a preconditioner for the steady state navier stokes equations we present a new method for solving the sparse linear system of equations arising from the discretization of the linearized steady state navier stokes equations also known as the oseen equations the solver is an iterative method of krylov subspace type for which we devise a preconditioner through a heuristic argument based on the fundamental solution tensor for the oseen operator the preconditioner may also be conceived through a weaker heuristic argument involving differential operators computations indicate that convergence for the preconditioned discrete oseen problem is only mildly dependent on the viscosity inverse reynolds number and most importantly that the number of iterations does not grow as the mesh size is reduced indeed since the preconditioner is motivated through analysis of continuous operators the number of iterations decreases for smaller mesh size which accords with better approximation of these operators

parameterization of the glottal area glottal flow and vocal fold contact area a new set of parameters is described for analysis and synthesis of glottal area vocal fold contact area and glottal volume flow parameters are all nondimensionalized and consist of an abduction quotient a shape quotient a phase quotient and a load quotient in addition to fundamental frequency and vibrational amplitude the parameters show promise in interpretation of electroglottographic photoglottographic and inverse filtered volume velocity waveforms in terms of the glottal configuration some comparisons between modeled and measured glottographic waveforms are made

on the validity of the maximum principle and of the euler lagrange equation for a minimum problem depending on the gradient we consider the limiting case alpha infty of the problem of minimizing int omega nabla u x alpha g u dx hbox on u in u 0 w 1 alpha 0 omega where g is differentiable and strictly monotone if this infimum is finite it is evidently attained we show that any minimizing function u satisfies the appropriate form of the euler lagrange equation i e for some function p div p x g u x quad rm for quad p x in partial j b nabla u x where jb is the indicator function of the closed unit ball in the euclidean norm of bbb r n and partial is the subdifferential of the convex function jb

nearly round spheres look convex we prove that a riemannian manifold m g close enough to the round sphere in the c 4 topology has uniformly convex injectivity domains so m appears uniformly convex in any exponential chart the proof is based on the ma trudinger wang nonlocal curvature tensor which originates from the regularity theory of optimal transport

effects of vocal loudness variation on spectrum balance as reflected by the alpha measure of long term average spectra of speech the overall slope of long term average spectrum ltas decreases if vocal loudness increases therefore changes of vocal loudness also affects the alpha measure defined as the ratio of spectrum intensity above and below 1000 hz the effect on alpha of loudness variation was analyzed in 15 male and 16 female voices reading a text at different degrees of vocal loudness the mean range of equivalent sound level l eq amounted to about 28 db and the mean range of alpha to 19 0 and 11 7 db for the female and male subjects the l eq vs alpha relationship could be approximated with a quadratic function or by a linear equation if softest phonation was excluded using such equations alpha was computed for all values of l eq observed for each subject and compared with observed values the maximum and the mean absolute errors were 2 4 db and between 0 1 and 0 6 db when softest phonation was disregarded and linear equations were used the maximum error was less than 2 db and the mean absolute errors were between 0 2 and 0 7 db the strong correlation between l eq and alpha indicates that for a voice l eq can be used for predicting alpha

holder regularity of the normal distance with an application to a pde model for growing sandpiles given a bounded domain omega in mathbb r 2 with smooth boundary the cut locus overline sigma is the closure of the set of nondifferentiability points of the distance d from the boundary of omega the normal distance to the cut locus tau x is the map which measures the length of the line segment joining x to the cut locus along the normal direction dd x whenever x notin overline sigma recent results show that this map restricted to boundary points is lipschitz continuous as long as the boundary of omega is of class c 2 1 our main result is the global holder regularity of tau in the case of a domain omega with analytic boundary we will also show that the regularity obtained is optimal as soon as the set of the so called regular conjugate points is nonempty in all the other cases lipschitz continuity can be extended to the whole domain omega the above regularity result for tau is also applied to derive the holder continuity of the solution of a system of partial differential equations that arises in granular matter theory and optimal mass transfer

the distance function from the boundary of a domain with corners abstract we study the regularity of the distance function to the boundary of a domain in r 2 with respect to some asymmetric norms we allow the boundary of the domain to have corners we obtain an explicit formula for the second derivative of these distance functions furthermore we study a generalized notion of the ridge of a domain which is the set of singularities of a distance function to the boundary of the domain we completely characterize the ridge by using a generalized notion of curvature

a note on preconditioning for indefinite linear systems preconditioners are often conceived as approximate inverses for nonsingular indefinite matrices of saddle point or kkt form we show how preconditioners incorporating an exact schur complement lead to preconditioned matrices with exactly two or exactly three distinct eigenvalues thus approximations of the schur complement lead to preconditioners which can be very effective even though they are in no sense approximate inverses

the free boundary of variational inequalities with gradient constraints abstract in this paper we prove that the free boundary of the minimizer of i v u 1 2 d v 2 v d x subject to the pointwise gradient constraint d v p 1 is as regular as the tangent bundle of the boundary of the domain to this end we study a generalized notion of ridge of a domain in the plane which is the set of singularity of the distance function in the p norm to the boundary of the domain

effects of subglottal pressure variation on professional baritone singers voice sources five professional operatic baritone singers voice source characteristics were analyzed by means of inverse filtering of the flow signal as captured by a flow mask the subjects sang a long sustained diminuendo from loudest to softest three times on the vowels a and ae at fundamental frequencies representing 25 50 and 75 of their total pitch range as measured in semitones during the diminuendos they repeatedly inserted the consonant p so that associated subglottal pressures could be estimated from the oral pressure during the p occlusions pooling the three takes of each condition ten subglottal pressures equidistantly spaced between highest and lowest were selected for analysis sound pressure levels spl peak to peak glottal airflow maximum flow declination rate closed quotient glottal dc flow and the level difference between the two lowest partials of the source spectrum h1 h2 were determined all parameters except the glottal dc flow showed a systematic variation with subglottal pressure or the fractional excess pressure over threshold the results are given in terms of equations representing the average across subjects for the relation between subglottal pressure and each of the mentioned voice source parameters

effects of bandwidth on glottal airflow waveforms estimated by inverse filtering the aim of this research was to examine the effect of the bandwidth on parameters that are used to quantify glottal airflow waveforms that have been obtained by inverse filtering the acoustic signals three bandwidths 1 2 and 4 khz were compared using a vowels of different phonation types glottal waveforms were characterized using three ratios computed from the flow open quotient speed quotient and closing quotient and two parameters extracted from the differentiated flow the amplitude of the negative peak and the return time from the negative peak to zero level the results show that especially in pressed phonation the bandwidth should be at least 4 khz distortion caused by an insufficient frequency range was most severe in the parameters extracted from the flow derivatives among the parameters computed from the flow signals the closing quotient was affected most when the bandwidth was reduced

hardyʼs inequality and curvature a hardy inequality of the form f x pdx p 1p p 1 a x f x p x pdx for all f c0 r is considered for p 1 p 1 where is a domain in rnrn n 2n 2 r r is the ridge of and x x is the distance from x x to the boundary the main emphasis is on determining the dependence of a a on the geometric properties of a hardy inequality is also established for any doubly connected domain in r2r2 in terms of a uniformization of that is any conformal univalent map of onto an annulus

sim simultaneous inverse filtering and matching of a glottal flow model for acoustic speech signals a new method simultaneous inverse filtering and model matching sim is proposed that allows one to calculate voice source measures without any user interaction it is based on the discrete all pole modeling dap technique for inverse filtering if which is modified to include a model of the glottal flow as integral part lf model fant et al stl qpsr stockholm 4 1985 1 13 1986 as the correct lf parameters are initially unknown they are estimated in an iterative procedure using multi dimensional optimization techniques that are initialized according to the results of an exhaustive search the error criteria applied reflect how well the if is performed after the spectral contribution of the glottal flow has been removed the resulting optimal lf parameter constellation serves as the basis to calculate 11 voice source measures the performance was evaluated using synthesized signals and recordings of natural utterances for the synthesized signals the accuracy to reproduce the original parameters was high correlations exceeding 0 88 for measures where the starting point of the glottal cycle did not enter explicitly errors were smaller compared to conventional estimation methods where the measures were estimated from the if signal the analysis of natural utterances indicates that problems still exist with regard to robustness but that under advantageous conditions the open quotient the speed quotient the closing quotient the parabolic spectral parameter and the negative peak amplitude of the glottal flow derivative can indeed be determined automatically by the sim method

group differences in measures of voice production and revised values of maximum airflow declination rate in previous reports aerodynamic and acoustic measures of voice production were presented for groups of normal male and female speakers holmberg et al j acoust soc am 84 511 529 1988 j voice 3 294 305 1989 that were used as norms in studies of voice disorders hillman et al j speech hear res 32 373 392 1989 j voice 4 52 63 1990 several of the measures were extracted from glottal airflow waveforms that were derived by inverse filtering a high time resolution oral airflow signal recently the methods have been updated and a new study of additional subjects has been conducted this report presents previous 1988 and current 1993 group mean values of sound pressure level fundamental frequency maximum airflow declination rate ac flow peak flow minimum flow ac dc ratio inferred subglottal air pressure average flow and glottal resistance statistical tests indicate overall group differences and differences for values of several individual parameters between the 1988 and 1993 studies some inter study differences in parameter values may be due to sampling effects and minor methodological differences however a comparative test of 1988 and 1993 inverse filtering algorithms shows that some lower 1988 values of maximum flow declination rate were due at least in part to excessive low pass filtering in the 1988 algorithm the observed differences should have had a negligible influence on the conclusions of our studies of voice disorders

glottal volume velocity waveform characteristics in subjects with and without vocal training related to gender sound intensity fundamental frequency and age glottal volume velocity waveform characteristics of 224 subjects categorized in four groups according to gender and vocal training were determined and their relations to sound pressure level fundamental frequency intra oral pressure and age were analyzed subjects phonated at three intensity conditions the glottal volume velocity waveforms were obtained by inverse filtering the oral flow glottal volume velocity waveforms were parameterized with flow based minimum flow ac flow average flow maximum flow declination rate and time based parameters closed quotient closing quotient speed quotient as well as with derived parameters vocal efficiency and glottal resistance higher sound pressure levels intra oral pressures and flow parameter values ac flow maximum flow declination rate were observed when compared with previous investigations these higher values might be the result of the specific phonation tasks stressed ae vowel in a word and a sentence or filtering processes few statistically significant p 0 01 differences in parameters were found between untrained and trained subjects the maximum flow declination rate and the closing quotient were higher in trained women p 0 001 and the speed quotient was higher in trained men p 0 005 several statistically significant parameter differences were found between men and women minimum flow ac flow average flow maximum flow declination rate closing quotient glottal resistance p 0 001 and closed quotient p 0 005 significant effects of intensity condition were observed on ac flow maximum flow declination rate closing quotient and vocal efficiency in women p 0 005 and on minimum flow ac flow average flow maximum flow declination rate closed quotient and vocal efficiency in men p 0 01

an amplitude quotient based method to analyze changes in the shape of the glottal pulse in the regulation of vocal intensity this study presents an approach to visualizing intensity regulation in speech the method expresses a voice sample in a two dimensional space using amplitude domain values extracted from the glottal flow estimated by inverse filtering the two dimensional presentation is obtained by expressing a time domain measure of the glottal pulse the amplitude quotient aq as a function of the negative peak amplitude of the flow derivative dpeak the regulation of vocal intensity was analyzed with the proposed method from voices varying from extremely soft to very loud with a spl range of approximately 55db when vocal intensity was increased the speech samples first showed a rapidly decreasing trend as expressed on the proposed aq dpeak graph when intensity was further raised the location of the samples converged toward a horizontal line the asymptote of a hypothetical hyperbola this behavior of the aq dpeak graph indicates that the intensity regulation strategy changes from laryngeal to respiratory mecha

fast iterative solution of stabilised stokes systems part ii using general block preconditioners mixed finite element approximation of the classical stokes problem describing slow viscous incompressible flow gives rise to symmetric indefinite systems for the discrete velocity and pressure variables iterative solution of such indefinite systems is feasible and is an attractive approach for large problems part i of this work described a conjugate gradient like method the method of preconditioned conjugate residuals which is applicable to symmetric indefinite problems a j wathen and d j silvester siam j numer anal 30 1993 pp 630 649 using simple arguments estimates for the eigenvalue distribution of the discrete stokes operator on which the convergence rate of the iteration depends are easily derived part i discussed the important case of diagonal preconditioning scaling this paper considers the more general class of block preconditioners where the partitioning into blocks corresponds to the natural partitioning into the velocity and pressure variables it is shown that provid

a variational approach to the macroscopic electrodynamics of anisotropic hard superconductors we consider bean s critical state model for anisotropic superconductors a variational problem solved by the quasi static evolution of the internal magnetic field is obtained as the limit of functionals arising from maxwell s equations combined with a power law for the dissipation moreover the quasi static approximation of the internal electric field is recovered using a first order necessary condition if the sample is a long cylinder subjected to an axial uniform external field the macroscopic electrodynamics is explicitly determined

significance of analysis window size in maximum flow declination rate most acoustic stability measures and aerodynamic measures have recommended data analysis methods to ensure accurate comparison across research studies although standard aerodynamic analysis methods exist for subglottal pressure and mean transglottal flow such standards do not exist for maximum flow declination rate mfdr as such it becomes difficult to compare results across studies with the wide range of analysis windows because mfdr is a strong indicator of laryngeal function and increasingly is being reported in aerodynamic studies it is necessary to determine whether a significant difference exists between analysis windows in data management this study finds significant differences in mfdr with comparison of four different data extraction methods on the same data set the contrasting data extractions compare differences between method a mfdr from entire 1000 ms segment excluding onset offset method b mfdr from middle 100 ms with center at midportion of entire segment method c mfdr from middle 100 ms with center at midportion of maximum mfdr value from entire segment and method d mfdr from 20 consecutive cycles with center at midportion of maximum mfdr value from entire segment for a sustained 7 syllable pa repetition at two fundamental frequencies

hardy inequalities for robin laplacians abstract in this paper we establish a hardy inequality for laplace operators with robin boundary conditions for convex domains in particular we show explicitly how the corresponding hardy weight depends on the coefficient of the robin boundary conditions we also study several extensions to non convex and unbounded domains

the distance function from the boundary in a minkowski space let the space be endowed with a minkowski structure that is is the gauge function of a compact convex set having the origin as an interior point and with boundary of class and let be the asymmetric distance associated to given an open domain of class let be the minkowski distance of a point from the boundary of we prove that a suitable extension of to which plays the role of a signed minkowski distance to is of class in a tubular neighborhood of and that is of class outside the cut locus of that is the closure of the set of points of nondifferentiability of in in addition we prove that the cut locus of has lebesgue measure zero and that can be decomposed up to this set of vanishing measure into geodesics starting from and going into along the normal direction with respect to the minkowski distance we compute explicitly the jacobian determinant of the change of variables that associates to every point outside the cut locus the pair where denotes the unique projection of on and we apply these techniques to the analysis of pdes of monge kantorovich type arising from problems in optimal transportation theory and shape optimization

an efficient and robust method for simulating two phase gel dynamics we develop a computational method for simulating models of gel dynamics where the gel is described by two phases a networked polymer and a fluid solvent the models consist of transport equations for the two phases two coupled momentum equations and a volume averaged incompressibility constraint which we discretize with finite differences volumes the momentum and incompressibility equations present the greatest numerical challenges since i they involve partial derivatives with variable coefficients that can vary quite significantly throughout the domain when the phases separate and ii their approximate solution requires the inversion of a large linear system of equations for solving this system we propose a box type multigrid method to be used as a preconditioner for the generalized minimum residual gmres method through numerical experiments of a model problem which exhibits phase separation we show that the computational cost of the method scales nearly linearly with the number of unknowns and performs consistently well over a wide range of parameters for solving the transport equation we use a conservative finite volume method for which we derive stability bounds

initial validation of an indirect measure of subglottal pressure during vowels some methods for direct measurement of subglottal pressure during speech are invasive and thus cannot be used on a routine basis the development of noninvasive techniques is thus desirable and a simple indirect method for measuring subglottal pressure from records of oral pressure during consonants has recently been proposed and applied to studies of glottal resistance during phonation in order to be useful indirect measurement procedures should be validated by comparisons with direct measurements and the present experiment was designed for such a comparison miniature pressure transducers were used to obtain records of pressure below and above the glottis results showed nonsignificant differences and a high correlation between the direct and indirect measurements this indirect method for measuring subglottal pressure thus appears to provide valid results

perceived loudness of speech based on the characteristics of glottal excitation source the impulse like characteristic of glottal excitation in speech production is an important factor in the perception of loudness of speech signals this characteristic is attributed to the abruptness of the closing phase in the glottal cycle in this paper an acoustic feature called strength of excitation is proposed to represent the impulse like nature of excitation the strength of excitation is derived from the linear prediction residual of speech signals where the residual can be considered as an estimate of the source of excitation since the loudness of speech is perceived over one or more utterances of speech it is hypothesized that the distribution of strength of excitation is indicative of the perceived loudness of speech the distribution of strength of excitation is shown to distinguish between soft and loud utterances of speakers the distribution can also help in discriminating between the loudness of two speakers the loudness measure obtained using the distribution of the strength of ex

the geodesic x ray transform with matrix weights author s paternain gp salo m uhlmann g zhou h abstract 2019 by johns hopkins university press consider a compact riemannian manifold of dimension 3 with strictly convex boundary such that the manifold admits a strictly convex function we show that the attenuated ray transform in the presence of an arbitrary connection and higgs field is injective modulo the natural obstruction for functions and one forms we also show that the connection and the higgs field are uniquely determined by the scattering relation modulo gauge transformations the proofs involve a reduction to a local result showing that the geodesic x ray transform with a matrix weight can be inverted locally near a point of strict convexity at the boundary and a detailed analysis of layer stripping arguments based on strictly convex exhaustion functions as a somewhat striking corollary we show that these integral geometry problems can be solved on strictly convex manifolds of dimension 3 having nonnegative sectional curvature similar results were known earlier in negative sectional curvature we also apply our methods to solve some inverse problems in quantum state tomography and polarization tomography

regularity of optimal transport in curved geometry the nonfocal case we explore some geometric and analytic consequences of a curvature condition introduced by ma trudinger and wang in relation to the smoothness of optimal transport in curved geometry we discuss a conjecture according to which a strict version of the ma trudinger wang condition is sufficient to prove regularity of optimal transport on a riemannian manifold we prove this conjecture under a somewhat restrictive additional assumption of nonfocality at the same time we establish the striking geometric property that the tangent cut locus is the boundary of a convex set partial extensions are presented to the case when there is no pure focalization on the tangent cut locus

semigroups of relations and subdifferentials of the minimal time function and of the geodesic distance given a closed subset s of a banach space x we study the minimal time function to reach a point x of x starting from s we relate this problem to the study of the geodesic distance from x to s associated with a riemannian metric or a finsler metric it appears that both cases can be treated simultaneously and yield solutions to a hamilton jacobi equation we detect simple links between the general framework we propose and multivalued semigroups new concepts of infinitesimal generators of such semigroups are considered

a geometric characterization of a sharp hardy inequality abstract in this paper we prove that the distance function of an open connected set in r n 1 with a c 2 boundary is superharmonic in the distribution sense if and only if the boundary is weakly mean convex we then prove that hardy inequalities with a sharp constant hold on weakly mean convex c 2 domains moreover we show that the weakly mean convexity condition cannot be weakened we also prove various improved hardy inequalities on mean convex domains along the line of brezis and marcus 1997 7

an efficient numerical algorithm for a multiphase tumour model abstract this paper is concerned with the development and application of optimally efficient numerical methods for the simulation of vascular tumour growth this model used involves the flow and interaction of four different but coupled phases which are each treated as incompressible fluids hubbard and byrne 2013 a finite volume scheme is used to approximate mass conservation with conforming finite element schemes to approximate momentum conservation and an associated equation the principal contribution of this paper is the development of a novel block preconditioner for solving the linear systems arising from the discrete momentum equations at each time step in particular the preconditioned system has both a solution time and a memory requirement that is shown to scale almost linearly with the problem size

generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains using three different notions of the generalized principal eigenvalue of linear second order elliptic operators in unbounded domains we derive necessary and sufficient conditions for the validity of the maximum principle as well as for the existence of positive eigenfunctions for the dirichlet problem relations between these principal eigenvalues their simplicity and several other properties are further discussed 2015 wiley periodicals inc

closing aubry sets ii given a tonelli hamiltonian h t m of class ck with k 2 we prove the following results 1 assume there exist a recurrent point of the projected aubry set and a critical viscosity subsolution u such that u is a c1 critical solution in an open neighborhood of the positive orbit of suppose further that u is c2 at then there exists a ck potential v m small in c2 topology for which the aubry set of the new hamiltonian h v is either an equilibrium point or a periodic orbit 2 if m is two dimensional 1 holds replacing c1 critical solution c2 at by cm3 critical subsolution these results can be considered as a first step through the attempt of proving the mane s conjecture in c2 topology in a second paper 27 we will generalize 2 to arbitrary dimension moreover such an extension will need the introduction of some new techniques which will allow us to prove in 27 the mane s density conjecture in c1 topology our proofs are based on a combination of techniques coming from finite dimensional control theory and hamilton jacobi theory together with some of the ideas that were used to prove c1 closing lemmas for dynamical systems 2014 wiley periodicals inc

normalized amplitude quotient for parametrization of the glottal flow normalized amplitude quotient naq is presented as a method to parametrize the glottal closing phase using two amplitude domain measurements from waveforms estimated by inverse filtering in this technique the ratio between the amplitude of the ac flow and the negative peak amplitude of the flow derivative is first computed using the concept of equivalent rectangular pulse a hypothetical signal located at the instant of the main excitation of the vocal tract this ratio is then normalized with respect to the length of the fundamental period comparison between naq and its counterpart among the conventional time domain parameters the closing quotient shows that the proposed parameter is more robust against distortion such as measurement noise that make the extraction of conventional time based parameters of the glottal flow problematic experiments with breathy normal and pressed vowels indicate that naq is also able to separate the type of phonation effectively

the lipschitz continuity of the distance function to the cut locus let n be a closed submanifold of a complete smooth riemannian manifold m and uv the total space of the unit normal bundle of n for each v c uv let p v denote the distance from n to the cut point of n on the geodesic y with the velocity vector tyv 0 v the continuity of the function p on uv is well known in this paper we prove that p is locally lipschitz on which p is bounded in particular if m and n are compact then p is globally lipschitz on uy therefore the canonical interior metric 6 may be introduced on each connected component of the cut locus of n and this metric space becomes a locally compact and complete length space let n be an immersed submanifold of a complete cc riemannian manifold m and 7 uv n the unit normal bundle of n for each positive integer k and vector v c uv let a number k v denote the parameter value of fy where 7yv denotes the geodesic for which the velocity vector is v at t 0 such that yv ak v is the k th focal point conjugate point for the case in which n is a point of n along y counted with focal or conjugate multiplicities a unit speed geodesic segment 0 a m emanating from n is called an n segment if t d n y t on 0 a by the first variation formula an n segment is orthogonal to n a point 7y to on an n segment 7y v e uv is called a cut point of n if there is no n segment properly containing y o to for each v c uv let p v denote the distance from n to the cut point on y of n whitehead 27 investigated the structure of the conjugate locus and the cut locus of a point on a real analytic finsler manifold he determined the structure of the conjugate locus around a conjugate point for which the conjugate multiplicity is locally constant on its neighborhood cf also 25 and proved the continuity of the function p in compact symmetric spaces t sakai 19 and m takeuchi 23 determined the detailed structure of the cut locus of a point the detailed structure of the cut locus of a point in a 2 dimensional riemannian manifold has been investigated by poincare myers and others 7 11 13 hartman first tried to show the absolute continuity of the function p when m is 2 dimensional he proved in 8 that if p is of bounded variation then p is absolutely continuous recently hebda 11 and the first named author 13 independently proved ambrose s problem by showing that p is absolutely continuous on a closed arc on which p is bounded when n is a point in a 2 dimensional riemannian manifold therefore the cut locus of a point in a compact 2 dimensional received by the editors october 14 1998 and in revised form april 13 1999 2000 mathematics subject classification primary 53c22 secondary 28a78 supported in part by a grant in aid for scientific research from the ministry of education science sports and culture japan 2000 american mathematical society

hardy inequalities for p laplacians with robin boundary conditions in this paper we study the best constant in a hardy inequality for the p laplace operator on convex domains with robin boundary conditions we show in particular that the best constant equals p

stability analysis for semilinear parabolic problems in general unbounded domains abstract we introduce several notions of generalised principal eigenvalue for a linear elliptic operator on a general unbounded domain under boundary condition of the oblique derivative type we employ these notions in the stability analysis of semilinear problems some of the properties we derive are new even in the dirichlet or in the whole space cases as an application we show the validity of the hair trigger effect for the fisher kpp equation on general uniformly smooth domains

fast iterative solution of stabilised stokes systems part i using simple diagonal preconditioners mixed finite element approximation of the classical stokes problem describing slow viscous incompressible flow gives rise to symmetric indefinite systems for the discrete velocity and pressure variables iterative solution of such indefinite systems is feasible and is an attractive approach for large problems the use of stabilisation methods for convenient but unstable mixed elements introduces stabilisation parameters we show how these can be chosen to obtain rapid iterative convergence we propose a conjugate gradient like method the method of preconditioned conjugate residuals which is applicable to symmetric indefinite problems describe the effects of stabilisation on the algebraic structure of the discrete stokes operator and derive estimates of the eigenvalue spectrum of this operator on which the convergence rate of the iteration depends here we discuss the simple case of diagonal preconditioning our results apply to both locally and globally stabilised mixed elements as well as to elements which are inherently stable we demonstrate that convergence rates comparable to that achieved using the diagonally scaled conjugate gradient method applied to the discrete laplacian are approachable for the stokes problem

on a system of partial differential equations of monge kantorovich type abstract we consider a system of pdes of monge kantorovich type arising from models in granular matter theory and in electrodynamics of hard superconductors the existence of a solution of such system in a regular open domain r n whose construction is based on an asymmetric minkowski distance from the boundary of was already established in g crasta a malusa the distance function from the boundary in a minkowski space trans amer math soc submitted for publication in this paper we prove that this solution is essentially unique a fundamental tool in our analysis is a new regularity result for an elliptic nonlinear equation in divergence form which is of some interest by itself