non element method of solving 2d boundary problems defined on polygonal domains modeled by navier equation the paper presents a non element method of solving boundary problems defined on polygonal domains modeled by corner points to solve these problems a parametric integral equation system pies is used the system is characterized by a separation of the approximation of boundary geometry from the approximation of boundary functions this feature makes it possible to effectively investigate the convergence of the obtained solutions with no need of performing the approximation of boundary geometry the testing examples included confirm high accuracy of the solutions

convergence of sph method for scalar nonlinear conservation laws this paper is devoted to the study of the convergence of weighted particle approximation of nonlinear multidimensional conservation laws for euler equations the method is closely related to the smooth particle hydrodynamics sph method extension of the original algorithm is proposed we use approximate riemann solvers instead of artificial viscosity in order to stabilize the scheme the mathematical analysis is performed by connecting this new approach with the finite volume scheme convergence of the approximate solution in l loc p p infty towards the unique weak entropy solution of the cauchy problem is obtained in the scalar nonlinear case by using uniqueness of measure valued solutions

solution of poisson and laplace equations by quadrilateral quadrature element the quadrature element method qem is a new concept in numerical methods which was introduced only recently a quadrilateral quadrature element is developed in the paper and applied to the solution of two dimensional potential problems governed by poisson or laplace equations the results of three examples are in good agreement with the available solutions it is shown that the present quadrilateral quadrature element is very efficient and effective most significantly it can be employed to solve differential equations of physical problems with irregular geometry and complex boundary conditions

on the convergence of a finite element method for a nonlinear hyperbolic conservation law we consider a space time finite element discretization of a time dependent nonlinear hyperbolic conservation law in one space dimension burgers equation the finite element method is higher order accurate and is a petrov galerkin method based on the so called streamline diffusion modification of the test functions giving added stability we first prove that if a sequence of finite element solutions converges boundedly almost everywhere as the mesh size tends to zero to a function u then u is an entropy solution of the conservation law this result may be extended to systems of conservation laws with convex entropy in several dimensions we then prove using a compensated compactness result of murat tartar that if the finite element solutions are uniformly bounded then a subsequence will converge to an entropy solution of burgers equation we also consider a further modification of the test functions giving a method with improved shock capturing finally we present the results of some numerical experiments

renormalized entropy solutions of scalar conservation laws with boundary condition we study an initial boundary value problem for a scalar conservation law u t div phi u f on a bounded domain existence and uniqueness of a renormalized entropy solution is established for general l 1 data phi is an element ofc r r n

convergence of relaxation schemes for initial boundary value problems for conservation laws abstract we consider a scalar conservation law with stiff source term in the quarter plan this equation is relaxed in a quasi linear hyperbolic system the relaxed system is approximated using an upwind scheme converging for fixed relaxation time and vanishing discretization mesh further we use chapman enskog expansion to obtain a viscous scheme for the equilibrium law and prove its convergence to the physical solution boundary information is carefully handled in an appropriate inequality linking the entropy numerical flux and the flux function an extension to general conservative schemes is also investigated

entropy formulation for parabolic degenerate equations with general dirichlet boundary conditions and application to the convergence of fv methods this paper is devoted to the analysis and the approximation of parabolic hyperbolic degenerate problems defined on bounded domains with nonhomogeneous boundary conditions it consists of two parts the first part is devoted to the definition of an original notion of entropy solutions to the continuous problem which can be adapted to define a notion of measure valued solutions or entropy process solutions the uniqueness of such solutions is established in the second part the convergence of the finite volume method is proved this result relies on weak estimates and on the theorem of uniqueness of the first part it also entails the existence of a solution to the continuous problem

c2 continuous elements for boundary element analysis overhauser s original idea of linearly blending two sets of quadratic c0 continuous basis functions to produce a set of c1 continuous basis functions is employed by linearly blending two sets of quadratic c1 continuous basis functions the result is a set of eight basis functions which are c2 continuous from element to element and can be used for boundary element analysis where post processing of the solution is required solutions to laplaces equation in simple geometries are used to demonstrate the accuracy of the solutions obtained with the new elements these new elements also provide more accurate values for the first and second derivatives of the solution in the tangential direction at all points on a smooth boundary and good approximations at corner points 1997 by john wiley sons ltd

a hermite interpolation algorithm for hypersingular boundary integrals this paper presents a conforming c1 boundary integral algorithm based on hermite interpolation this work is motivated by the requirement that the surface function multiplying a hypersingular kernel be differentiable at the collocation nodes the unknown surface derivatives utilized by the hermite approximation are determined consistent with other boundary values by writing a tangential hypersingular equation hypersingular equations are primarily invoked for solving crack problems and the focus herein is on developing a suitable approximation for this geometry test calculations for the laplace equation in two dimensions indicate that the algorithm is a promising technique for three dimensional problems

convergence of a shock capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions convergence of a shock capturing streamline diffusion nite element method for a conservation law in two space dimensions

cubic spline boundary elements the boundary integral method is formulated and applied using cubic spline interpolation along the boundary for both the geometry and the primary variables the cubic spline interpolation has continuous first and second derivatives between elements thus allowing the accurate calculation of derivative dependent functions on the boundary such as velocity in potential flow the spline functions also smooth the geometry and can represent curved sections with fewer nodes the results of numerical experiments indicate that the accuracy of the boundary integral equation method is improved for a given number of elements by using cubic spline interpolation it is however necessary to use numerical quadrature the quadrature slows calculation and or degrades the accuracy the numerical experiments indicate that most problems run faster for a given accuracy using linear interpolation there seems to be a class of problems however which requires higher order interpolation and or continuous derivatives for which the cubic spline interpolation works much better than linear interpolation

adjustment of provisional mortality series the dynamic linear model with structured measurement errors abstract we consider the problem of adjusting provisional time series using a bivariate structural model with correlated measurement errors maximum likelihood estimators and a minimum mean squared error adjustment procedure are derived for a provisional and final series containing common trend and seasonal components the model also includes measurement errors common to both series and errors that are specific to the provisional series we illustrate the technique by using provisional data to forecast ischemic heart disease mortality

well posedness of general boundary value problems for scalar conservation laws in this paper we investigate well posedness for the problem u t div ph u f on 0 t times om om subset r n with initial condition u 0 cdot u 0 on om and with general dissipative boundary conditions varphi u cdot nu in beta t x u on 0 t times ptl om here for a e t x in 0 t times ptl om beta t x cdot is a maximal monotone graph on r this includes as particular cases dirichlet neumann robin obstacle boundary conditions and their piecewise combinations as for the well studied case of the dirichlet condition one has to interprete the it formal boundary condition given by beta by replacing it with the adequate it effective boundary condition such effective condition can be obtained through a study of the boundary layer appearing in approximation processes such as the vanishing viscosity approximation we claim that the formal boundary condition given by beta should be interpreted as the effective boundary condition given by another monotone graph tilde beta which is defined from beta by the projection procedure we describe we give several equivalent definitions of entropy solutions associated with tilde beta and thus also with beta for the notion of solution defined in this way we prove existence uniqueness and l 1 contraction monotone and continuous dependence on the graph beta convergence of approximation procedures and stability of the notion of entropy solution are illustrated by several results

an application of the seasonal fractionally differenced model to the monetary aggregates abstract in this article three significant variables used by the u s federal reserve as targets to shape monetary policy the monetary aggregates m1 m2 and m3 are examined using a seasonal fractionally differenced model the sample autocorrelation functions of these monetary variables exhibit a decay pattern at the seasonal lags that is typical of a fractional model the seasonal fractionally differenced model is found to remove a great deal of the autocorrelation at the seasonal lags especially when a series is extended by splicing together earlier monetary data some monte carlo evidence as to the efficacy of this technique is presented finally one year ahead out of sample forecasts of m1 are made using both the box jenkins airline model and the seasonal fractionally differenced model

renormalized meshfree schemes i consistency stability and hybrid methods for conservation laws this paper is devoted to the study of a new kind of meshfree scheme based on a new class of meshfree derivatives the renormalized meshfree derivatives which improve the consistency of the original weighted particle methods the weak renormalized meshfree scheme built from the weak formulation of general conservation laws turns out to be l 2 stable under some geometrical conditions on the distribution of particles and some regularity conditions of the transport field a time discretization is then performed by analogy with finite volume methods and the l 1 l infty and bv stabilities of the obtained time discretized scheme are studied from the same analogy with finite volume methods a hybrid particle scheme is built using the godunov method and is numerically compared to the weak renormalized scheme

the effect of seasonal adjustment filters on tests for a unit root abstract we consider the effect of seasonal adjustment filters in univariate dynamic models we concentrate our analysis on the behavior of the least squares estimator of the sum of the autoregressive coefficients in a regression we show the existence of a limiting upward bias with the x 11 filter when the process does not contain a unit root we quantify the extent of this bias for a range of models and filtering procedures the asymptotic bias has interesting implications with respect to the power of tests for a unit root in order to assess the importance of this effect we present an extensive simulation study of both the size and power of the usual dickey fuller 1979 and phillips perron 1988 statistics we show that in many cases there is considerable reduction in power compared to the benchmark cases where the data is unfiltered finally some practical implications of our study are addressed with respect to tests for unit roots with seasonally adjusted data

a cubic spline boundary integral method for two dimensional free surface flow problems a cubic spline boundary integral equation method is presented for solution of free surface potential problems in two dimensions in this scheme it is possible to enforce a condition of conitnuous velocity through a geometric corner point in addition to the condition of continuous potential only the latter condition is possible in a linear element version of the model a detailed description of the method is provided test computations concerning a propagating linear wave show a remarkable improvement in the performance of the method compared to the linear and constant element versions both of which are prevalent in free surface hydrodynamics applications what is particularly emphasized is the level of accuracy that can be achieved from the presented method both globally and locally at and near the corner

on nonlinear diffusion problems with strong degeneracy in this paper we study the triply degenerate problem b v t g v div v f on q 0 t b v 0 b v0 on and g v g a on some part of the boundary 0 t in the case of continuous nonhomogeneous and nonstationary boundary data a the functions b g are assumed to be continuous locally lipschitz nondecreasing and to verify the normalization condition b 0 g 0 0 and the range condition r b g r using monotonicity and penalization methods we prove existence of a weak renormalized entropy solution in the spirit of k ammar j carrillo p wittbold scalar conservation laws with general boundary condition and continuous flux function j differential equations 228 2006 111 139

the effects of asymmetric filters on seasonal factor revisions abstract recent data seasonally adjusted by moving average methods are subject to revisions due to differences in the properties of the linear filters for the same seasonal adjustment when later data become available this article introduces a measure of the total revision associated with the concurrent and forecasting seasonal filters and applies it to the census method ii x 11 variant and the x 11 arima method to consider the fact that the spectrum of many economic indicators tends to have higher peaks at the lower seasonal frequencies than at the higher the revision measures are calculated both over all the seasonal frequencies and over selected seasonal frequency intervals

stability of the 1d ibvp for a non autonomous scalar conservation law we prove the stability with respect to the flux of solutions to initial boundary value problems for scalar non autonomous conservation laws in one space dimension key estimates are obtained through a careful construction of the solutions

a separation of the boundary geometry from the boundary functions in pies for 3d problems modeled by the navier lame equation abstract in this paper we present a modification of the somigliana identity for the 3d navier lame equation in order to analytically include in its mathematical formalism the boundary represented by coons and bezier parametric surface patches as a result the equations called the parametric integral equation system pies with integrated boundary shape are obtained the pies formulation is independent from the boundary shape representation and it is always for any shape defined in the parametric domain and not on the physical boundary as in the traditional boundary integral equations bie this feature is also helpful during numerical solving of pies as from a formal point of view a separation between the approximation of the boundary and the boundary functions is obtained in this paper the generalized chebyshev series are used to approximate the boundary functions numerical examples demonstrate the effectiveness of the presented strategy for boundary representation and indicate the high accuracy of the obtained results

the numerical interface coupling of nonlinear hyperbolic systems of conservation laws i the scalar case we study the theoretical and numerical coupling of two general hyperbolic conservation laws the coupling preserves in a weak sense the continuity of the solution at the interface without imposing the overall conservativity of the coupled model in order to analyze the convergence of the coupled numerical scheme we first revisit the approximation of the boundary value problems we then prove the convergence and characterize the limit solution of the coupled schemes in a few simple but significative coupling situations the general coupling problem is analyzed for riemann initial data and illustrated by numerical simulations resume nous nous interessons a une nouvelle forme de couplage de deux systemes hyperboliques de lois de conservation ce couplage assure de facon faible la continuite de la solution a l interface sans imposer la conservativite du modele couple pour etudier la convergence du schema d approximation numerique nous commencons par reprendre les resultats concernant l approximation du probleme aux limites nous demontrons ensuite la convergence du schema couple dans un certain nombre de cas interessants le cas general du couplage est etudie et illustre numeriquement pour une donnee initiale de riemann

convergence of the finite volume method for multidimensional conservation laws we establish the convergence of the finite volume method applied to multidimensional hyperbolic conservation laws and based on monotone numerical flux functions our technique applies with a fairly unrestrictive assumption on the triangulations flat elements are allowed and to lipschitz continuous flux functions we treat the initial and boundary value problem and obtain the strong convergence of the scheme to the unique entropy discontinuous solution in the sense of kruzkov the proof of convergence is based on a convergence framework coquel and lefloch math comp 57 1991 pp 169 210 and j numer anal 30 1993 pp 675 700 from a convex decomposition of the scheme we derive a new estimate for the rate of entropy dissipation and a new formulation of the discrete entropy inequalities these estimates are shown to be sufficient for the passage to the limit in the discrete equation convergence follows from diperna s uniqueness result in the class of entropy measure valued solutions

errors in variables and seasonal adjustment procedures abstract seasonal adjustment procedures attempt to estimate the sample realizations of an unobservable economic time series in the presence of both seasonal and irregular factors in this article we consider a factor that has not been considered explicitly in previous treatments of seasonal adjustment measurement error because of the sample design used in the current population survey measurement error will not be a white noise process but instead it will be characterized by serial correlation of a known form we first consider what effect the serially correlated measurement error has on estimation of the nonseasonal component in seasonal adjustment models we also consider the effect of measurement error on the widely used seasonal adjustment process x 11 estimated unobserved components models are used to estimate the precision root mean squared error of the official and optimal seasonally adjusted data

an arima model based approach to seasonal adjustment abstract this article proposes a model based procedure to decompose a time series uniquely into mutually independent additive seasonal trend and irregular noise components the series is assumed to follow the gaussian arima model properties of the procedure are discussed and an actual example is given

sensitivity analysis of seasonal adjustments empirical case studies abstract three detailed case studies illustrating the seasonal analysis of economic time series are presented using component models for seasonal and nonseasonal behavior analyses are performed within a semi bayesian framework where inferences for target quantities of interest such as seasonally adjusted values are obtained as posterior distributions conditional on observed data and fitted parameter values such an approach is similar to previous model based methods of seasonal analysis but new models and algorithms are used and more important a sensitivity analysis is performed to determine the extent to which conclusions vary across a range of plausible fitted models it is found that sensitivity to variation across plausible models is not unusual in practice the logical conclusion of the investigation is that a fully bayesian analysis is required that averages conditional posteriors over a posterior distribution for the model parameters such an analysis is necessarily sensitive to the choice of

a theory of l 1 dissipative solvers for scalar conservation laws with discontinuous flux we propose a general framework for the study of l1 contractive semigroups of solutions to conservation laws with discontinuous flux u t mathfrak f x u x 0 qquad mathfrak f x u left begin array ll f l u x 0 end array right quad quad quad rm cl where the fluxes fl fr are mainly assumed to be continuous developing the ideas of a number of preceding works baiti and jenssen in j differ equ 140 1 161 185 1997 towers in siam j numer anal 38 2 681 698 2000 towers in siam j numer anal 39 4 1197 1218 2001 towers et al in skr k nor vidensk selsk 3 1 49 2003 adimurthi et al in j math kyoto university 43 1 27 70 2003 adimurthi et al in j hyperbolic differ equ 2 4 783 837 2005 audusse and perthame in proc roy soc edinburgh a 135 2 253 265 2005 garavello et al in netw heterog media 2 159 179 2007 burger et al in siam j numer anal 47 1684 1712 2009 we claim that the whole admissibility issue is reduced to the selection of a family of elementary solutions which are piecewise constant weak solutions of the form c x c l11 left x 0 right we refer to such a family as a germ it is well known that cl admits many different l1 contractive semigroups some of which reflect different physical applications we revisit a number of the existing admissibility or entropy conditions and identify the germs that underly these conditions we devote specific attention to the vanishing viscosity germ which is a way of expressing the condition of diehl j hyperbolic differ equ 6 1 127 159 2009 for any given germ we formulate germ based admissibility conditions in the form of a trace condition on the flux discontinuity line x 0 in the spirit of vol pert math ussr sbornik 2 2 225 267 1967 and in the form of a family of global entropy inequalities following kruzhkov math ussr sbornik 10 2 217 243 1970 and carrillo arch ration mech anal 147 4 269 361 1999 we characterize those germs that lead to the l1 contraction property for the associated admissible solutions our approach offers a streamlined and unifying perspective on many of the known entropy conditions making it possible to recover earlier uniqueness results under weaker conditions than before and to provide new results for other less studied problems several strategies for proving the existence of admissible solutions are discussed and existence results are given for fluxes satisfying some additional conditions these are based on convergence results either for the vanishing viscosity method with standard viscosity or with specific viscosities adapted to the choice of a germ or for specific germ adapted finite volume schemes

modeling time series with calendar variation abstract the modeling of time series data that include calendar variation is considered autocorrelation trends and seasonality are modeled by arima models trading day variation and easter holiday variation are modeled by regression type models the overall model is a sum of arima and regression models methods of identification estimation inference and diagnostic checking are discussed the ideas are illustrated through actual examples

signal extraction for finite nonstationary time series summary for a signal plus noise model where both signal and noise are generated by nonstation ary arima autoregressive integrated moving average models we use the transformation approach of ansley kohn 1985 to construct an estimate of the signal and obtain its mean squared error given a finite number of observations a method for efficient computa tion of the signal estimate and its mean squared error is also presented consider observations z t generated by the signal plus noise nmodel z t s t n t 1s1 where both signal s t and noise n t follow nonstationary arima processes we give a solution to the finite sample signal extraction problem by defining an estimate of the signal s t given observations z 1 z n and finding its mean squared error the major difficulty in handling the model with nonstationary components is that the distribution of the observations is not defined unless assumptions are made about the initial values of the series moreover it is usually very difficult to formulate reasonable assumptions about the initial values because they affect the correlation structure of the whole series see for example the discussion of bell 1984 p 652 kohn ansley 1986 use a transformation approach to overcome the initial value problem in defining the likelihood and obtaining predittors and interpolators for an arima model which may have missing values this approach does not require any assumptions about the initial values and generalizes the usual differencing approach of box jenkins 1976 for the case where there are no missing observations in the present paper we apply the transformation approach of kohn ansley 1986 and ansley kohn 1985 to solve the signal extraction problem we define a linear estimator a t of s t so that s t sa t is invariant to the initial values and furthermore is unbiased in the sense that e s t s t 0 moreover it has minimum mean squared error amongst all such estimators our approach allows missing observations and extends to signal extraction for several additive signals when each is an arima process we also show how to compute the signal estimate and its mean squared error efficiently by writing the model in state space form placing a diffuse prior on the initial values of the process and then using the modified kalman filter and the modified smoothing algorithm of ansley kohn 1985 and kohn ansley 1986 gersch kitagawa 1983 kitagawa gersch 1984 and harvey todd 1983 use

sharp cfl discrete kinetic formulation and entropic schemes for scalar conservation laws we consider semidiscrete and fully discrete conservative finite volume schemes approximating the solution to one dimensional scalar conservation law we show that all e schemes are associated with a discrete kinetic formulation with a nonnegative kinetic defect measure this construction provides an alternative proof of the discrete local entropy inequalities with simple expressions of the discrete entropy fluxes in contrast to the known results which are restricted to cfl of the form lambda q leq 1 2 our proof holds under sharp cfl conditions

bezier curves in the modification of boundary integral equations bie for potential boundary values problems the paper presents a modification of the classical boundary integral equation method biem for two dimensional potential boundary values problems the proposed modification consists in describing the boundary geometry by means of bezier curves as a result of this analytical modification of the biem a new parametric integral equation system pies was obtained the kernels of these equations include the geometry of the boundary this new pies is no longer defined on the boundary as in the case of the biem but on the straight line for any given domain the solution of the new pies does not require a boundary discretization since it can be reduced merely to an approximation of boundary functions to solve this pies a pseudospectral method has been proposed and the results obtained were compared with exact solutions

nonhomogeneous dirichlet problems for degenerate parabolic hyperbolic equations the aim of the paper is to give a formulation for the initial boundary value problem of parabolic hyperbolic type in the case of nonhomogeneous boundary data a 0 here u u x t with x t q 0 t where is a bounded domain in n with smooth boundary and t 0 the function b is assumed to be nondecreasing allowing degeneration zones where b is constant is locally lipschitz continuous and g l 0 b after introducing the definition of an entropy solution to the above problem in the spirit of otto 14 we prove uniqueness of the solution in the proposed setting moreover we prove that the entropy solution previously defined can be obtained as the limit of solutions of regularized equations of nondegenerate parabolic type specifically the diffusion function b is approximated by functions b that are strictly increasing

limit boundary conditions for finite volume approximations of some physical problems in the industrial context finite volume schemes are used to compute an approximation of the solution of a system of equations set on a certain domain when this domain is bounded some numerical boundary conditions have to be implemented in order to complete the computation of the finite volume scheme this is a tricky step in the elaboration of the scheme which is still not mastered in fact at a closer sight it appears that there is a deep interaction between the understanding of the physical phenomena at the boundary of the domain and the implementation of the numerical boundary conditions unfortunately this link is not always completely intelligible and a reason for this lack of clarity is the fact that whereas the the continuous equation satisfied by the limit of the numerical solution is known the boundary conditions satisfied by this very limit are not well understood the purpose of this paper is to clarify this point in three industrial situations of one dimensional two phase flows

renormalized meshfree schemes ii convergence for scalar conservation laws we establish a convergence rate of the renormalized meshfree numerical scheme applied to scalar conservation laws renormalization is a tool introduced in order to eliminate the smoothed particle hydrodynamics sph lack of consistency a conservative scheme the weak renormalized scheme is derived from the general conservation laws weak formulation and is time discretized by using finite volume techniques because of the new form of the derivative approximation the convergence proof of the classical sph method cannot be applied thus we use a kruskov technique to obtain an l 1 norm comparison between the approximate solution and the solution of a regularized conservation law the pseudoviscous problem

hydrodynamics and hydrostatics for a class of asymmetric particle systems with open boundaries we consider attractive particle systems in mathbb z d with product invariant measures we prove that when particles are restricted to a subset of mathbb z d with birth and death dynamics at the boundaries the hydrodynamic limit is given by the unique entropy solution of a conservation law with boundary conditions in the sense of bardos et al comm part diff equ 4 1017 1034 1979 for the hydrostatic limit between parallel hyperplanes we prove a multidimensional version of the phase diagram conjectured in popkov and schutz europhys lett 48 257 263 1999 and show that it is robust with respect to perturbations of the boundaries

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

bayesian analysis of long memory and persistence using arfima models abstract this paper provides a bayesian analysis of autoregressive fractionally integrated moving average arfima models we discuss in detail inference on impulse responsens and show how bayesian methods can be used to i test arfima models against arima alternatives and ii take model uncertainty into account when making inferences on quantities of interest our methods are then used to investigate the persistence properties of real u s gnp

homogeneous dirichlet problems for quasilinear anisotropic degenerate parabolic hyperbolic equations the aim of this paper is to prove the well posedness existence and uniqueness of entropy solutions to the general anisotropic degenerate parabolic hyperbolic equations with l initial data and homogeneous dirichlet boundary condition we use the doubling variables device to prove a comparison theorem which implies the uniqueness the existence of entropy solutions can be obtained by finding the limit of solutions for the regularized equation of strictly parabolic type

the initial boundary value problem for general non local scalar conservation laws in one space dimension we prove global well posedness results for weak entropy solutions of bounded variation bv of scalar conservation laws with non local flux on bounded domains under suitable regularity assumptions on the flux function in particular existence is obtained by proving the convergence of an adapted lax friedrichs algorithm lipschitz continuos dependence from initial and boundary data is derived applying kru hkov s doubling of variable technique

convergence of an explicit finite volume scheme for first order symmetric systems this paper is devoted to the derivation of a o h1 2 error estimate for the classical upwind explicit in time finite volume scheme for linear first order symmetric systems such a result already existed for the corresponding implicit in time finite volume scheme since it can be interpreted as a particular case of the space time discontinuous galerkin method but the technique of proof used in that case does not extend to explicit schemes the general framework recently developed to analyse the convergence rate of finite volume schemes for non linear scalar conservation laws can not be used either because it is not adapted for systems even linear in this article we propose a new technique which takes advantage of the linearity of the problem the first step consists in controlling the approximation error u u h l2 by an expression of the form 2 where u is the exact solution g is a particular smooth function and h h are some linear forms depending on the approximate solution u h the second step consists in carefully estimating the error terms and by using uniform stability results for the discrete problem and regularity properties of the continuous solution

application of cubic hermitian algorithms to boundary element analysis of heat conduction this paper presents the application of cubic hermitian interpolation based finite element schemes for the time integration of the differential algebraic system arising in the dual reciprocity boundary element formulation of transient diffusion problems weighted residual procedure is used to obtain the desired recurrence relations numerical results presented for three representative problems involving different types of boundary conditions amply demonstrate the high accuracy of the cubic hermitian schemes

on concurrent seasonal adjustment abstract concurrent seasonal adjustment uses all information up to and including the current month s figure and thus should provide more accurate estimates of final seasonally adjusted data than the prevalent official method where the current month s component is forecasted from data through the preceding december this article evaluates the expected gain from employing concurrent seasonal adjustment including the case in which the data contain both nonseasonal and seasonal revisions the theoretical results are then applied to a linearized x 11 arima procedure using a group of common seasonal autoregressive integrated moving average arima models and to an analysis of actual series containing preliminary data error concurrent adjustment is consistently found to afford greater accuracy though to a smaller degree when not seasonally adjusted nsa data are also preliminary the problem of how best to seasonally adjust current data arises because both the usual x 11 and the optimal in a signal extr

measure valued solutions of scalar conservation laws with boundary conditions we define a solution concept for measure valued solutions to scalar conservation laws with initial conditions and boundary conditions and prove a uniqueness theorem for such solutions this result may be used to prove convergence towards the unique solution for approximate solutions which are uniformly bounded in l weakly consistent with certain entropy inequalities and strongly consistent with the initial condition i e without using derivative estimates as an example convergence of a finite element method is demonstrated

hermitian cubic boundary elements for two dimensional potential problems a hermite interpolation based formulation is presented for the boundary element analysis of two dimensional potential problems two three noded hermitian cubic elements hce are introduced for the modelling of corners or points with non unique tangents on the boundary these elements along with the usual two noded hce are used in numerical examples the results obtained show that faster convergence can be achieved using hce compared with using lagrange interpolation type quadratic elements qe for about the same amount of computing resources

error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method in this paper we derive a priori and a posteriori error estimates for cell centered finite volume approximations of nonlinear conservation laws on polygonal bounded domains numerical experiments show the applicability of the a posteriori result for the derivation of local adaptive solution strategies

convergence of finite volume monotone schemes for scalar conservation laws on bounded domains this paper is devoted to the study of the finite volume methods used in the discretization of conservation laws defined on bounded domains general assumptions are made on the data the initial condition and the boundary condition are supposed to be measurable bounded functions using a generalized notion of solution to the continuous problem namely the notion of entropy process solution see 9 and a uniqueness result on this solution we prove that the numerical solution converges to the entropy weak solution of the continuous problem in l p loc for every p in 1 infty this also yields a new proof of the existence of an entropy weak solution

a boundary value problem for a class of anisotropic degenerate parabolic hyperbolic equations we consider a mixed type boundary value problem for a class of degenerate parabolic hyperbolic equations namely we consider a cartesian product domain and split its boundary into two parts in one of them we impose a dirichlet boundary condition in the other we impose a neumann condition we apply a normal trace formula for l 2 divergence measure fields to prove a new strong trace property in the part of the boundary where the neumann condition is imposed we prove the existence and uniqueness of the entropy solution

formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary we study nonlinear hyperbolic conservation laws posed on a differential n 1 manifold with boundary referred to as a spacetime and defined from a prescribed flux field of n forms depending on a parameter the unknown variable a class of equations proposed by lefloch and okutmustur far east j math sci 31 49 83 2008 our main result is a proof of the convergence of the finite volume method for weak solutions satisfying suitable entropy inequalities a main difference with previous work is that we allow for slices with a boundary and in addition introduce a new formulation of the finite volume method involving the notion of total flux functions under a natural global hyperbolicity condition on the flux field and the spacetime and by assuming that the spacetime admits a foliation by compact slices with boundary we establish an existence and uniqueness theory for the initial and boundary value problem and we prove a contraction property in a geometrically natural l 1 type distance

entropy solutions for nonlinear degenerate problems we consider a class of elliptic hyperbolic degenerate equations g u delta b u divg phi u f with dirichlet homogeneous boundary conditions and a class of elliptic parabolic hyperbolic degenerate equations g u t delta b u divg phi u f with homogeneous dirichlet conditions and initial conditions existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function satisfying rather general conditions comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for continuous

kinetic approximation of a boundary value problem for conservation laws we design numerical schemes for systems of conservation laws with boundary conditions these schemes are based on relaxation approximations taking the form of discrete bgk models with kinetic boundary conditions the resulting schemes are riemann solver free and easily extendable to higher order in time or in space for scalar equations convergence is proved we show numerical examples including solutions of euler equations

numerical viscosity and convergence of finite volume methods for conservation laws with boundary conditions the authors study the convergence of finite volume schemes for general multidimensional conservation laws with boundary conditions a unique result for a measure valued solution which generalizes those of diperna for unbounded domains and szepessy for bounded domains is proved it gives us sufficient conditions to get convergence by studying carefully the entropy production for one dimensional e schemes we are able to prove convergence of finite volume e schemes under general assumption

first order quasilinear equations with boundary conditions in the l framework abstract we study a class of first order quasilinear equations on bounded domains in the l framework using the semi kru kov entropy flux pairs we define a weak entropy solution state an existence and uniqueness result and a maximum principle

on the convergence of shock capturing streamline diffusion finite element methods for hyperbolic conservation laws we extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the meh size with this term present we prove a maximum norm bound for finite element solutionsof burgers equation an thus complete an earlier convergence proof for this equation we further prove using entropy variables that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality asociated with the entropy variables results of some numerical experiments for the time dependent compressible euler equations in two dimensions are also reported

a smoothness priors state space modeling of time series with trend and seasonality abstract a smoothness priors modeling of time series with trends and seasonalities is shown an observed time series is decomposed into local polynomial trend seasonal globally stationary autoregressive and observation error components each component is characterized by an unknown variance white noise perturbed difference equation constraint the constraints or bayesian smoothness priors are expressed in state space model form trading day factors are also incorporated in the model a kalman predictor yields the likelihood for the unknown variances hyperparameters likelihoods are computed for different constraint order models in different subsets of constraint equation model classes akaike s minimum aic procedure is used to select the best model fitted to the data within and between the alternative model classes smoothing is achieved by using a fixed interval smoother algorithm examples are shown