non perturbative solution of the klein gordon zakharov equation abstract the initial value problem for the klein gordon zakharov equation is solved by decomposition for x r 3

analysis of a fourth order scheme for a three dimensional convection diffusion model problem we derive closed form expressions for the eigenvalues and discrete solution arising from a 19 point compact discretization of a three dimensional convection diffusion problem it is shown that the coefficient matrix is positive definite when the cell reynolds number is greater than some critical value by analyzing the terms composing the discrete solution we prove that an oscillation free discrete solution is guaranteed whenever the cell reynolds number exceeds a value which is grid size dependent an interesting result is that as the mesh size is refined this value approaches the golden mean

stability and convergence of a class of enhanced strain methods a stability and convergence analysis is presented of a recently proposed variational formulation and finite element method for elasticity which incorporates an enhanced strain field the analysis is carried out for problems posed on polygonal domains in r n the finite element meshes of which are generated by affine maps from a master element the formulation incorporates as a special case the classical method of incompatible modes the problem initially has three variables viz displacement stress and enhanced strain but the stress is later eliminated by imposing a condition of orthogonality with respect to the enhanced strains two other conditions on the choice of finite element spaces ensure that the approximations are stable and convergent some features of nearly incompressible and incompressible problems are also investigated for these cases it is possible to argue that locking will not occur and that the only spurious pressures present are the so called checkerboard modes it is shown th

least squares methods for linear elasticity based on a discrete minus one inner product abstract the purpose of this paper is to develop and analyze least squares approximations for elasticity problems the major advantage of the least squares formulation is that it does not require that the classical ladyzhenskaya bab ska brezzi lbb condition be satisfied by employing least squares functionals which involve a discrete inner product which is related to the inner product in h 1 the sobolev space of order minus one on we develop a finite element method which is unconditionally stable for problems with traction type of boundary conditions and for almost and incompressible elastic media the use of such inner products applied to second order problems was proposed in an earlier paper by bramble lazarov and pasciak math comp 66 1997 935

uniform convergence and a posteriori error estimation for assumed stress hybrid finite element methods assumed stress hybrid methods are known to improve the performance of standard displacement based finite elements and are widely used in computational mechanics the methods are based on the hellinger reissner variational principle for the displacement and stress variables this work analyzes two existing 4 node hybrid stress quadrilateral elements due to pian and sumihara t h h pian k sumihara rational approach for assumed stress finite elements int j numer methods engrg 20 9 1984 1685 1695 and due to xie and zhou x p xie t x zhou optimization of stress modes by energy compatibility for 4 node hybrid quadrilaterals int j numer methods engrg 59 2004 293 313 which behave robustly in numerical benchmark tests for the finite elements the isoparametric bilinear interpolation is used for the displacement approximation while different piecewise independent 5 parameter modes are employed for the stress approximation we show that the two schemes are free from poisson locking in the sense that the error bound in the a priori estimate is independent of the relevant lame constant we also establish the equivalence of the methods to two assumed enhanced strain schemes finally we derive reliable and efficient residual based a posteriori error estimators for the stress in l2 norm and the displacement in h1 norm and verify the theoretical results by some numerical experiments

convergence of an efficient and compact finite difference scheme for the klein gordon zakharov equation a compact and semi explicit finite difference scheme is proposed and analyzed for the klein gordon zakharov kgz equation the new scheme is decoupled and linearized in practical computation i e at each time step only two tri diagonal systems of linear algebraic equations need to be solved by thomas algorithm so the new scheme is more efficient and more accurate than the classical finite difference schemes unique solvability of the difference solution is proved by using the energy method besides the standard energy method in order to overcome the difficulty in obtaining the a priori estimate an induction argument is introduced to prove that the new scheme is convergent for u x t in the discrete h 1 norm and respectively for m x t in the discrete l 2 norm at the order of o 2 h 4 with time step and mesh size h numerical results are reported to verify the theoretical analysis

a review of a posteriori error estimation techniques for elasticity problems within the framework of linearized elasticity we give an overview of the most popular a posteriori error estimators we discuss their common features the main differences and the underlying principles this will allow us to judge the quality of the different approaches and their suitability for nonlinear problems we also briefly describe a general framework which allows the construction of a posteriori error estimators for nonlinear elasticity

on the convergence of a high accuracy conservative scheme for the zakharov equations abstract in this paper a high accuracy conservative difference scheme is presented to solve the initial boundary value problem of the zakharov equations which preserves the original conservative properties the proposed scheme is based on finite difference method the scheme is second order accuracy in time and fourth order accuracy in space a detailed numerical analysis of the scheme is presented including a convergence analysis result numerical examples are given to confirm the proposed scheme is efficient reliable and of high accuracy

enhanced assumed strain elements and locking in membrane problems abstract the assumptions which guarantee convergence of eas elements first introduced by simo and rifai can be reduced to two postulates specifically the stability condition refers to a relaxed stability of an associated hu washizu principle we investigate the problem of volume locking of membrane problems estimates of a certain type which for instance imply volume locking of the q1 element are fortunately not present with eas elements finally we verify an equivalence of the eas concept with a hellinger reissner method which was observed in numerical computations by andelfinger and ramm

convergence of fourth order compact difference schemes for three dimensional convection diffusion equations we consider a dirichlet boundary value problem for the three dimensional convection diffusion equations with constant coefficients in the unit cube a high order compact finite difference scheme is constructed on a 19 point stencil using the steklov averaging operators we prove that the finite difference scheme converges in discrete w 2 m omega norm with the convergence rate o h s m where the real parameter s satisfies the condition max 1 5 m s le m 4 m 0 1 2 and the exact solution belongs to the sobolev space w 2 s omega

fourth order compact and energy conservative difference schemes for the nonlinear schrodinger equation in two dimensions abstract in this paper a fourth order compact and energy conservative difference scheme is proposed for solving the two dimensional nonlinear schrodinger equation with periodic boundary condition and initial condition and the optimal convergent rate without any restriction on the grid ratio at the order of o h 4 2 in the discrete l 2 norm with time step and mesh size h is obtained besides the standard techniques of the energy method a new technique and some important lemmas are proposed to prove the high order convergence in order to avoid the outer iteration in implementation a linearized compact and energy conservative difference scheme is derived numerical examples are given to support the theoretical analysis

convergence in the incompressible limit of finite element approximations based on the hu washizu formulation the classical hu washizu mixed formulation for plane problems in elasticity is examined afresh with the emphasis on behavior in the incompressible limit the classical continuous problem is embedded in a family of hu washizu problems parametrized by a scalar for which alpha lambda big mu corresponds to the classical formulation with and being the lame parameters uniform well posedness in the incompressible limit of the continuous problem is established for 1 finite element approximations are based on the choice of piecewise bilinear approximations for the displacements on quadrilateral meshes conditions for uniform convergence are made explicit these conditions are shown to be met by particular choices of bases for stresses and strains and include bases that are well known as well as newly constructed bases though a discrete version of the spherical part of the stress exhibits checkerboard modes it is shown that a independent a priori error estimate for the displacement can be established furthermore a independent estimate is established for the post processed stress the theoretical results are explored further through selected numerical examples

on locking and robustness in the finite element method a numerical scheme for the approximation of a parameter dependent problem is said to exhibit locking if the accuracy of the approximations deteriorates as the parameter tends to a limiting value a robust numerical scheme for the problem is one that is essentially uniformly convergent for all values of the parameter precise mathematical definitions for these terms are developed their quantitative characterization is given and some general theorems involving locking and robustness are proven a model problem involving heat transfer is analyzed in detail using this mathematical framework and various related computational results are described applications to some different problems involving locking are presented

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 convergence condition for the quadrilateral wilson element the paper deals with the convergence properties of the nonconforming quadrilateral wilson element which violates the patch test the convergence of the element is proved under a certain condition on mesh subdivisions without any modifications of the variational formulation this result extends the range of applicability of wilson s element the necessity of the proposed condition is also discussed

a priori and a posteriori analysis for a locking free low order quadrilateral hybrid finite element for reissner mindlin plates this paper proposes a quadrilateral finite element method of the lowest order for reissner mindlin r m plates on the basis of hellinger reissner variational principle which includes variables of displacements shear stresses and bending moments this method uses continuous piecewise isoparametric bilinear interpolation for the approximation of transverse displacement and rotation the piecewiseindependent shear stress bending moment approximation is constructed by following a self equilibrium criterion and a shear stress enhanced condition a priori and reliable a posteriori error estimates are derived and shown to be uniform with respect to the plate thickness t numerical experiments confirm the theoretical results

alternative ways for formulation of hybrid stress elements an element stiffness matrix can be derived by the conventional potential energy principle and indirectly also by generalized variational principles such as the hu washizu principle and the hellinger reissner principle the present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the hellinger reissner principle it is found that the resulting scheme is equivalent to that considered by tong 1982 for the construction of hybrid stress elements in tong s scheme the inversion of a large flexibility matrix can be avoided it is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the hellinger reissner principle and the hu washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method

optimization of stress modes by energy compatibility for 4 node hybrid quadrilaterals optimal hybrid stress quadrilaterals can be obtained by adopting appropriate stresses and displacements and satisfying the energy compatibility condition is shown to be an ultimate key to obtaining optimal stress modes by using compatible isoparametric bilinear q4 displacements and 5 parameter energy compatible stresses of the combined hybrid finite element ch 0 1 a robust 4 node plane stress element ecq4 is derived equivalence to another hybrid stress element lq6 with 9 parameter complete linear stresses based on a modified hellinger reissner principle is established a convergence analysis is given and numerical experiments show that elements ecq4 lq6 have high performance i e are accurate at coarse meshes insensitive to mesh distortions and free from locking copyright 2003 john wiley sons ltd

a rational approach for choosing stress terms for hybrid finite element formulations a new approach for choosing the stress terms for hybrid stress elements is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacements examples using 4 node plane stress elements have shown that when the incompatible displacements also satisfy the constant strain patch test the resulting element will provide the most accurate solutions

a simple and efficient hellinger reissner type mixed finite element for nearly incompressible elasticity abstract the mixed finite element method is a promising approach in order to overcome locking phenomena of classical displacement based finite elements in the nearly incompressible regime for the elasticity problem in this work we present a novel element based on hellinger reissner s principle for linear elasticity essential for the construction of the element is a restriction of the solution space for the stresses resulting in a formulation with displacements in h 1 b and stresses in h div b the symmetry of the stresses is achieved in a weak sense without the necessity of additional degrees of freedom this formulation leads for the case of lowest order interpolation to a very efficient and robust finite element even satisfying the numerical inf sup test in two and three dimensions

advanced resource connector middleware for lightweight computational grids as computational grids move away from the prototyping state reliability performance and ease of use and maintenance become focus areas of their adoption in this paper we describe arc advanced resource connector grid middleware where these issues have been given special consideration we present an in depth view of the existing components of arc and discuss some of the new components functionalities and enhancements currently under development this paper also describes architectural and technical choices that have been made to ensure scalability stability and high performance the core components of arc have already been thoroughly tested in demanding production environments where it has been in use since 2002 the main goal of this paper is to provide a first comprehensive description of arc

nonconforming finite element methods for the equations of linear elasticity in the adaptation of nonconforming finite element methods to the equations of elasticity with traction boundary conditions the main difficulty in the analysis is to prove that an appropriate discrete version of korn s second inequality is valid such a result is shown to hold for nonconforming piecewise quadratic and cubic finite elements and to be false for nonconforming piecewise linears optimal order error estimates uniform for poisson ratio v e 0 1 2 are then derived for the corresponding p2 and p3 methods this contrasts with the use of c finite elements where there is a deterioration in the convergence rate as v 1 2 for piecewise polynomials of degree 3 modifications of the continuous methods and the nonconforming linear method which also give uniform optimal order error estimates are discussed

analysis of some quadrilateral nonconforming elements for incompressible elasticity in this work some nonconforming elements on arbitrary quadrilateral meshes in solving incompressible elastic equations are analyzed a uniform optimal convergence rate is established at the incompressible limit nu 0 5 for both displacement and stresses or pressure in the case of incompressible flow

error estimate of fourth order compact scheme for linear schrodinger equations a fourth order compact difference scheme is proposed for two dimensional linear schrodinger equations with periodic boundary conditions by using the discrete energy method it is proven that the difference scheme is uniquely solvable unconditionally stable and convergent a maximum norm error estimate and thus an asymptotic expansion of the discrete solution are also obtained using the expansion of the difference solution high order approximations could be achieved by richardson extrapolations extension to three dimensional problems is also discussed numerical experiments are included to support the theoretical results and comparisons with the crank nicolson method are presented to show the effectiveness of our method

uniform convergence and a posteriori error estimators for the enhanced strain finite element method enhanced strain elements frequently employed in practice are known to improve the approximation of standard non enhanced displacement based elements in finite element computations the first contribution in this work towards a complete theoretical explanation for this observation is a proof of robust convergence of enhanced element schemes it is shown that such schemes are locking free in the incompressible limit in the sense that the error bound in the a priori estimate is independent of the relevant lame constant the second contribution is a residual based a posteriori error estimate the l 2 norm of the stress error is estimated by a reliable and efficient estimator that can be computed from the residuals

time compact high order difference methods for wave propagation we construct one step explicit difference methods for solution of wave propagation problems with fourth order accuracy in both space and time by using a principle that can be generalized to arbitrary order we use the first order system form and a staggered grid the fourth order accuracy in time is obtained by transferring time derivatives in the truncation error to space derivatives discontinuous coefficients corresponding to interfaces between different materials are considered as a special case of variable coefficients and the method is applied across the discontinuities the accuracy is much improved compared to second order methods even for this type of problem a certain norm is shown to be conserved ensuring good accuracy even for long time integration

an exponential wave integrator sine pseudospectral method for the klein gordon zakharov system an exponential wave integrator sine pseudospectral method is presented and analyzed for discretizing the klein gordon zakharov kgz system with two dimensionless parameters 0 varepsilon le 1 and 0 gamma le 1 which are inversely proportional to the plasma frequency and the speed of sound respectively the main idea in the numerical method is to apply the sine pseudospectral discretization for spatial derivatives followed by using an exponential wave integrator for temporal derivatives in phase space the method is explicit symmetric in time and it is of spectral accuracy in space and second order accuracy in time for any fixed varepsilon varepsilon 0 and gamma gamma 0 in the mathcal o 1 plasma frequency and speed of sound regime i e varepsilon mathcal o 1 and gamma mathcal o 1 we establish rigorously error estimates for the numerical method in the energy space h 1 times l 2 we also study numerically the resolution of the method in the simultaneous high plasma fr

compact finite difference schemes with high accuracy for one dimensional nonlinear schrodinger equation abstract in this paper two compact finite difference schemes are presented for the numerical solution of the one dimensional nonlinear schrodinger equation the discrete l 2 norm error estimates show that convergence rates of the present schemes are of order o h 4 2 numerical experiments on some model problems show that the present schemes preserve the conservation laws of charge and energy and are of high accuracy

a systematic construction of b bar functions for linear and non linear mixed enhanced finite elements for plane elasticity problems in a previous paper a modified hu washizu variational formulation has been used to derive an accurate four node plane strain stress finite element denoted qe2 for the mixed element qe2 two enhanced strain terms are used and the assumed stresses satisfy the equilibrium equations a priori for the linear elastic case in this paper an alternative approach is discussed the new formulation leads to the same accuracy for linear elastic problems as the qe2 element however it turns out to be more efficient in numerical simulations especially for large deformation problems using orthogonal stress and strain functions we derive b functions which avoid numerical inversion of matrices the b strain matrix is sparse and has the same structure as the strain matrix b obtained from a compatible displacement field the implementation of the derived mixed element is basically the same as the one for a compatible displacement element the only difference is that we have to compute a b strain matrix instead of the standard b matrix accordingly existing subroutines for a compatible displacement element can be easily changed to obtain the mixed enhanced finite element which yields a higher accuracy than the q4 and qm6 elements copyright 1999 john wiley sons ltd

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

a quadrilateral mixed finite element with two enhanced strain modes summary an improved plane strain stress element is derived using a hu washizu variational formulation with bilinear displacement interpolation seven strain and stress terms and two enhanced strain modes the number of unknowns of the four node element is increased from eight to ten degrees of freedom for linear and non linear applications the two unknowns associated with the enhanced strain terms can be eliminated by static condensation so that eight displacement degrees of freedom remain for the proposed element which is denoted by qe2 the excellent performance of the proposed element is demonstrated using several linear and non linear examples

analysis of a family of hdg methods for second order elliptic problems in this paper we analyze a family of hybridizable discontinuous galerkin hdg methods for second order elliptic problems in two and three dimensions the methods use piecewise polynomials of degree k 0 for both the flux and numerical trace and piecewise polynomials of degree k 1 for the potential we establish error estimates for the numerical flux and potential under the minimal regularity condition moreover we construct a local postprocessing for the flux which produces a numerical flux with better conservation numerical experiments in two space dimensions confirm our theoretical results

a local regularization operator for triangular and quadrilateral finite elements this paper develops a local regularization operator on triangular or quadrilateral finite elements built on structured or unstructured meshes this operator is a variant of the regularization operator of clement however ours is constructed via a local projection in a reference domain we prove in this paper that it has the same optimal approximation properties as the standard interpolation operator and we present some applications

a unified analysis for stress strain hybrid methods of high performance abstract several methods have been developed in the literatures of computational mechanics to improve the performance of the conventional lower order displacement finite elements which yield poor results for problems with bending and for nearly incompressible medium this paper is devoted to a unified analysis of convergence for pian sumihara s chen cheung s and piltner taylor s enhanced stress strain schemes by virtue of the energy compatibility and the rank condition error estimates for these typical finite elements of high performance are obtained in a unified framework and especially weakly locking free error estimates with respect to the poisson s ratio in energy norms are obtained uniformly for 1 ch 2 as h 0 where c is a constant independent of and the mesh size h very much the same about the three methods is pointed out

decoupling with stability for linear periodic systems in this paper the classical row by row decoupling problem with stability through the use of a dynamic compensator is studied for linear periodic discrete time systems the necessary and sufficient conditions for the existence of a solution are found and a design procedure of the dynamic compensator is provided by the sufficiency proof and also for the case of a dead beat requirement for the state free response

numerical analysis for fourth order compact conservative difference scheme to solve the 3d rosenau rlw equation in this paper a fourth order compact and energy conservative difference scheme for three dimensional rosenau rlw equation is proposed the scheme is a two level and nonlinear implicit scheme it is proved by the discrete energy method that the compact scheme is solvable the convergence and stability of the difference scheme is obtained and its numerical convergence order is o 2 h4 in the l norm we discuss an iterative algorithm for solving the nonlinear algebraical system generated by the nonlinear compact scheme and prove its convergence numerical experiment results show that the theory is accurate and the method is efficient and reliable

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

time compact difference methods for wave propagation in discontinuous media in b gustafsson and e mossberg siam j sci comput 26 2004 pp 259 271 a fourth order one step method was constructed for the solution of wave propagation problems the method is based on the first order system form of the pde and uses a staggered grid both in space and time the method was also applied with good results to a problem with discontinuous coefficients without using any special procedure across the discontinuity in this paper we will analyze a model problem from acoustics and demonstrate the theoretical foundation for this behavior furthermore we shall present more detailed numerical experiments which confirm the theoretical results

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

relations between incompatible displacement model and hybrid stress model an examination of the variational formulations confirms the similarity between the incompatible displacement model and the assumed stress hybrid model that was pointed out by irons in 1972 but the basic differences between the two are also identified for 8 node solid elements the assumed stress terms obtained through a rational procedure also agree with those deduced by irons purely from his physical insight

optimal error estimates of finite difference methods for the gross pitaevskii equation with angular momentum rotation we analyze finite difference methods for the gross pitaevskii equation with an angular momentum rotation term in two and three dimensions and obtain the optimal convergence rate for the conservative crank nicolson finite difference cnfd method and semi implicit finite difference sifd method at the order of o h2 2 in the l2 norm and discrete h1 norm with time step and mesh size h besides the standard techniques of the energy method the key technique in the analysis for the sifd method is to use the mathematical induction and resp for the cnfd method is to obtain a priori bound of the numerical solution in the l norm by using the inverse inequality and the l2 norm error estimate in addition for the sifd method we also derive error bounds on the errors between the mass and energy in the discretized level and their corresponding continuous counterparts respectively which are at the same order of the convergence rate as that of the numerical solution itself finally numerical results are reported to confirm our error estimates of the numerical methods

global smooth solution for the klein gordon zakharov equations in this paper the initial value problem to the klein gordon zakharov equations in two dimensions is discussed without assuming that the cauchy data are small we prove the existence and uniqueness of the global smooth solution for the problem via the so called continuous method and delicate a priori estimates also the asymptotic behaviour of the solution to the k g z equations with a small parameter approaching zero is studied