using conforming finite element spaces in h div and h 1 respectively the inherent fulfillment of coupling conditions when modeling fluid structure interaction problems is given a priori therefore the applicability is also examined by two simplified fsi problems for small deformations in order to represent the main characteristics of the presented approach

on the classification of subalgebras of cendn and gcn the problem of classification of infinite subalgebras of cendn and of gcn that acts irreducibly on c n is discussed in this paper

rosenbrock methods for partial differential equations and fractional orders of convergence the authors apply rosenbrock methods for the solution of initial value problems for linear partial differential equations u t x t mathcal l x partial u x t f x t under weak assumptions on the operator mathcal l and the source function f a sharp lower bound for the order of convergence of these numerical methods is given it is further shown that the order of convergence is in general fractional it depends on the l r norm used to estimate the global error this analysis also applies to systems arising from spatial discretization of partial differential equations by finite differences or finite element techniques numerical examples illustrate the results

irreducible modules over finite simple lie pseudoalgebras ii primitive pseudoalgebras of type k abstract one of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a lie conformal algebra a lie pseudoalgebra is a generalization of the notion of a lie conformal algebra for which c is replaced by the universal enveloping algebra h of a finite dimensional lie algebra the finite i e finitely generated over h simple lie pseudoalgebras were classified in our previous work bakalov et al 2001 2 the present paper is the second in our series on representation theory of simple lie pseudoalgebras in the first paper we showed that any finite irreducible module over a simple lie pseudoalgebra of type w or s is either an irreducible tensor module or the kernel of the differential in a member of the pseudo de rham complex in the present paper we establish a similar result for lie pseudoalgebras of type k with the pseudo de rham complex replaced by a certain reduction called the contact pseudo de rham complex this reduction in the context of contact geometry was discovered by rumin

adaptive time step control for the incompressible navier stokes equations abstract adaptive time stepping is an important tool in computational fluid dynamics for controlling the accuracy of simulations and for enhancing their efficiency this paper presents a systematic study of three classes of implicit and linearly implicit time stepping schemes with adaptive time step control applied to a 2d laminar flow around a cylinder schemes diagonal implicit runge kutta dirk methods and rosenbrock wanner row methods the time step is controlled using embedded methods it is shown that several row methods clearly outperform the more standard schemes and the dirk methods the results depend on a prescribed tolerance in the time step control algorithm whose appropriate choice varies from scheme to scheme

effects of degradation of intensity time or frequency content on speech intelligibility for normal hearing and hearing impaired listeners many hearing impaired listeners suffer from distorted auditory processing capabilities this study examines which aspects of auditory coding i e intensity time or frequency are distorted and how this affects speech perception the distortion sensitivity model is used the effect of distorted auditory coding of a speech signal is simulated by an artificial distortion and the sensitivity of speech intelligibility to this artificial distortion is compared for normal hearing and hearing impaired listeners stimuli speech plus noise are wavelet coded using a complex sinusoidal carrier with a gaussian envelope 14 octave bandwidth intensity information is distorted by multiplying the modulus of each wavelet coefficient by a random factor temporal and spectral information are distorted by randomly shifting the wavelet positions along the temporal or spectral axis respectively measured were 1 detection thresholds for each type of distortion and 2 speech reception thresholds for various degrees

relations between frequency selectivity temporal fine structure processing and speech reception in impaired hearing frequency selectivity temporal fine structure tfs processing and speech reception were assessed for six normal hearing nh listeners ten sensorineurally hearing impaired hi listeners with similar high frequency losses and two listeners with an obscure dysfunction od tfs processing was investigated at low frequencies in regions of normal hearing through measurements of binaural masked detection tone lateralization and monaural frequency modulation fm detection lateralization and fm detection thresholds were measured in quiet and in background noise speech reception thresholds were obtained for full spectrum and lowpass filtered sentences with different interferers both the hi listeners and the od listeners showed poorer performance than the nh listeners in terms of frequency selectivity tfs processing and speech reception while a correlation was observed between the monaural and binaural tfs processing deficits in the hi listeners no relation was found between tfs processing and frequency selectivity the effect of noise on tfs processing was not larger for the hi listeners than for the nh listeners finally tfs processing performance was correlated with speech reception in a two talker background and lateralized noise but not in amplitude modulated noise the results provide constraints for future models of impaired auditory signal processing

adaptive time step control for higher order variational time discretizations applied to convection diffusion reaction equations abstract higher order variational time stepping schemes allow an efficient post processing for computing a higher order solution this paper presents an adaptive algorithm whose time step control utilizes the post processed solution the algorithm is applied to convection dominated convection diffusion reaction equations it is shown that the length of the time step properly reflects the dynamics of the solution with respect to the performance accuracy efficiency the variational time stepping schemes are compared with an adaptive crank nicolson scheme whose time step control relies on comparing two solutions computed with schemes of the same order

on conformal bialgebras abstract we study conformal algebras from the point of view of conformal dual of classical lie coalgebra structures we define the notions of lie conformal coalgebra and bialgebra we obtain a conformal analog of the cybe the manin triples and drinfeld s double with the definition of vertex duals we obtain a natural description of the lie algebra associated to a conformal algebra as a convolution algebra clarifying the classical constructions in the theory of conformal algebras and vertex algebras

leibniz h pseudoalgebras abstract we define a leibniz h pseudoalgebra over a cocommutative hopf algebra h and a tensor product of leibniz h pseudoalgebras and prove that every leibniz h pseudoalgebra of free rank one over h is a lie h pseudoalgebra to characterize simple leibniz h pseudoalgebras we define the leibniz cohomology of leibniz h pseudoalgebras and determine some simple leibniz h pseudoalgebras by calculating leibniz cohomological groups of finite simple lie h pseudoalgebras defined in 2

γ conformal algebras conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points we classify these algebras and their representations in terms of lie algebras and their representations with an action of the group to every conformal algebra and a character of we associate a lie algebra generated by fields with the ope with simple poles examples include twisted affine kac moody algebras the sin algebra which is a conformal analogue of the general linear algebra and its analogues the algebra of pseudodifferential operators on the circle etc

improved traditional rosenbrock wanner methods for stiff odes and daes rosenbrock wanner methods usually have order reduction if they are applied to stiff ordinary differential or differential algebraic equations therefore in several papers further order conditions are derived to reduce this effect in rang 2014 the example of prothero and robinson 1974 is analysed to find further order conditions in this paper we consider traditional row methods such as ros3p lang and verwer 2001 ros3pw rang and angermann 2005 ros3pl lang and teleaga 2008 and rodasp steinebach 1995 and improve these methods such that these further order conditions are satisfied numerical examples show the advantages of the new methods

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

cohomology of conformal algebras the notion of a conformal algebra encodes an axiomatic description of the operator product expansion of chiral fields in conformal field theory on the other hand it is an adequate tool for the study of infinite dimensional lie algebras satisfying the locality property the main examples of such lie algebras are those based on the punctured complex plane such as the virasoro algebra and loop lie algebras in the present paper we develop a cohomology theory of conformal algebras with coefficients in an arbitrary module it possesses standards properties of cohomology theories for example it describes extensions and deformations we offer explicit computations for the most important examples

on the impact of the scheme for solving the higher dimensional equation in coupled population balance systems summary population balance systems are models for processes in nature and industry that lead to a coupled system of equations navier stokes equations transport equations etc where the equations are defined in domains with different dimensions this paper will study the impact of using different schemes for solving the three dimensional 3d equation of a precipitation process in a two dimensional flow domain the numerical schemes for the 3d equation are assessed with respect to the median of the volume fraction of the particle size distribution and the computational costs it turns out that in the case of a structured flow field with small variations in time all schemes give qualitatively the same results for a highly timedependent flow field the evolution of the median of the volume fraction differs considerably between first order and higher order schemes copyright q 2010 john wiley sons ltd

pressure corrected implicit θ schemes for the incompressible navier stokes equations abstract in this note the crank nicolson and the fractional step scheme are applied on the semi discretised incompressible navier stokes equations in a first step the formulation of the methods is modified such that the methods have optimal order for the pressure p i e the pressure p 0 is included in the scheme the main idea of this paper is that the fractional step scheme can be written as a diagonally implicit runge kutta method dirk method in this context it can easily be shown that the fractional step schemes have only stage order q 1 whereas the crank nicolson scheme has stage order q 2 hence the fractional step scheme may have order reduction if the method is applied on stiff odes and daes i e the semi discretised incompressible navier stokes equations some theoretical results and numerical examples illustrate this phenomena moreover it is shown that it is impossible to improve the fractional step method such that the scheme has the stage order q 2 and is strongly a stable or has the order p 3

a variational multiscale method for turbulent flow simulation with adaptive large scale space in turbulent flows it is only feasible to simulate large flow structures variational multiscale vms methods define these flow structures by projections onto appropriate function spaces this paper presents a finite element vms method which chooses the large scale projection space adaptively the adaption controls the influence of an eddy viscosity model and it is based on the size of the so called resolved small scales the adaptive procedure is described in detail numerical studies at a turbulent channel flow and a turbulent flow around a cylinder are presented it is shown that the method selects the large scale space in a reasonable way and that appropriately chosen parameters improve the results compared to the basic method which uses the same local large scale space in the whole domain and for all times

finite element approximations of the nonstationary navier stokes problem part iv error estimates for second order time discretization this paper provides an error analysis for the crank nicolson method of time discretization applied to spatially discrete galerkin approximations of the nonstationary navier stokes equations second order error estimates are proven locally in time under realistic assumptions about the regularity of the solution for approximations of an exponentially stable solution these local error estimates are extended uniformly in time as text t to infty

frequency discrimination of complex signals frequency selectivity and speech perception in hearing impaired subjects frequency discrimination of spectral envelopes of complex stimuli frequency selectivity measured with psychophysical tuning curves and speech perception were determined in hearing impaired subjects each having a relatively flat sensory neural loss both the frequency discrimination and speech perception measures were obtained in quiet and noise most of these subjects showed abnormal susceptibility to ambient noise with regard to speech perception frequency discrimination in quiet and frequency selectivity did not correlate significantly at low signal to noise ratios frequency discrimination correlated significantly with frequency selectivity speech perception in noise correlated significantly with frequency selectivity and with frequency discrimination at low signal to noise ratios the frequency discrimination data are discussed in terms of an excitation pattern model however they neither support nor refute the model

finite element les and vms methods on tetrahedral meshes finite element methods for problems given in complex domains are often based on tetrahedral meshes this paper demonstrates that the so called rational large eddy simulation model and a projection based variational multiscale method can be extended in a straightforward way to tetrahedral meshes numerical studies are performed with an inf sup stable second order pair of finite elements with discontinuous pressure approximation

a comparison of time discretization linearization approaches for the incompressible navier stokes equations abstract this paper presents a numerical study of two ways for discretizing and linearizing the time dependent incompressible navier stokes equations one approach consists in first applying a semi discretization in time by a fully implicit scheme then in each discrete time the equations are linearized by a fixed point iteration the number of iterations to reach a given stopping criterion is a priori unknown in this approach in the second approach rosenbrock schemes with s stages are used as temporal discretization the non linearity of the navier stokes equations is treated internally in the rosenbrock methods in each discrete time exactly s linear systems of equations have to be solved the numerical study considers five two dimensional problems with distinct features four implicit time stepping schemes and five rosenbrock methods are involved

a spectral deferred correction method for incompressible flow with variable viscosity abstract this paper presents a semi implicit spectral deferred correction sdc method for incompressible navier stokes problems with variable viscosity and time dependent boundary conditions the proposed method integrates elements of velocity and pressure correction schemes which yields a simpler pressure handling and a smaller splitting error than the sdpc method of minion and saye j comput phys 375 797 822 2018 combined with the discontinuous galerkin spectral element method for spatial discretization it can in theory reach arbitrary order of accuracy in time and space numerical experiments in three space dimensions demonstrate up to order 12 in time and 17 in space for constant as well as varying solution dependent viscosity compared to sdpc the present method yields a substantial improvement of accuracy and robustness against order reduction caused by time dependent boundary conditions

stability and convergence of the numerical solution for the species equation of a model for pemfcs abstract many mathematical models for fuel cells are presented in the literature however few studies of numerical analysis of these models are found the novelty of this work is the proof of stability and convergence of the equation of chemical species providing greater reliability to the mathematical model in this work a mathematical model is proposed that calculates the flow and concentration of species for proton exchange membrane fuel cells using the finite element method for spatial discretization and the crank nicolson method for temporal discretization the model takes into account the losses overpotentials at the anode and at the cathode the numerical results confirm the proof of convergence which is demonstrated in this work finally a numerical result is shown for the fuel cell power relative to current density and the result has good relation with the experimental data

on pseudo bialgebras abstract we study pseudoalgebras from the point of view of pseudo dual of classical lie coalgebra structures we define the notions of lie h coalgebra and lie pseudo bialgebra we obtain the analog of the cybe the manin triples and drinfeld s double for lie pseudo bialgebras we also get a natural description of the annihilation algebra associated to a pseudoalgebra as a convolution algebra clarifying this construction in the theory of pseudoalgebras

numerical studies of finite element variational multiscale methods for turbulent flow simulations different realizations of variational multiscale vms methods within the framework of finite element methods are studied in turbulent channel flow simulations one class of vms methods uses bubble functions to model resolved small scales whereas the other class contains the definition of the resolved small scales by an explicit projection in its set of equations all methods are employed with eddy viscosity models of smagorinsky type the simulations are performed on grids for which a direct numerical simulation blows up in finite time

a local projection stabilization continuous galerkin petrov method for incompressible flow problems abstract a local projection stabilization lps method in space is considered to approximate the evolutionary oseen equations optimal error bounds with constants independent of the viscosity parameter are obtained in the continuous in time case for both the velocity and pressure approximation in addition the fully discrete case in combination with higher order continuous galerkin petrov cgp methods is studied error estimates of order k 1 are proved where k denotes the polynomial degree in time assuming that the convective term is time independent numerical results show that the predicted order is also achieved in the general case of time dependent convective terms

numerical methods for nonlinear second order hyperbolic partial differential equations ii rothe s techniques for 1 d problems abstract two families of rothe s methods that are based on the discretization of the time variable and keeping the spatial one continuous for the solution of second order hyperbolic equations with damping and nonlinear source terms are presented the first family is based on time integration and results in a volterra integro differential equation which upon approximating certain time integrals can be written as an ordinary differential equation in space upon discretizing the spatial derivatives by means of finite difference formula this family results in nonlinear algebraic equations which contain exponential terms that depend on the time step and its accuracy is shown to be lower than that of an explicit second order accurate discretization in both space and time of second order hyperbolic equations the second family of methods is based on the discretization of the time derivatives and time linearization and results in linear ordinary differential equations in space upon freezing the coefficients of these equations one can integrate analytically the resulting linear ordinary differential equations to obtain piecewise exponential solutions which are continuous in space and three point finite difference equations which depend exponentially on the time step spatial grid size and the diffusion relaxation damping and reaction times the finite difference equations are shown to result in non diagonally dominant matrices unless the time step is smaller than the characteristic relaxation diffusion damping and reaction times to avoid this problem two rothe s techniques that do not account for the jacobian of the reaction terms in the ordinary differential operator are developed and it is shown that the rothe s techniques belonging to the second family are as accurate as the linearly implicit methods presented in part i provided that the relaxation time is smaller than the critical time and the solution does not oscillate in space when the relaxation time is greater than the critical one rothe s methods have been found to be less accurate than the finite difference techniques of part i the rothe s techniques belonging to the second family are generalized to systems of nonlinear second order hyperbolic equations and mixed systems of parabolic and second order hyperbolic partial differential equations