a new a posteriori error estimate for the morley element in this paper we present a posteriori error analysis for the nonconforming morley element of the fourth order elliptic equation we propose a new residual based a posteriori error estimator and prove its reliability and efficiency these results refine those of beirao da veiga et al numer math 106 165 179 2007 by dropping two edge jump terms in both the energy norm of the error and the estimator and those of wang and zhang local a priori and a posteriori error estimates of finite elements for biharmonic equation research report 13 2006 by showing the efficiency in the sense of verfurth a review of a posteriori error estimation and adaptive mesh refinement techniques wiley teubner new york 1996 moreover the normal component in the estimators of beirao da veiga et al numer math 106 165 179 2007 and wang and zhang local a priori and a posteriori error estimates of finite elements for biharmonic equation research report 13 2006 is dropped and therefore only the tangential component of the stress on each edge comes into the estimator in addition we generalize these results to three dimensional case

the closure properties on real numbers under limits and computable operators in effective analysis various classes of real numbers are discussed for example the classes of computable semi computable weakly computable recursively approximable real numbers etc all these classes correspond to some kind of weak computability of the real numbers in this paper we discuss mathematical closure properties of these classes under the limit effective limit and computable function among others we show that the class of weakly computable real numbers is not closed under effective limit and partial computable functions while the class of recursively approximable real numbers is closed under effective limit and partial computable functions

chaitin ω numbers solovay machines and godel incompleteness computably enumerable c e reals can be coded by chaitin machines through their halting probabilities tuning solovay s construction of a chaitin universal machine for which zfc if arithmetically sound cannot determine any single bit of the binary expansion of its halting probability we show that every c e random real is the halting probability of a universal chaitin machine for which zfc cannot determine more than its initial block of 1 bits as soon as you get a 0 it is all over finally a constructive version of chaitin information theoretic incompleteness theorem is proven

a second order accurate difference scheme for an extended fisher kolmogorov equation in this paper we present a crank nicolson type finite difference scheme to approximate the nonlinear evolutionary extended fisher kolmogorov efk equation we prove the existence of the solution by using the well known browder fixed point theorem the stability of this scheme is established in l norm the uniqueness and convergence of the solution are analyzed we discuss an iterative algorithm for solving the difference scheme and prove its convergence

a robust prolongation operator for non nested finite element methods the paper is to present a general framework for designing a prolongation operator for general nonnested finite element methods the main idea is to take the inclusion interpolation in the unrefined region that consists of all unrefined elements and the canonical interpolation of the quasi interpolation in the quasi strict refined region that consists of children elements which are not neighbors of the unrefined region and define a careful mixture in the small layer between these two regions this leads to a robust prolongation operator that has both local projection and uniform boundedness properties for most of nonnested finite element methods in literature

new a posteriori error estimate and quasi optimal convergence of the adaptive nonconforming wilson element in this paper we establish the quasi optimal convergence of the adaptive nonconforming wilson element on the rectangular mesh the main ingredients are a new a posteriori error estimator and a crucial observation that there is some special orthogonality between the conforming part and the nonconforming part in the energy inner product which helps us to show the quasi orthogonality and the discrete reliability finally we integrate these components in a usual way to achieve the quasi optimal convergence

a posteriori error estimates for nonconforming finite element methods computable a posteriori error bounds for a large class of nonconforming finite element methods are provided for a model poisson problem in two and three space dimensions besides a refined residual based a posteriori error estimate an averaging estimator is established and an l 2 estimate is included the a posteriori error estimates are reliable and efficient the proof of reliability relies on a helmholtz decomposition

symmetrization and concentration inequalities for multilinear forms with applications to zero one laws for levy chaos we consider stochastic processes x x t t t represented as a levy chaos of finite order that is as a finite sum of multiple stochastic integrals with respect to a symmetric infinitely divisible random measure for a measurable subspace v of r t we prove a very general zero one law p x v 0 or 1 providing a complete analog to the corresponding situation in the case of symmetric infinitely divisible processes single integrals with respect to an infinitely divisible random measure our argument requires developing a new symmetrization technique for multi linear rademacher forms as well as generalizing kanter s concentration inequality to multiple sums

a type of adaptive c0 non conforming finite element method for the helmholtz transmission eigenvalue problem abstract the transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering in this paper for the helmholtz transmission eigenvalue problem in r d d 2 3 we discuss the a posteriori error estimates and adaptive algorithm of a type of c 0 non conforming finite elements including the morley zienkiewicz element and the modified zienkiewicz element we give the a posteriori error estimators for approximate eigenpair and prove their reliability and efficiency for eigenfunctions we also analyze their reliability for eigenvalues numerical results not only in r 2 but also in r 3 indicate that the a posteriori error estimators are sharp and the adaptive algorithm is efficient for computing real and complex transmission eigenvalues as expected

the adaptive ciarlet raviart mixed method for biharmonic problems with simply supported boundary condition abstract in this paper we study the adaptive fashion of the ciarlet raviart mixed method for biharmonic equation eigenvalue problem with simply supported boundary condition in r d we propose an a posteriori error indicator of the ciarlet raviart approximate solution for the biharmonic equation and an a posteriori error indicator of the ciarlet raviart approximate eigenfuction and prove the reliability and efficiency of the indicators we also give an a posteriori error indicator for the approximate eigenvalue and prove its reliability we design an adaptive ciarlet raviart mixed method with piecewise polynomials of degree less than or equal to m and numerical experiments show that numerical eigenvalues obtained by the method can achieve the optimal convergence order o d o f 2 m d d 2 m 2 3 d 3 m 3

nonconforming finite element analysis for a plate contact problem in this paper we analyze nonconforming finite element methods for solving a fourth order elliptic variational inequality of the second kind arising in a plate frictional contact problem the variational inequality involves a nondifferentiable term due to the frictional contact optimal order error estimates are derived for both continuous and discontinuous nonconforming finite elements

an anisotropic superconvergent nonconforming plate finite element the classical finite element convergence analysis relies on the following regularity condition there exists a constant c independent of the element k and the mesh such that h k r k

error reduction of the adaptive conforming and nonconforming finite element methods with red green refinement in this paper we analyze the convergence of the adaptive conforming and nonconforming p 1 finite element methods with red green refinement based on standard dorfler marking strategy since the mesh after refining is not nested into the one before the usual galerkin orthogonality or quasi orthogonality for newest vertex bisection does not hold for this case to overcome such a difficulty we develop some new quasi orthogonality instead under certain condition on the initial mesh condition a consequently we show convergence of the adaptive methods by establishing the reduction of some total errors to weaken the condition on the initial mesh we propose a modified red green refinement and prove the convergence of the associated adaptive methods under a much weaker condition on the initial mesh condition b furthermore we also develop an initial mesh generator which guarantee that all the interior triangles are equilateral triangles satisfy condition a and the other triangles containing at least one vertex on the boundary satisfy condition b

convergence of quadratic forms in p stable random variables and theta sub p radonifying operators abstract necessary and sufficient conditions are given for the almost sure convergence of a quadratic form where m sub j is a sequence of i i d p stable random variables a connection is established between the convergence of the quadratic form and a radonifying property of the infinite matrix operator f sub kj author

a morley finite element method for the displacement obstacle problem of clamped kirchhoff plates abstract we study a morley finite element method for the displacement obstacle problem of clamped kirchhoff plates on polygonal domains error estimates are derived in the energy norm and the l norm the performance of the method is illustrated by numerical experiments

error estimators for nonconforming finite element approximations of the stokes problem in this paper we define and analyze a posteriori error estimators for nonconforming approximations of the stokes equations we prove that these estimators are equivalent to an appropriate norm of the error for the case of piecewise linear elements we define two estimators both of them are easy to compute but the second is simpler because it can be computed using only the right hand side and the approximate velocity we show how the first estimator can be generalized to higher order elements finally we present several numerical examples in which one of our estimators is used for adaptive refinement

adaptive finite element methods with convergence rates adaptive finite element methods for numerically solving elliptic equations are used often in practice only recently 12 17 have these methods been shown to converge however this convergence analysis says nothing about the rates of convergence of these methods and therefore does in principle not guarantee yet any numerical advantages of adaptive strategies versus non adaptive strategies the present paper modifies the adaptive method of morin nochetto and siebert 17 for solving the laplace equation with piecewise linear elements on domains in 2 by adding a coarsening step and proves that this new method has certain optimal convergence rates in the energy norm which is equivalent to the h1 norm namely it is shown that whenever s 0 and the solution u is such that for each n 1 it can be approximated to accuracy o n s in the energy norm by a continuous piecewise linear function on a triangulation with n cells using complete knowledge of u then the adaptive algorithm constructs an approximation of the same type with the same asymptotic accuracy while using only information gained during the computational process moreover the number of arithmetic computations in the proposed method is also of order o n for each n 1 the construction and analysis of this adaptive method relies on the theory of nonlinear approximation

a unifying theory of a posteriori error control for nonconforming finite element methods residual based a posteriori error estimates were derived within one unifying framework for lowest order conforming nonconforming and mixed finite element schemes in carstensen numer math 100 617 637 2005 therein the key assumption is that the conforming first order finite element space v h c annulates the linear and bounded residual l written v h c subseteq rm ker ell that excludes particular nonconforming finite element methods ncfems on parallelograms in that v h c not subset rm ker ell the present paper generalises the aforementioned theory to more general situations to deduce new a posteriori error estimates also for mortar and discontinuous galerkin methods the key assumption is the existence of some bounded linear operator pi v h c rightarrow v h nc with some elementary properties it is conjectured that the more general hypothesis h1 h3 can be established for all known ncfems applications on various nonstandard finite element schemes for the laplace stokes and navier lame equations illustrate the presented unifying theory of a posteriori error control for ncfem

double set parameter finite element method for two sided displacement obstacle problem of clamped plate abstract double set parameter nonconforming finite element method fem for the two sided displacement obstacle problem of clamped plate is considered firstly a double set parameter nonconforming triangular element named veubeke zienkiewicz element is introduced which has the same global dimension as zienkiewicz element and can pass the generalized patch test for any mesh secondly we skillfully construct an enriching operator for connecting the veubeke zienkiewicz and the c 1 conforming bell element spaces with the help of this operator and an auxiliary obstacle problem built as a bridge between the continuous and discrete obstacle problems we present the optimal order error estimates in the broken energy norm and l norm respectively finally we establish a general framework of double set parameter nonconforming elements approximating for the two sided displacement obstacle problem of clamped plate

the limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions it is shown that the limits of the nested subclasses of five classes of infinitely divisible distributions on mathbb r d which are the jurek class the goldie steutel bondesson class the class of selfdecomposable distributions the thorin class and the class of generalized type g distributions are identical with the closure of the class of stable distributions more general results are also given

adaptive wick malliavin approximation to nonlinear spdes with discrete random variables we propose an adaptive wick malliavin wm expansion in terms of the malliavin derivative of order q to simplify the propagator of general polynomial chaos gpc of order p a system of deterministic equations for the coefficients of gpc and to control the error growth with respect to time specifically we demonstrate the effectiveness of the wm method by solving a stochastic reaction equation and a burgers equation with several discrete random variables exponential convergence is shown numerically with respect to q when q geq p 1 we also analyze the computational complexity of the wm method and identify a significant speedup with respect to gpc especially in high dimensions

a unifying theory of a posteriori finite element error control residual based a posteriori error estimates are derived within a unified setting for lowest order conforming nonconforming and mixed finite element schemes the various residuals are identified for all techniques and problems as the operator norm l of a linear functional of the form in the variable of a sobolev space v the main assumption is that the first order finite element space is included in the kernel ker l of l as a consequence any residual estimator that is a computable bound of l can be used within the proposed frame without further analysis for nonconforming or mixed fe schemes applications are given for the laplace stokes and navier lame equations

a new error analysis of nonconforming bergan s energy orthogonal element for the extended fisher kolmogorov equation abstract a nonconforming finite element method fem for short is proposed and analyzed for the fourth order extended fisher kolmogorov efk for short equation by employing the bergan s energy orthogonal plate element because the shape function and its first derivatives of this element are discontinuous at the element s vertices which is quite different from the conventional finite elements used in the existing literature a series of novel approaches including some a priori bounds and interpolation function splitting are developed to present a new error analysis for deriving optimal estimates of order o h in energy norm for both the semi discrete and backward euler fully discrete schemes at last numerical experiments are also provided to verify the theoretical analysis

orthogonal cubic spline collocation method for the extended fisher kolmogorov equation a second order splitting combined with orthogonal cubic spline collocation method is formulated and analysed for the extended fisher kolmogorov equation with the help of lyapunov functional a bound in maximum norm is derived for the semidiscrete solution optimal error estimates are established for the semidiscrete case finally using the monomial basis functions we present the numerical results in which the integration in time is performed using radau 5 software library

convergence of adaptive finite element methods adaptive finite element methods fems have been widely used in applications for over 20 years now in practice they converge starting from coarse grids although no mathematical theory has been able to prove this assertion ensuring an error reduction rate based on a posteriori error estimators together with a reduction rate of data oscillation information missed by the underlying averaging process we construct a simple and efficient adaptive fem for elliptic partial differential equations we prove that this algorithm converges with linear rate without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance extensions to higher order elements and applications to saddle point problems are discussed as well

relations between the s selfdecomposable and selfdecomposable measures the classes of the s selfdecomposable and decomposable probability measures are related to the limit distributions of sequences of random variables deformed by some nonlinear or linear transformations respectively both are characterized in many different ways among others as distributions of some random integrals in particular we get that each selfdecomposable probability measure is s selfdecomposable this and other relations between these two classes seem to be rather unexpected

periodic and homoclinic solutions of extended fisher kolmogorov equations in this paper we study the existence of periodic solutions of the fourth order equations uiv pu a x u b x u3 0 and uiv pu a x u b x u3 0 where p is a positive constant and a x and b x are continuous positive 2l periodic functions the boundary value problems p1 and p2 for these equations are considered respectively with the boundary conditions u 0 u l u 0 u l 0 existence of nontrivial solutions for p1 is proved using a minimization theorem and a multiplicity result using clark s theorem existence of nontrivial solutions for p2 is proved using the symmetric mountain pass theorem we study also the homoclinic solutions for the fourth order equation uiv pu a x u b x u2 c x u3 0 where p is a constant and a x b x and c x are periodic functions the mountain pass theorem of brezis and nirenberg and concentration compactness arguments are used

a new error analysis for discontinuous finite element methods for linear elliptic problems the standard a priori error analysis of discontinuous galerkin methods requires additional regularity on the solution of the elliptic boundary value problem in order to justify the galerkin orthogonality and to handle the normal derivative on element interfaces that appear in the discrete energy norm in this paper a new error analysis of discontinuous galerkin methods is developed using only the h k weak formulation of a boundary value problem of order 2k this is accomplished by replacing the galerkin orthogonality with estimates borrowed from a posteriori error analysis and by using a discrete energy norm that is well defined for functions in h k

a quadrilateral morley element for biharmonic equations in this paper we propose a morley type finite element for quadrilateral meshes to solve biharmonic problems for each quadrilateral q the finite element space is defined by the span of p 2 q plus two functions in p 3 q each of the cubic polynomials is the product of a pair of equations of opposite edges and the equation of the bimedian between them the degrees of freedom consist of the values at vertices and integrals of normal derivatives over edges optimal orders of convergence are proved both in discrete h 2 and h 1 seminorms several numerical tests confirm the convergence analysis

a posteriori error estimates for nonconforming finite element methods for fourth order problems on rectangles the a posteriori error analysis of conforming finite element discretisations of the biharmonic problem for plates is well established but nonconforming discretisations are more easy to implement in practice the a posteriori error analysis for the morley plate element appears very particular because two edge contributions from an integration by parts vanish simultaneously this crucial property is lacking for popular rectangular nonconforming finite element schemes like the nonconforming rectangular morley finite element the incomplete biquadratic finite element and the adini finite element this paper introduces a novel methodology and utilises some conforming discrete space on macro elements to prove reliability and efficiency of an explicit residual based a posteriori error estimator an application to the morley triangular finite element shows the surprising result that all averaging techniques yield reliable error bounds numerical experiments confirm the reliability and efficiency for the established a posteriori error control on uniform and graded tensor product meshes

finite difference discretization of the extended fisher kolmogorov equation in two dimensions approximate solutions are considered for the extended fisher kolmogorov efk equation in two space dimension with dirichlet boundary conditions by a crank nicolson type finite difference scheme a priori bounds are proved using lyapunov functional further existence uniqueness and convergence of difference solutions with order o h 2 k 2 in the l norm are proved numerical results are also given in order to check the properties of analytical solutions

divergence bounded computable real numbers a real x is called h bounded computable for some function h n n if there is a computable sequence xs of rational numbers which converges to x such that for any n at most h n non overlapping pairs of its members are separated by a distance larger than 2 n in this paper we discuss properties of h bounded computable reals for various functions h we will show a simple sufficient condition for a class of functions h such that the corresponding h bounded computable reals form an algebraic field a hierarchy theorem for h bounded computable reals is also shown besides we compare semi computability and weak computability with the h bounded computability for special functions h

a characterization of c e random reals a real is computably enumerable if it is the limit of a computable increasing converging sequence of rationals a real is random if its binary expansion is a random sequence our aim is to offer a self contained proof based on the papers calude et al in m morvan c meinel d krob eds proc 15th symp on theoretical aspects of computer science paris springer berlin 1998 pp 596 606 chaitin j assoc comput mach 22 1975 329 slaman manuscript 14 december 1998 2 pp solovay unpublished manuscript ibm thomas j watson research center yorktown heights new york may 1975 215 pp of the following theorem a real is c e and random if and only if it is a chaitino real i e the halting probability of some universal self delimiting turing machine

on the necessity and sufficiency of the patch test for convergence of nonconforming finite elements this paper proposes a weak patch test that improves both the patch test and the generalized patch test under a weak superapproximation assumption which can be obtained from certain approximation and weak continuity property it is shown that the weak patch test is equivalent to the generalized patch test thus if a nonconforming finite element passes the patch test and satisfies some approximation and weak continuity property its convergence is then guaranteed furthermore the consistency term of such a nonconforming element can be proved to be of order o h it is shown that if a nonconforming element does not pass the patch test and a condition relative to subdividing a domain by the element is true then one can find a family of triangulations for which the element is divergent

convergence analysis and error estimates of the element free galerkin method for the second kind of elliptic variational inequalities abstract this paper is presented for the convergence analysis of the element free galerkin method for the second kind of elliptic variational inequalities of which the dirichlet boundary conditions are imposed by the penalty method the error estimates illustrate that the convergence order depends not only on the nodal spacing and the number of basis functions in the moving least squares approximation but also the penalty factor a numerical example verifies the theoretical results of the element free galerkin method

quasi optimal convergence rate for an adaptive finite element method we analyze the simplest and most standard adaptive finite element method afem with any polynomial degree for general second order linear symmetric elliptic operators as is customary in practice the afem marks exclusively according to the error estimator and performs a minimal element refinement without the interior node property we prove that the afem is a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops this geometric decay is instrumental to derive the optimal cardinality of the afem we show that the afem yields a decay rate of the energy error plus oscillation in terms of the number of degrees of freedom as dictated by the best approximation for this combined nonlinear quantity

robust a posteriori error estimation for the nonconforming fortin soulie finite element approximation we obtain a computable a posteriori error bound on the broken energy norm of the error in the fortin soulie finite element approximation of a linear second order elliptic problem with variable permeability this bound is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms the estimator is completely free of unknown constants and provides a guaranteed numerical bound on the error

on series representations of infinitely divisible random vectors general results on series representations involving arrival times in a poisson process are established for infinitely divisible banach space valued random vectors without gaussian components applying these results various generalization of lepage s representation are obtained in a unified way certain conditionally gaussian infinitely divisible random vectors are characterized and some problems related to a gaussian randomization method are investigated

a new error analysis of bergan s energy orthogonal element for two sided displacement obstacle problem of clamped plate abstract the main aim of this paper is to present a new error analysis of the bergan s energy orthogonal plate element for the two sided displacement obstacle problem of clamped plate due to the exact solution does not belong to h l o c 4 and the shape function and its first derivatives are discontinuous at the element s vertices while all previous theoretical analysis always required the continuity of the shape function at element s vertices for the conventional finite elements a series of novel approaches including the definition of approximation subset the constructions of a one to one transferring operator and an enriching operator are developed to derive error estimates of order o h both in energy norm and l norm it seems that these results have never been seen in the existing literature

recursively enumerable reals and chaitin ω numbers a real is called recursively enumerable if it is the limit of a recursive increasing converging sequence of rationals following solovay unpublished manuscript ibm thomas j watson research center yorktown heights new york may 1975 215 pp and chaitin ibm j res develop 21 1977 350 359 496 we say that an r e real dominates an r e real if from a good approximation of from below one can compute a good approximation of from below we shall study this relation and characterize it in terms of relations between r e sets solovay s unpublished manuscript ibm thomas j watson research center yorktown heights new york may 1975 215 pp like numbers are the maximal r e real numbers with respect to this order they are random r e real numbers the halting probability of a universal self delimiting turing machine chaitin s number j assoc comput mach 22 1975 329 340 is also a random r e real solovay showed that any chaitin number is like in this paper we show that the converse implication is true as well any like real in the unit interval is the halting probability of a universal self delimiting turing machine

a fully discrete c0 interior penalty galerkin approximation of the extended fisher kolmogorov equation a fully discrete c 0 interior penalty finite element method is proposed and analyzed for the extended fisher kolmogorov efk equation u email protected d email protected u 3 u 0 with appropriate initial and boundary conditions where c is a positive constant we derive a regularity estimate for the solution u of the efk equation that is explicit in c and as a consequence we derive a priori error estimates that are robust in c

fast computation in adaptive tree approximation adaptive methods of approximation arise in many settings including numerical methods for pdes and image processing they can usually be described by a tree which records the adaptive decisions this paper is concerned with the fast computation of near optimal trees based on n adaptive decisions the best tree based on n adaptive decisions could be found by examining all such possibilities however this is exponential in n and could be numerically prohibitive the main result of this paper is to show that it is possible to find near optimal trees using computations linear in n

convergence and optimality of adaptive mixed finite element methods the convergence and optimality of adaptive mixed finite element methods for the poisson equation are established in this paper the main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure of orthogonality a quasi orthogonality property is proved using the fact that the error is orthogonal to the divergence free subspace while the part of the error that is not divergence free can be bounded by the data oscillation using a discrete stability result this discrete stability result is also used to get a localized discrete upper bound which is crucial for the proof of the optimality of the adaptive approximation

convergence and optimality of the adaptive morley element method this paper is devoted to the convergence and optimality analysis of the adaptive morley element method for the fourth order elliptic problem a new technique is developed to establish a quasi orthogonality which is crucial for the convergence analysis of the adaptive nonconforming method by introducing a new parameter dependent error estimator and further establishing a discrete reliability property sharp convergence and optimality estimates are then fully proved for the fourth order elliptic problem

framework for the a posteriori error analysis of nonconforming finite elements this paper establishes a unified framework for the a posteriori error analysis of a large class of nonconforming finite element methods the theory assures reliability and efficiency of explicit residual error estimates up to data oscillations under the conditions h1 h2 and applies to several nonconforming finite elements the crouzeix raviart triangle element the han parallelogram element the nonconforming rotated nr parallelogram element of rannacher and turek the constrained nr parallelogram element of hu and shi the p 1 element on parallelograms due to park and sheen and the dssy parallelogram element the theory is extended to include 1 irregular meshes with at most one hanging node per edge

random integral representations for classes of limit distributions similar to levy class l0 iii for 1 0 subclasses u of the levy class l o of selfdecomposable measures on banach spaces are examined they are defined as limit distributions in certain summation schemes the main result in section 1 theorem 1 2 shows that each measure i from u is a convolution of a strictly stable measure with exponent and a probability distribution of random integral int 0 1 tdy t beta where y is a levy process with finite th moment the situation differs essentially from that with positive u theorem 2 2 in section 2 shows that the natural mapping pounds y 1 to pounds int 0 1 tdy t beta is a homeomorphism which immediately gives so called generators for the classu in addition potential applications of measures from u in the ising model for ferromagnetism are indicated finally remark 3 b shows that the classes u constitute a filtration of the semigroup id of all infinitely divisible measures

a new factorization property of the selfdecomposable probability measures we prove that the convolution of a selfdecomposable dis tribution with its background driving law is again selfdecomposable if and only if the background driving law is s selfdecomposable we will refer to this as the factorization property of a selfdecomposable distribution let l f denote the set of all these distributions the algebraic structure and various characterizations of l f are studied some examples are discussed the most interesting one being given by the levy stochastic area integral a nested family of subclasses l f n 0 or a filtration of the class l f is given

semi discrete stabilized finite element methods for navier stokes equations with nonlinear slip boundary conditions based on regularization procedure based on the pressure projection stabilized methods the semi discrete finite element approximation to the time dependent navier stokes equations with nonlinear slip boundary conditions is considered in this paper because this class of boundary condition includes the subdifferential property then the variational formulation is the navier stokes type variational inequality problem using the regularization procedure we obtain a regularized problem and give the error estimate between the solutions of the variational inequality problem and the regularized problem with respect to the regularized parameter varepsilon which means that the solution of the regularized problem converges to the solution of the navier stokes type variational inequality problem as the parameter varepsilon longrightarrow 0 moreover some regularized estimates about the solution of the regularized problem are also derived under some assumptions about the physical data the pressure projection stabilized finite element methods are used to the regularized problem and some optimal error estimates of the finite element approximation solutions are derived

the f e m test for convergence of nonconforming finite elements on etablit un nouveau critere de convergence pour les elements finis non conformes qui est facilement verifiable le long de chaque interface

new error estimates of the morley element for the plate bending problems in this paper we derive some new error estimates of a nonconforming morley element for the plate bending problems our aim is fourfold first it shows that the consistency error of the morley element can be controlled by its corresponding approximation error up to an arbitrarily high order term especially which can be of arbitrary order provided that f on the right hand side is piecewise smooth enough thus the total energy norm is dominated alone by the approximation error second as a byproduct we derive the error estimate under the regularity assumption u h 2 s with s 0 1 which fills the gap in the a priori error estimate of the morley element with low regularity for s 0 1 2 third based on this new error bound a robust convergence is proved even if the solution is exactly in h 2 finally by a slight modification of the variational formulation a new error estimate is also derived for the case f h 1 the key role is played by some quasi interpolation operators and the weak continuous properties of morley finite element space the main ideas and results presented here are motivated by mao and shi 2010 and can be viewed as its extension to fourth order problems

data oscillation and convergence of adaptive fem data oscillation is intrinsic information missed by the averaging process associated with finite element methods fem regardless of quadrature ensuring a reduction rate of data oscillation together with an error reduction based on a posteriori error estimators we construct a simple and efficient adaptive fem for elliptic partial differential equations pdes with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance

c 0 nonconforming tetrahedral and cuboid elements for the three dimensional fourth order elliptic problem in this paper a theoretical framework is constructed on how to develop c 0 nonconforming elements for the fourth order elliptic problem by using the bubble functions a simple practical method is presented to construct one tetrahedral c 0 nonconforming element and two cuboid c 0 nonconforming elements for the fourth order elliptic problem in three spacial dimensions it is also proved that one element is of first order convergence and other two are of second order convergence from the best knowledge of us this is the first success in constructing the second order convergent nonconforming element for the fourth order elliptic problem

non gaussian ornstein uhlenbeck based models and some of their uses in financial economics non gaussian processes of ornstein uhlenbeck ou type offer the possibility of capturing important distributional deviations from gaussianity and for flexible modelling of dependence structures this paper develops this potential drawing on and extending powerful results from probability theory for applications in statistical analysis their power is illustrated by a sustained application of ou processes within the context of finance and econometrics we construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive ou processes and we study these models in relation to financial data and theory

a discrete helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes the discrete reliability of a finite element method is a key ingredient to prove optimal convergence of an adaptive mesh refinement strategy and requires the interchange of a coarse triangulation and some arbitrary refinement of it one approach for this is the careful design of an intermediate triangulation with one level refinements and with the remaining difficulty to design some interpolation operator which maps a possibly nonconforming approximation into the finite element space based on the finer triangulation this paper enfolds the second possibility of some novel discrete helmholtz decomposition for the nonconforming morley finite element method this guarantees the optimality of a standard adaptive mesh refining algorithm for the biharmonic equation numerical examples illustrate the crucial dependence of the bulk parameter and the surprisingly short pre asymptotic range of the adaptive morley finite element method

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

high level excursion set geometry for non gaussian infinitely divisible random fields nsa grant mspf 05g 049 aro grant w911nf 07 1 0078 us israel binational science foundation grant 2004064

on asymptotic errors in discretization of processes we study the rate at which the difference xnt xt x nt n between a process x and its time discretization converges when x is a continuous semimartingale it is known that under appropriate assumptions the rate is n so we focus here on the discontinuous case then nxn explodes for any sequence n going to infinity so we consider integrated errors of the form ynt t0xnsds or zn pt t0 xns pds for p 0 we essentially prove that the variables sups t nyns and sups tnzn ps are tight for any finite t when x is an arbitrary semimartingale provided either p 2 or break p 0 2 and x has no continuous martingale part and the sum s t xs p converges a s for all t and in addition x is the sum of its jumps when p 1 under suitable additional assumptions we even prove that the discretized processes nyn nt n and nzn p nt n vadjust vspace 1pt converge in law to nontrivial processes which are explicitly given as a by product we also obtain a generalization of ito s formula for functions that are not twice continuously differentiable and which may be of interest by itself

quasi monte carlo method for infinitely divisible random vectors via series representations an infinitely divisible random vector without gaussian component admits representations of shot noise series due to possible slow convergence of the series they have not been investigated as a device for monte carlo simulation in this paper we investigate the structure of shot noise series representations from a simulation point of view and discuss the effectiveness of quasi monte carlo methods applied to series representations the structure of series representations in nature tends to decrease their effective dimension and thus increase the efficiency of quasi monte carlo methods thanks to the greater uniformity of low discrepancy sequence in the lower dimension we illustrate the effectiveness of our approach through numerical results of moment and tail probability estimations for stable and gamma random variables

an inexpensive method for the evaluation of the solution of the lowest order raviart thomas mixed method for the model problem operatorname div a nabla u f we show how the approximate solution produced by the raviart thomas lecture notes in mathematics 606 springer verlag berlin 1977 mixed method of lowest degree can be obtained from the solution of the p 1 nonconforming galerkin method modified in a virtually cost free manner

the completion of locally refined simplicial partitions created by bisection recently in found comput math 7 2 2007 245 269 we proved that an adaptive finite element method based on newest vertex bisection in two space dimensions for solving elliptic equations which is essentially the method from sinum 38 2000 466 488 by morin nochetto and siebert converges with the optimal rate the number of triangles n in the output partition of such a method is generally larger than the number m of triangles that in all intermediate partitions have been marked for bisection because additional bisections are needed to retain conforming meshes a key ingredient to our proof was a result from numer math 97 2004 219 268 by binev dahmen and devore saying that n n 0 cm for some absolute constant c where n 0 is the number of triangles from the initial partition that have never been bisected in this paper we extend this result to bisection algorithms of n simplices with that generalizing the result concerning optimality of the adaptive finite element method to general space dimensions

a posteriori error estimates for the morley plate bending element a local a posteriori error indicator for the well known morley element for the kirchhoff plate bending problem is presented the error indicator is proven to be both reliable and efficient the technique applied is general and it is shown to have also other applications

convergence analysis of an adaptive nonconforming finite element method an adaptive nonconforming finite element method is developed and analyzed that provides an error reduction due to the refinement process and thus guarantees convergence of the nonconforming finite element approximations the analysis is carried out for the lowest order crouzeix raviart elements and leads to the linear convergence of an appropriate adaptive nonconforming finite element algorithm with respect to the number of refinement levels important tools in the convergence proof are a discrete local efficiency and a quasi orthogonality property the proof does neither require regularity of the solution nor uses duality arguments as a consequence on the data control no particular mesh design has to be monitored

on infinitely divisible semimartingales stricker s theorem states that a gaussian process is a semimartingale in its natural filtration if and only if it is the sum of an independent increment gaussian process and a gaussian process of finite variation see stricker z wahrsch verw geb 64 3 303 312 1983 we consider extensions of this result to non gaussian infinitely divisible processes first we show that the class of infinitely divisible semimartingales is so large that the natural analog of stricker s theorem fails to hold then as the main result we prove that an infinitely divisible semimartingale relative to the filtration generated by a random measure admits a unique decomposition into an independent increment process and an infinitely divisible process of finite variation consequently the natural analog of stricker s theorem holds for all strictly representable processes as defined in this paper since gaussian processes are strictly representable due to hida s multiplicity theorem the classical stricker s theorem follows from our result another consequence is that the question when an infinitely divisible process is a semimartingale can often be reduced to a path property when a certain associated infinitely divisible process is of finite variation this gives the key to characterize the semimartingale property for many processes of interest along these lines using basse o connor and rosinski stoch process appl 123 6 1871 1890 2013a we characterize semimartingales within a large class of stationary increment infinitely divisible processes this class includes many infinitely divisible processes of interest including linear fractional processes mixed moving averages and supou processes as particular cases the proof of the main theorem relies on series representations of jumps of cadlag infinitely divisible processes given in basse o connor and rosinski ann probab 41 6 4317 4341 2013b combined with techniques of stochastic analysis