a critical evaluation of the resolution properties of b spline and compact finite difference methods resolution properties of b spline and compact finite difference schemes are compared using fourier analysis in periodic domains and tests based on solution of the wave and heat equations in finite domains with uniform and nonuniform grids results show that compact finite difference schemes have a higher convergence rate and in some cases better resolution however b spline schemes have a more straightforward and robust formulation particularly near boundaries on nonuniform meshes

reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics abstract galerkin and stabilized galerkin least squares and galerkin gradient least squares finite element methods for solving problems of time harmonic acoustics are presented and analyzed the error of discretization is related to spurious representation of physical phenomena namely dispersion anisotropy and reflection all of which decrease with mesh refinement the performance of the stabilized methods in terms of dispersion and anisotropy is identical both are superior to the galerkin method relaxing wave resolution requirements further insight into the design of these methods is provided by the analyses the stabilized methods differ in the degree of spurious reflection that is engendered by transitions in mesh size the performance of galerkin gradient least squares deteriorates on non uniform meshes however galerkin least squares maintains its enhanced performance exhibiting low sensitivity to transitions in mesh size thereby reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics guidelines for discretization pertaining to mesh orientation and wave resolution are presented

koszul duality of affine kac moody algebras and cyclotomic rational double affine hecke algebras abstract we give a proof of the parabolic singular koszul duality for the category o of affine kac moody algebras the main new tool is a relation between moment graphs and finite codimensional affine schubert varieties we apply this duality to q schur algebras and to cyclotomic rational double affine hecke algebras this yields a proof of a conjecture of chuang miyachi relating the level rank duality with the ringel koszul duality of cyclotomic rational double affine hecke algebras

representations of semisimple lie algebras in prime characteristic and the noncommutative springer resolution we prove most of lusztig s conjectures on the canonical basis in homology of a springer ber the conjectures predict that this basis controls numerics of representations of the lie algebra of a semisimple algebraic group over an algebraically closed eld of positive characteristic we check this for almost all characteristics to this end we construct a noncommutative resolution of the nilpotent cone which is derived equivalent to the springer resolution on the one hand this noncommutative resolution is closely related to the positive characteristic derived localization equivalences obtained earlier by the present authors and rumynin on the other hand it is compatible with the t structure arising from an equivalence with the derived category of perverse sheaves on the ane ag variety of the langlands dual group this equivalence established by arkhipov and the rst author ts the framework of local geometric langlands duality the latter compatibility allows one to apply frobenius purity theorem to deduce the desired properties of the basis we expect the noncommutative counterpart of the springer resolution to be of independent interest from the perspectives of algebraic geometry and geometric langlands duality

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

the solution of elastostatic and elastodynamic problems with chebyshev spectral finite elements chebyshev spectral finite elements are applied to the solution of elastostatic and elastodynamic problems in two dimensions the accuracy of the spectral approach is judged by examining the dispersion of the solutions it is shown that the spectral approach can achieve nearly zero dispersion for a wide range of spatial and temporal discretizations even coarse mesh solutions using the explicit lumped capacitance approach demonstrate exceptional accuracy a brief description of the development of the chebyshev spectral elements is included

koszul duality and modular representations of semi simple lie algebras in this paper we prove that if g is a connected simply connected semi simple algebraic group over an algebraically closed field of sufficiently large characteristic then all the blocks of the restricted enveloping algebra of the lie algebra of g can be endowed with a koszul grading extending results of andersen jantzen soergel we also give information about the koszul dual rings in the case of the block associated to a regular character x of the harish chandra center the dual ring is related to modules over the enveloping algebra specialized at x with generalized trivial frobenius character our main tool is the localization theory developed by bezrukavnikov mirkovic rumynin

dispersive and dissipative behaviour of high order discontinuous galerkin finite element methods the dispersive and dissipative properties of hp version discontinuous galerkin finite element approximation are studied in three different limits for the small wave number limit hk 0 we show the discontinuous galerkin gives a higher order of accuracy than the standard galerkin procedure thereby confirming the conjectures of hu and atkins j comput phys 182 2 2002 516 if the mesh is fixed and the order p is increased it is shown that the dissipation and dispersion errors decay at a super exponential rate when the order p is much larger than hk finally if the order is chosen so that 2p 1 hk for some fixed constant 1 then it is shown that an exponential rate of decay is obtained

grid dispersion and stability criteria of some common finite element methods for acoustic and elastic wave equations purely numerical methods based on finite element approximation of the acoustic or elastic wave equation are becoming increasingly popular for the generation of synthetic seismograms we present formulas for the grid dispersion and stability criteria for some popular finite element methods fem for wave propagation namely classical and spectral fem we develop an approach based on a generalized eigenvalue formulation to analyze the dispersive behavior of these fems for acoustic or elastic wave propagation that overcomes difficulties caused by irregular node spacing within the element and the use of high order polynomials as is the case for spectral fem analysis reveals that for spectral fem of order four or greater dispersion is less than 0 2 at four to five nodes per wavelength and dispersion is not angle dependent new results can be compared with grid dispersion results of some classical finite difference methods fdm used for acoustic or elastic wave propagation analysis reveals that fdm and classical fem require a larger sampling ratio than a spectral fem to obtain results with the same degree of accuracy the staggered grid fdm is an efficient scheme but the dispersion is angle dependent with larger values along the grid axes on the other hand spectral fem of order four or greater is isotropic with small dispersion making it attractive for simulations with long propagation times

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

dispersion of elastic waves in the contact impact problem of a long cylinder numerical dispersion of two dimensional finite elements was studied the outcome of the dispersion study was verified by the numerical and analytical solutions to the longitudinal impact of two long cylindrical bars in accordance with the results of the dispersion analysis it was demonstrated that the quadratic elements showed better accuracy than the linear ones

assessment of methods for computing the closest point projection penetration and gap functions in contact searching problems summary in computational contact mechanics problems local searching requires calculation of the closest point projection of a contactor point onto a given target segment it is generally supposed that the contact boundary is locally described by a convex region however because this assumption is not valid for a general curved segment of a three dimensional quadratic serendipity element an iterative numerical procedure may not converge to the nearest local minimum to this end several unconstrained optimization methods are tested the newton raphson method the least square projection the sphere and torus approximation method the steepest descent method the broyden method the broyden fletcher goldfarb shanno method and the simplex method the effectiveness and robustness of these methods are tested by means of a proposed benchmark problem it is concluded that the newton raphson method in conjunction with the simplex method significantly increases the robustness of the local contact search procedure of pure penalty contact methods whereas the torus approximation method can be recommended for contact searching algorithms which employ the lagrange method or the augmented lagrangian method copyright 2015 john wiley sons ltd

a multiquadric quasi interpolations method for cev option pricing model abstract the pricing of option contracts when the underlying process follows the constant elasticity of variance cev model is considered for cev european options the closed form solutions involve the non central chi square distribution whose computations by the current literatures are rather unstable and extremely expensive based on multiquadric quasi interpolation methods this study suggests a stable and fast numerical algorithm for cev option pricing model the method is confirmed to be a multinomial tree in which the underlying variable moves from its initial value to an infinity of possible values of the next time step the probabilities in the associated tree are ensured to be positive which is a sufficient condition for stability and convergence the method is flexible since it is simple to implement with the nonuniform knots moreover the method is easy to value the greek letters which are important parameters in financial engineering as the multiquadric function is infinitely continuously differentiable besides the method does not require solving a resultant full matrix the ill conditioning problem arising when using the radial basis functions as a global interpolant can be avoided numerical experiments imply that the method is highly effective to calculate the stock options and its greeks under the cev model

singular blocks of restricted sl3 abstract we compute generators and relations for the basic algebra of a non semisimple singular block of the restricted enveloping algebra of sl 3 over an algebraically closed field of characteristic p 3 working directly with the basic algebra we compute its centre and the internal degree zero part of its first hochschild cohomology and show its verma modules are koszul

approximation to the k th derivatives by multiquadric quasi interpolation method quasi interpolation is very useful in the study of approximation theory and its applications since it can yield solutions directly without the need to solve any linear system of equations based on the good performance simple to evaluate of multiquadric functions the advantages approximation order convexity and monotonlcity preserving of multiquadric quasi interpolation have been widely discussed however it is usually only for the approximation properties of the function itself and the good properties for derivatives whereas the high order derivatives have been largely ignored in this paper we go further into the approximation properties to the k th derivatives by using multiquadric quasi interpolation furthermore we develop two kinds of multiquadric quasi interpolation schemes on bounded interval x 0 x n whose derivatives converge to the corresponding derivatives of the approximated functions finally the numerical experiments are presented to confirm the accuracy of the presented scheme both theoretical results and numerical examples show this scheme provides good accuracy even if the data points in x 0 x n are irregularly distributed

dynamically knots setting in meshless method for solving time dependent propagations equation abstract in order to display a function with some finite discrete sampling data efficiently we require more sampling data where the function is more oscillatory and less sampling data where the function is more flat if the function is happen to be a solution of partial differential equation and is solved by finite elements method then we should construct finer element near the singularity however we do not know where the oscillation or even shocks will happen to a function which is a solution of non linear partial differential equation therefore we cannot preset the finer elements near such points a trivial method is taking very dense knots or very fine elements everywhere to keep the accuracy this strategy cost the computation time another idea is to move the position of the sampling points according to the varying of the function with the time we observed that this approach could be achieved by lagrangian formulation for finite difference method however the lagrangian formulation does not possess shape preserving and variation diminishing properties it is difficult to achieve the approach for finite elements methods too because the moving knots will destroy the topology of the mesh recently the meshless method becomes to topic to solve partial differential equation numerically the meshless method does not require any mesh or any structure of the knots sampling points therefore we can move the knots freely to simulate the problem the only restriction is to keep the knots no overlapping this paper is a test of our approach for the burger s equation with radial basis quasi interpolation

a galerkin least squares finite element method for the two dimensional helmholtz equation in this paper a galerkin least squares gls finite element method in which residuals in least squares form are added to the standard galerkin variational equation is developed to solve the helmholtz equation in two dimensions an important feature of gls methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes previous work has accomplished this for the one dimensional helmholtz equation using dispersion analysis in this paper the selection of the gls mesh parameter for two dimensions is considered and leads to elements that exhibit improved phase accuracy for any given direction of wave propagation an optimal gls mesh parameter is determined using two dimensional fourier analysis in general problems the direction of wave propagation will not be known a priori in this case an optimal gls parameter is found which reduces phase error for all possible wave vector orientations over elements the optimal gls parameters are derived for both consistent and lumped mass approximations several numerical examples are given and the results compared with those obtained from the galerkin method the extension of gls to higher order quadratic interpolations is also presented

grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics summary the spatial discretisation of a continuum by the fem introduces dispersion errors to the numerical solution of stress wave propagation errors of phase and group velocities and the scatter of wave propagation are induced when these propagating phenomena are modelled by the fem the speed of a single harmonic wave depends on its frequency parasitic effects do not exist in an ideal unbounded continuum with higher order finite elements there are optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefronts in principle the dispersion errors and the spurious oscillations cannot be removed from these solutions but can be suppressed to a certain extent for reliable numerical solutions by the fem the dispersion errors should be analysed and determined the dispersion properties of a plane square biquadratic serendipity finite element are examined and compared with a bilinear one dispersion analysis is carried out for the consistent and lumped mass matrices a dispersive improved lumped mass matrix for biquadratic serendipity elements is proposed the paper closes with the recommendation of a choice of permissible dimensionless wavelengths for bilinear and biquadratic serendipity finite element meshes copyright 2013 john wiley sons ltd

modified integration rules for reducing dispersion error in finite element methods abstract this paper describes a simple but effective technique for reducing dispersion errors in finite element solutions of time harmonic wave propagation problems the method involves a simple shift of the integration points to locations away from conventional gauss or gauss lobatto integration points for bilinear rectangular elements such a shift results in fourth order accuracy with respect to dispersion error error in wavelength as opposed to the second order accuracy resulting from conventional integration numerical experiments involving distorted meshes indicate that the method has superior performance in comparison with other dispersion reducing finite elements

a generalized finite element method for solving the helmholtz equation in two dimensions with minimal pollution when using the galerkin fem for solving the helmholtz equation in two dimensions the error of the corresponding solution differs substantially from the error of the best approximation and this effect increases with higher wave number k in this paper we will design a generalized finite element method gfem for the helmholtz equation such that the pollution effect is minimal

discrete dispersion relation for hp version finite element approximation at high wave number the dispersive properties of high order finite element schemes are analyzed in the setting of the helmholtz equation and an explicit form of the discrete dispersion relation is obtained for elements of arbitrary order it is shown that the numerical dispersion displays three different types of behavior depending on the size of the order of the method relative to the mesh size and the wave number quantitative estimates are obtained for the behavior and rates of decay of the dispersion error in the differing regimes all estimates are fully explicit and are shown to be sharp limits are obtained where transitions between the different regimes occur and used to provide guidelines for the selection of the mesh size and the polynomial order in terms of the wave number so that the dispersion error is controlled

accuracy of finite difference and finite element modeling of the scalar and elastic wave equations numerical solutions of the scalar and elastic wave equations have greatly aided geophysicists in both forward modeling and migration of seismic wave fields in complicated geologic media and they promise to be invaluable in solving the full inverse problem this paper quantitatively compares finite difference and finite element solutions of the scalar and elastic hyperbolic wave equations for the most popular implicit and explicit time domain and frequency domain techniques in addition to versatility and ease of implementation it is imperative that one choose the most cost effective solution technique for a fixed degree of accuracy to be of value a solution technique must be able to minimize 1 numerical attenuation or amplification 2 polarization errors 3 numerical anisotropy 4 errors in phase and group velocities 5 extraneous numerical parasitic modes 6 numerical diffraction and scattering and 7 errors and transmission coefficients this paper shows that in homogeneous media the

dispersion corrected explicit integration of the wave equation a simple dispersion correction is introduced into the centered difference explicit time integration scheme for wave propagation problems the extra term introduces a change of the wave speed depending on local wave characteristics a rigorous theoretical analysis is provided for the scalar wave equation on a regular mesh and a notable improvement in the ability to conserve wave fronts is demonstrated by two numerical examples the correction is reinterpreted to apply to a typical finite element formulation in terms of mass and stiffness matrices resulting in a general dispersion correction of the explicit centered difference time integration algorithm for acoustic and elastic wave propagation problems

group velocity in finite difference schemes the relevance of group velocity to the behavior of finite difference models of time dependent partial differential equations is surveyed and illustrated applications involve the propagation of wave packets in one and two dimensions numerical dispersion the behavior of parasitic waves and the stability analysis of initial boundary value problems

canonical tilting relative generators abstract given a relatively projective birational morphism f x y of smooth algebraic spaces with dimension of fibers bounded by 1 we construct tilting relative over y generators t x f and s x f in d b x we develop a piece of general theory of strict admissible lattice filtrations in triangulated categories and show that d b x has such a filtration l where the lattice is the set of all birational decompositions f x g z h y with smooth z the t structures related to t x f and s x f are proved to be glued via filtrations left and right dual to l we realise all such z as the fine moduli spaces of simple quotients of o x in the heart of the t structure for which s x g is a relative projective generator over y this implements the program of interpreting relevant smooth contractions of x in terms of a suitable system of t structures on d b x

the fractional and mixed fractional cev model abstract the continuous observation of the financial markets has identified some stylized facts which challenge the conventional assumptions promoting the born of new approaches on the one hand the long range dependence has been faced replacing the traditional gauss wiener process brownian motion characterized by stationary independent increments by a fractional version on the other hand the cev model addresses the leverage effect and smile skew phenomena efficiently in this paper these two insights are merging and both the fractional and mixed fractional extensions for the cev model are developed using the fractional versions of both the ito s calculus and the fokker planck equation the transition probability density function of the asset price is obtained as the solution of a non stationary feller process with time varying coefficients getting an analytical valuation formula for a european call option besides the greeks are computed and compared with the standard case

an artificial boundary method for american option pricing under the cev model the black scholes asset price dynamics is well known to be inadequate for capturing the volatility smile in the financial market therefore the constant elasticity of variance cev model has become a popular alternative to valuing options fitting to the smile american option pricing however is computationally intensive as there are no analytical formulas available this paper proposes an artificial boundary method for partial differential equations pdes to compute american option prices and greeks under the cev model the idea is to reduce the infinite computational domain to a finite one by introducing an artificial boundary on which an exact boundary condition is derived we then develop a crank nicolson scheme to solve the pde with the artificial boundary condition implemented with a numerical laplace inversion with a finite computational domain the optimal exercise boundary can be determined efficiently our numerical examples show that the proposed scheme is accurate robust with respect to

dispersion analysis of a non conforming finite element method for the helmholtz and elastodynamic equations summary we investigate the dispersive properties of a non conformingnite element method to solve the two dimensional helmholtz and elastodynamics equations the study is performed by deriving and analysing the dispersion relations and by evaluating the derived quantities such as the dimensionless phase and group velocities also the phase dierence between exact and numerical solutions is investigated the studied method which yields a linear spatial approximation is shown to be less dispersive than a conforming bilinearnite element method in the two cases shown herein moreover it almost halves the number of points per wavelength necessary to reach a given accuracy when calculating the mentioned velocities in both cases here presented copyright 2003 john wiley sons ltd

spurious reflection of elastic waves due to gradually changing finite element size summary when a homogeneous elastic continuum is modelled by a non uniform finite element grid the differences in the size of adjacent finite elements can cause a spurious wave reflection which does not exist in the continuum extending previous studies in which the spurious wave reflection was investigated for the case of two uniform grids with a sudden element size change from one grid to the other the present study deals with the case when the two uniform grids of different element sizes are separated by a transition zone through which the element size varies gradually either by a geometric progression or by an arithmetic progression the solution is carried out in complex variables and numerical plots of the results are given when the ratio of wavelength to the largest element size is as low as 4 1 the spurious wave reflection is very significant while for the ratios over 10 1 it is insignificant inserting a transition zone with gradually varying element size between the two uniform parts of the grid somewhat mitigates the phenomenon of spurious reflection but this is significant only when the ratio of element sizes in the uniform grids is small less than about 1 5 1 varying the element size throughout the transition zone in an arithmetic progression seems slightly better than in a geometric progression the spurious wave reflection is less pronounced for higher order elements in particular for linear strain elements as compared to constant strain elements the spurious reflection is also less severe for consistent mass than for lumped mass

the influence of the mass matrix on the dispersive nature of the semi discrete second order wave equation abstract the application of discrete solution methods to the second order wave equation can yield a dispersive representation of the non dispersive wave propagation problem resulting in a phase speed that depends not only upon the wavelength of the signal being propagated but also upon the direction of propagation in this work the dependence of the dispersive errors on the wave propagation direction mesh aspect ratio and wave number is investigated with the goal of understanding and hopefully reducing the phase and group errors associated with the two dimensional bilinear finite element an analysis of the dispersive effects associated with the consistent row sum lumped and higher order mass matrices has led to a reduced coupling penta diagonal mass matrix that yields improved phase and group errors with respect to wavelength and propagation direction the influence of row sum lumping the finite element mass matrix is demonstrated to always introduce lagging phase and group error while a linear combination of the lumped and consistent mass matrices i e a higher order mass matrix is shown to improve the dispersion characteristics of both the reduced and full integration element using a 2 5 phase error metric the higher order mass matrix can reduce the mesh resolution requirements relative to the lumped mass matrix by nearly a factor of two in one dimension a factor of 4 in two dimensions similarly the reduced coupling mass matrix can reduce the grid requirements by a factor of approximately four relative to the lumped mass matrix a factor of 16 in two dimensions although the reduced coupling mass matrix requires additional storage relative to the lumped mass the factor of 16 reduction in grid requirements promises tremendous overall savings for computing a fixed wavelength spectrum or alternatively for resolving shorter wavelengths with a fixed grid resolution

variationally consistent inertia templates for b spline and nurbs based fem inertia scaling and customization abstract in this contribution variationally consistent inertia templates for b spline and nurbs based finite elements are proposed as a unified concept for two different purposes customization of the template allows construction of masses and reciprocal masses with desired properties like higher order accuracy or improved dispersion behavior inertia scaling allows substantial speed up for explicit dynamics by increased critical time steps the derivation of the template is based on a three field parametrized functional as in previous works of the authors group but with modified primary variables namely displacement velocity and mass specific linear momentum the latter allows for mass preservation for non constant density throughout the domain and is therefore an enhancement to the formulation proposed in tkachuk and bischoff 2015 with the focus on b spline and nurbs based finite elements the proposed template provides alternatives to the row sum lumped mass matrix which is only 2nd order accurate independent of the polynomial order earlier proposed algebraically constructed higher order masses from the literature can be reconstructed in the variational setting described here as special instances furthermore higher order reciprocal masses can be constructed from the template they are especially attractive for explicit dynamics as there is no extra expense per time step compared with lumped mass for linear problems for non linear problems only small overhead is expected but this paper focuses on linear problems only and mainly undistorted meshes tuning the method towards inertia scaling a reduction of the maximum eigenfrequency by 25 40 is obtained in the examples herein whereas the accuracy is higher than for lumped or consistent mass

reductive groups the loop grassmannian and the springer resolution in this paper we prove equivalences of categories relating the derived category of a block of the category of representations of a connected reductive algebraic group over an algebraically closed field of characteristic p bigger than the coxeter number and a derived category of equivariant coherent sheaves on the springer resolution or a parabolic counterpart in the case of the principal block combined with previous results this provides a modular version of celebrated constructions due to arkhipov bezrukavnikov ginzburg for lusztig s quantum groups at a root of unity as an application we prove a graded version of a conjecture of finkelberg mirkovic describing the principal block in terms of mixed perverse sheaves on the dual affine grassmannian and deduce a new proof of lusztig s conjecture in large characteristic

modelling wave propagation in two dimensional structures using finite element analysis a method is described by which the dispersion relations for a two dimensional structural component can be predicted from a finite element fe model the structure is homogeneous in two dimensions but the properties might vary through the thickness this wave finite element wfe method involves post processing the mass and stiffness matrices found using conventional fe methods of a segment of the structure this is typically a 4 noded rectangular segment although other elements can be used periodicity conditions are applied to relate the nodal degrees of freedom and forces the wavenumbers real imaginary or complex and the frequencies then follow from various resulting eigenproblems the form of the eigenproblem depends on the nature of the solution sought and may be a linear quadratic polynomial or transcendental eigenproblem numerical issues are discussed examples of a thin plate an asymmetric laminated plate and a laminated foam cored sandwich panel are presented for the last two examples developing an analytical model is a formidable task at best the method is seen to give accurate predictions at very little computational cost furthermore since the element matrices are typically found using a commercial fe package the meshing capabilities and the wealth of existing element libraries can be exploited

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

a fourier analysis of spurious mechanisms and locking in the finite element method a fourier analysis technique is used to examine spurious mechanisms and the element locking phenomena engendered by different finite element discretizations it is shown that these phenomena can be identified by examining the uncoupled discrete fourier operators and corresponding characteristic equations and are caused in terms of discrete filter concepts by either a spurious mode carrier or by violating the unlocking condition specified in the paper the analysis is performed for two simple problems wave propagation in a bar and vibration of a timoshenko beam which when discretized by linear shape functions succinctly manifest the two phenomena as being directly traceable to specific components of the finite element discretizations

on the derived categories of degree d hypersurface fibrations we provide descriptions of the derived categories of degree d hypersurface fibrations which generalize a result of kuznetsov for quadric fibrations and give a relative version of a well known theorem of orlov using a local generator and morita theory we re interpret the resulting matrix factorization category as a derived equivalent sheaf of dg algebras on the base then applying homological perturbation methods we obtain a sheaf of a infty algebras which gives a new description of homological projective duals for relative d veronese embeddings recovering the sheaf of clifford algebras obtained by kuznetsov in the case when d 2

effects of spatial discretization on dispersion and spurious oscillations in elastic wave propagation the dispersive and spurious oscillation properties of one dimensional uniform finite element meshes are investigated using the information provided by the frequency response functions of the finite element meshes the modal superposition method in which the effects of temporal discretization are eliminated is employed to integrate the discretized equations of motion