accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

the accuracy of the fractional step method we analyze the accuracy of the fractional step method of kim and moin j comput phys 59 1985 pp 308 323 for the incompressible navier stokes equations we show that the boundary conditions cannot be exactly satisfied in the projection step and that this limits the accuracy of the method we also show that the pressure in any projection method can be at best first order accurate our analysis is simpler and more direct than the previous analyses of this method we also show that there is no numerical boundary layer for velocity or pressure but there is one for the auxiliary pressure variable

on error estimates of the projection methods for the navier stokes equations second order schemes we present in this paper a rigorous error analysis of several projection schemes for the approximation of the unsteady incompressible navier stokes equations the error analysis is accomplished by interpreting the respective projection schemes as second order time discretizations of a perturbed system which approximates the navier stokes equations numerical results in agreement with the error analysis are also presented

regularity of the maxwell equations in heterogeneous media and lipschitz domains abstract this note establishes regularity estimates for the solution of the maxwell equations in lipschitz domains with non smooth coefficients and minimal regularity assumptions the argumentation relies on elliptic regularity estimates for the poisson problem with non smooth coefficients

the c algebras of finitely aligned higher rank graphs we generalise the theory of cuntz krieger families and graph algebras to the class of finitely aligned k graphs this class contains in particular all row finite k graphs the cuntz krieger relations for non row finite k graphs look significantly different from the usual ones and this substantially complicates the analysis of the graph algebra we prove a gauge invariant uniqueness theorem and a cuntz krieger uniqueness theorem for the c algebras of finitely aligned k graphs

on the error estimates for the rotational pressure correction projection methods in this paper we study the rotational form of the pressure correction method that was proposed by timmermans minev and van de vosse we show that the rotational form of the algorithm provides better accuracy in terms of the h1 norm of the velocity and of the l2 norm of the pressure than the standard form

affine buildings tiling systems and higher rank cuntz krieger algebras to an r dimensional subshift of finite type satisfying certain special properties we associate a c algebra a this algebra is a higher rank version of a cuntz krieger algebra in particular it is simple purely infinite and nuclear we study an example if is a group acting freely on the vertices of an a2 building with finitely many orbits and if is the boundary of that building then c o is the algebra associated to a certain two dimensional subshift

approximation of the eigenvalue problem for the time harmonic maxwell system by continuous lagrange finite elements we propose and analyze an approximation technique for the maxwell eigenvalue problem using h1 conforming finite elements the key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional sobolev space h with 1 2 1 the method is shown to be convergent and spectrally correct

analysis of the three dimensional tongue shape using a three index factor analysis model three dimensional tongue shape during vowel production is analyzed using the three mode parafac parallel factors model three dimensional mri images of five speakers 9 vowels are analyzed sixty five virtual fleshpoints 13 segments along the rostral caudal dimension and 5 segments along the right left direction are chosen based on the interpolated tongue shape images methods used to adjust the alignment of mri images to set up the fleshpoints and to measure the position of the fleshpoints are presented parafac analysis of this 3d coordinate data results in a stable two factor solution that explains about 70 of the variance

projection method i convergence and numerical boundary layers this is the first of a series of papers on the subject of projection methods for viscous incompressible flow calculations the purpose of these papers is to provide a thorough understanding of the

a nodal based finite element approximation of the maxwell problem suitable for singular solutions a new mixed finite element approximation of maxwell s problem is proposed its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term which yields a very weak control on the divergence of the unknown the method is shown to be stable and convergent in the natural h rm mathbf curl 0 omega norm for this unknown in particular convergence also applies to singular solutions for which classical nodal based interpolations are known to suffer from spurious convergence upon mesh refinement

synergistic modes of vocal tract articulation for american english vowels the purpose of this study was to investigate the spatial similarity of vocal tract shaping patterns across speakers and the similarity of their acoustic effects vocal tract area functions for 11 american english vowels were obtained from six speakers three female and three male using magnetic resonance imaging mri each speaker s set of area functions was then decomposed into mean area vectors and representative modes eigenvectors using principal components analysis pca three modes accounted for more than 90 of the variance in the original data sets for each speaker the general shapes of the first two modes were found to be highly correlated across all six speakers to demonstrate the acoustic effects of each mode both in isolation and combined a mapping between the mode scaling coefficients and f1 f2 pairs was generated for each speaker the mappings were unique for all six speakers in terms of the exact shape of the f1 f2 vowel space but the general effect of the modes was the same

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

primitive ideal space of higher rank graph c algebras and decomposability abstract in this paper we describe primitive ideal space of the c algebra c associated to any locally convex row finite k graph to do this we will apply the farthing s desourcifying method on a recent result of carlsen kang shotwell and sims we also characterize certain maximal ideals of c furthermore we study the decomposability of c we apply the description of primitive ideals to show that if i is a direct summand of c then it is gauge invariant and isomorphic to a certain k graph c algebra so we may characterize decomposable higher rank c algebras by giving necessary and sufficient conditions for the underlying k graphs moreover we determine all such c algebras which can be decomposed into a direct sum of finitely many indecomposable c algebras

technique for tuning vocal tract area functions based on acoustic sensitivity functions a technique for modifying vocal tract area functions is developed by using sum and difference combinations of acoustic sensitivity functions to perturb an initial vocal tract configuration first sensitivity functions e g fant and pauli proc speech comm sem 74 1975 are calculated for a given area function at its specific formant frequencies the sensitivity functions are then multiplied by scaling coefficients that are determined from the difference between a desired set of formant frequencies and those supported by the current area function the scaled sensitivity functions are then summed together to generate a perturbation of the area function this produces a new area function whose associated formant frequencies are closer to the desired values than the previous one this process is repeated iteratively until the coefficients are equal to zero or are below a threshold value

a comparison of vocal tract perturbation patterns based on statistical and acoustic considerations the purpose of this study was to investigate the relation between vocal tract deformation patterns obtained from statistical analyses of a set of area functions representative of a vowel repertoire and the acoustic properties of a neutral vocal tract shape acoustic sensitivity functions were calculated for a mean area function based on seven different speakers specific linear combinations of the sensitivity functions corresponding to the first two formant frequencies were shown to possess essentially the same amplitude variation along the vocal tract length as the statistically derived deformation patterns reported in previous studies

on error estimates of projection methods for navier stokes equations first order schemes in this paper projection methods or fractional step methods are studied in the semi discretized form for the navier stokes equations in a two or three dimensional bounded domain error estimates for the velocity and the pressure of the classical projection scheme are established via the energy method a modified projection scheme which leads to improved error estimates is also proposed

error analysis of fully discrete velocity correction methods for incompressible flows a fully discrete version of the velocity correction method proposed by guermond and shen 2003 for the time dependent navier stokes equations is introduced and analyzed it is shown that when accounting for space discretization additional consistency terms which vanish when space is not discretized have to be added to establish stability and optimal convergence error estimates are derived for both the standard version and the rotational version of the method these error estimates are consistent with those by guermond and shen 2003 as far as time discretiztion is concerned and are optimal in space for finite elements satisfying the inf sup condition

unconditionally stable operator splitting algorithms for the incompressible magnetohydrodynamics system discretized by a stabilized finite element formulation based on projections summary in this article we propose different splitting procedures for the transient incompressible magnetohydrodynamics mhd system that are unconditionally stable we consider two levels of splitting on one side we perform the segregation of the fluid pressure and magnetic pseudo pressure from the vectorial fields computation at the second level the fluid velocity and induction fields are also decoupled this way we transform a fully coupled indefinite multi physics system into a set of smaller definite ones clearly reducing the cpu cost with regard to the finite element approximation we stick to an unconditionally convergent stabilized finite element formulation because it introduces convection stabilization allows to circumvent inf sup conditions clearly simplifying implementation issues and is able to capture non smooth solutions of the magnetic subproblem however residual based finite element formulations are not suitable for segregation because they lose the skew symmetry of the off diagonal blocks therefore in this work we have proposed a novel term by term stabilization of the mhd system based on projections that is still unconditionally convergent copyright 2012 john wiley sons ltd

a least squares finite element method using elsasser variables for magnetohydrodynamic equations abstract there are various different forms of magnetohydrodynamic mhd equations and they have been studied for years due to its complicated coupling between variables this paper proposes to use an equivalently transformed mhd equations with elsasser variables and the least squares finite element method to find the approximation to them introducing new variables by combining fluid velocity and magnetic field yields a navier stokes like system then the first order system least squares method using displacement recasts the transformed mhd equations into a system of first order partial differential equations and the newton s algorithm linearizes the problem an l 2 residual functional is defined to minimize and the unique existence of corresponding weak solution is shown finally the convergence of proposed approximation is analyzed and several numerical examples are presented to verify the theory

on the lingual organization of the german vowel system a hybrid parafac and principal component model of tongue configuration in vowel production is presented using a corpus of german vowels in multiple consonant contexts fleshpoint data for seven speakers at two speech rates from electromagnetic articulography the parafac approach is attractive for explicitly separating speaker independent and speaker dependent effects within a parsimonious linear model however it proved impossible to derive a parafac solution of the complete dataset estimated to require three factors due to complexities introduced by the consonant contexts accordingly the final model was derived in two stages first a two factor parafac model was extracted this succeeded the result was treated as the basic vowel model second the parafac model error was subjected to a separate principal component analysis for each subject this revealed a further articulatory component mainly involving tongue blade activity associated with the flanking consonants however the subject specific details of the mapping from raw fleshpoint coordinates to this component were too complex to be consistent with the parafac framework the final model explained over 90 of the variance and gave a succinct and physiologically plausible articulatory representation of the german vowel space

vowel and consonant contributions to vocal tract shape the purpose of this study was to develop a method by which a vowel consonant vowel vcv utterance based on x ray microbeam articulatory data could be separated into a vowel to vowel transition and a consonant superposition function the result is a model that represents a vowel sequence as a time dependent perturbation of the neutral vocal tract shape governed by coefficients of canonical deformation patterns consonants were modeled as superposition functions that can force specific portions of the vocal tract shape to be constricted or expanded over a specific time course the three vcvs p t and k produced by one female speaker were analyzed and reconstructed with the developed model they were shown to be reasonable approximations of the original vcvs as assessed qualitatively by visual inspection and quantitatively by calculating rms error and correlation coefficients this establishes a method for future modeling of other speech material

the primitive ideals of the cuntz krieger algebra of a row finite higher rank graph with no sources abstract we catalogue the primitive ideals of the cuntz krieger algebra of a row finite higher rank graph with no sources each maximal tail in the vertex set has an abelian periodicity group of finite rank at most that of the graph the primitive ideals in the cuntz krieger algebra are indexed by pairs consisting of a maximal tail and a character of its periodicity group the cuntz krieger algebra is primitive if and only if the whole vertex set is a maximal tail and the graph is aperiodic

an interface fitted subspace projection method for finite element simulations of particulate flows abstract a novel finite element method for the direct numerical simulation of particles in a newtonian carrier fluid is presented the proposed method is based on a fictitious or one domain formulation and a subspace projection method to account for the rigid body motion of the particles underlying equations are posed in an ale arbitrary lagrangian eulerian formulation allowing for moving computational meshes the mesh is adapted to the particles by a novel mesh smoothing approach guaranteeing both mesh optimality and a sharp representation of the particles boundaries we show that by using quadratic taylor hood finite elements for the discretization of the navier stokes equations and isoparametric elements to represent the geometry second order convergence with respect to the energy norm can be achieved as opposed to a sharp h 1 2 result which holds if no mesh adaptation is performed we present numerical examples in 2d confirming the theoretical convergence results furthermore we validate the approach by simulating the sedimentation process of a single particle and show the potential of the method by simulating a lid driven cavity flow with 100 particles

weighted regularization of maxwell equations in polyhedral domains we present a new method of regularizing time harmonic maxwell equations by a bf grad div term adapted to the geometry of the domain this method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions in the presence of reentrant corners or edges the usual regularization is known to produce wrong solutions due the non density of smooth fields in the variational space we get rid of this undesirable effect by the introduction of special weights inside the divergence integral standard finite elements can then be used for the approximation of the solution this method proves to be numerically efficient

on an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics in this work we propose a new stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations the novelty of this formulation is the fact that it always converges to the physical solution even for singular ones a detailed set of numerical experiments have been performed in order to validate our approach

velocity correction projection methods for incompressible flows we introduce and study a new class of projection methods namely the velocity correction methods in standard form and in rotational form for solving the unsteady incompressible navier stokes equations we show that the rotational form provides improved error estimates in terms of the h1 norm for the velocity and of the l2 norm for the pressure we also show that the class of fractional step methods introduced in s a orsag m israeli and m deville j sci comput 1 1986 pp 75 111 and k e karniadakis m israeli and s a orsag j comput phys 97 1991 pp 414 443 can be interpreted as the rotational form of our velocity correction methods thus to the best of our knowledge our results provide the first rigorous proof of stability and convergence of the methods in those papers we also emphasize that contrary to those of the above groups our formulations are set in the standard l2 setting and consequently they can be easily implemented by means of any variational approximation techniques in particular the finite element methods

a mixed finite element method with exactly divergence free velocities for incompressible magnetohydrodynamics abstract we introduce and analyze a mixed finite element method for the numerical discretization of a stationary incompressible magnetohydrodynamics problem in two and three dimensions the velocity field is discretized using divergence conforming brezzi douglas marini bdm elements and the magnetic field is approximated by curl conforming nedelec elements the h 1 continuity of the velocity field is enforced by a dg approach a central feature of the method is that it produces exactly divergence free velocity approximations and captures the strongest magnetic singularities we prove that the energy norm error is convergent in the mesh size in general lipschitz polyhedra under minimal regularity assumptions and derive nearly optimal a priori error estimates for the two dimensional case we present a comprehensive set of numerical experiments which indicate optimal convergence of the proposed method for two dimensional as well as three dimensional problems

nodal based finite element methods with local projection stabilization for linearized incompressible magnetohydrodynamics abstract we consider the linearized resistive magnetohydrodynamics mhd model in incompressible media and its numerical solution conforming nodal based finite element approximations of the mhd model both for inf sup stable and equal order finite elements with respect to velocity and pressure are considered as opposed to a residual based stabilization method by badia et al 2013 we consider a local projection stabilization for the numerical solution a detailed stability and error analysis for the arising discrete problem is given some numerical experiments like hartmann s mhd problem and singular solutions are examined

efficient spectral galerkin method i direct solvers of second and fourth order equations using legendre polynomials this paper presents some efficient algorithms based on the legendre galerkin approximations for the direct solution of the second and fourth order elliptic equations the key to the efficiency of these algorithms is to construct appropriate base functions which lead to systems with sparse matrices for the discrete variational formulations the complexities of the algorithms are a small multiple of n d 1 operations for a d dimensional domain with n 1 d unknowns while the convergence rates of the algorithms are exponential for problems with smooth solutions in addition the algorithms can be effectively parallelized since the bottlenecks of the algorithms are matrix matrix multiplications

projection method iii spatial discretization on the staggered grid in e liu siam j numer anal 1995 we studied convergence and the structure of the error for several projection methods when the spatial variable was kept continuous we call this the semi discrete case in this paper we address similar questions for the fully discrete case when the spatial variables are discretized using a staggered grid we prove that the numerical solution in velocity has full accuracy up to the boundary despite the fact that there are numerical boundary layers present in the semi discrete solutions