existence and blow up of solution of cauchy problem for the generalized damped multidimensional boussinesq equation we consider the existence both locally and globally in time and the blow up of solutions for the cauchy problem of the generalized damped multidimensional boussinesq equation

the pointwise estimates of diffusion wave for the navier stokes systems in odd multi dimensions we study the dissipation of solutions of the isentropic navier stokes equations in odd multi dimensions pointwise estimates of the time asymptotic shape of the solutions are obtained and shown to exhibit the generalized huygen s principle our approach is based on the detailed analysis of the green function of the linearized system this is used to study the coupling of nonlinear diffusion waves

an implicit scheme for solving the convection diffusion reaction equation in two dimensions in this paper we consider a passive scalar transported in two dimensional flow the governing equation is that of the convection diffusion reaction equation for purposes of computational efficiency we apply an alternating direction implicit scheme akin to that proposed by polezhaev use of this implicit operator splitting scheme allows the application of a tridiagonal thomas solver to obtain the solution within each solution step a semidiscretization scheme is applied to discretize the differential equation in one dimension we approximate the time derivative term using a forward time stepping scheme the resulting inhomogeneous differential equation has only the spatial derivative terms and is solved using a newly proposed nodally exact steady state convection diffusion reaction scheme details on the development of the flux discretization scheme are provided modified equation analysis fourier stability analysis and a study on scheme monotonicity are also performed to shed further light on the proposed transient scheme to validate the proposed scheme we first consider test problems which are amenable to analytic solutions good agreement is obtained with both one and two dimensional steady unsteady problems thus demonstrating the validity of the method c 2000 academic press

applications of the pseudo residual free bubbles to the stabilization of convection diffusion reaction problems it is known that the enrichment of the polynomial finite element space of degree 1 by bubble functions results in a stabilized scheme of the supg type for the convection diffusion reaction problems in particular the residual free bubbles rfb can assure stabilized methods but they are usually difficult to compute unless the configuration is simple therefore it is important to devise numerical algorithms that provide cheap approximations to the rfb functions contributing a good stabilizing effect to the numerical method overall here we propose a stabilization technique based on the rfb method and particularly designed to treat the most interesting case of small diffusion we replace the rfb functions by their cheap yet efficient approximations which retain the same qualitative behavior the approximate bubbles are computed on a suitable sub grid the choice of whose nodes are critical and determined by minimizing the residual of a local problem with respect to l 1 norm the resulting numerical method has similar stability features with the rfb method for the whole range of problem parameters this fact is also confirmed by numerical experiments we also note that the location of the sub grid nodes suggested by the strategy herein coincides with the one in brezzi et al math models methods appl sci 13 445 461 2003

l p convergence rates of planar waves for multi dimensional euler equations with damping abstract in this paper the l p convergence rates of planar diffusion waves for multi dimensional euler equations with damping are considered the analysis relies on a newly introduced frequency decomposition and green function based energy method it is a combination of the l p estimate on the low frequency component by using an approximate green function and l 2 estimate on the high frequency component through the energy method by noticing that the low frequency component in the approximate green function has the algebraic decay which governs the large time behavior while the high frequency component has the exponential decay but with singularity their combination leads to a global algebraic decay estimate to use the decay property only of the low frequency component in the approximate green function avoids the singularity in the high frequency component so that it simplifies and improves the previous works on this system this new approach of the combination of the green function and energy method through the frequency decomposition can also be applied to the hyperbolic parabolic systems satisfying the kawashima condition and also the systems whose derivatives of the coefficients have suitable time decay properties

galerkin gradient least squares formulations for transient conduction heat transfer this paper presents the benefits provided by the use of the galerkin gradient least squares ggls method for transient conduction heat transfer the consistency of the gls method for this type of problem is also discussed the ggls method is compared with standard galerkin formulation on problems having an analytical solution a semi infinite solid solved on one and three dimensional meshes and a three dimensional thin plate for three dimensional applications the principle of including gradient least squares terms is extended to stabilize robin convection boundary conditions numerical simulations show that additional boundary gradient least squares terms improve the behavior of the solution on boundaries subject to convection boundary conditions new procedures used to obtain the gls and ggls stabilized finite element formulations are also presented the methodology consists in modifying the equation to be solved and then to obtain the variational equation by a standard galerkin method

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

design of galerkin generalized least squares methods for timoshenko beams abstract a class of finite element methods the galerkin generalized least squares methods are developed and applied to model the steady state response of timoshenko beams an optimal method is designed using a linear interpolation of the response such that there is zero finite element dispersion error the classical method of selective reduced integration and a modified version of selective reduced integration with mass lumping are shown to fall under the galerkin generalized least squares framework numerical experiments in wave propagation demonstrate the dramatic superiority of the new optimal method over the standard approaches the goal of the new methods is to decrease the computational burden required to achieve a desired accurcy level at a particular frequency thereby enabling larger scale higher frequency computations for a given platform

pointwise estimates and lp convergence rates to diffusion waves for p system with damping abstract by introducing a new approximate green function we obtain the pointwise estimates on the solutions of euler equations with linear frictional damping from which we can deduce the optimal l p 1 p convergence rates to the nonlinear diffusion waves the pointwise estimates and l p 1 p convergence rates given in this paper are new

towards multiscale functions enriching finite element spaces with local but not bubble like functions in this paper we propose a novel way via finite elements to treat problems that can be singular perturbed a reaction diffusion equation in our case we enrich the usual piecewise linear or bilinear finite element trial spaces with local solutions of the original problem as in the residual free bubble rfb setting but do not require these functions to vanish on each element edge a departure from the rfb paradigm such multiscale functions have an analytic expression for triangles and rectangles bubbles are the choice for the test functions allowing static condensation thus our method is of petrov galerkin type we perform several numerical validations which confirm the good performance of the method 2004 elsevier b v all rights reserved

large time behavior of solutions for the nonlinear wave equation with viscosity in odd dimensions abstract we study the dissipation of solutions of the cauchy problem for the nonlinear dissipative wave equation in odd multi spatial dimensions pointwise estimates of the time asymptotic shape of the solutions are obtained and shown to exhibit the generalized huygens principle our approach is based on the detailed analysis of the green function of the linearized system this is used to study the coupling of nonlinear diffusion waves

an accurate fic fem formulation for the 1d advection diffusion reaction equation abstract in this paper we present an accurate stabilized fic fem formulation for the 1d advection diffusion reaction equation in the exponential and propagation regimes using two stabilization parameters both the steady state and transient solutions are considered the stabilized formulation is based on the standard galerkin fem solution of the governing differential equations derived via the finite increment calculus fic method the steady state problem is considered first the optimal value of the two stabilization parameters ensuring an exact nodal fem solution using uniform meshes of linear 2 noded elements is obtained in the absence of the absorption term the formulation simplifies to the standard one parameter petrov galerkin method for the advection diffusion problem for the diffusion reaction case one stabilization parameter is just needed and the diffusion type stabilization term is identical to that obtained by felippa and onate 2007 using a variational fic approach a procedure for computing the stabilization parameters for the transient problem is proposed the accuracy of the new fic fem formulation is demonstrated in the solution of steady state and transient 1d advection diffusion radiation problems for a the range of physical parameters and boundary conditions

variational multiscale stabilization of high order spectral elements for the advection diffusion equation one major issue in the accurate solution of advection dominated problems by means of high order methods is the ability of the solver to maintain monotonicity this problem is critical for spectral elements where gibbs oscillations may pollute the solution however typical filter based stabilization techniques used with spectral elements are not monotone in this paper residual based stabilization methods originally derived for finite elements are constructed and applied to high order spectral elements in particular we show that the use of the variational multiscale vms method greatly improves the solution of the transport diffusion equation by reducing over and under shoots and can be therefore considered an alternative to filter based schemes we also combine these methods with discontinuity capturing schemes dc to suppress oscillations that may occur in proximity of boundaries or internal layers additional improvement in the solution is also obtained when a method that we call fos for first order subcells is used in combination with vms and dc in the regions where discontinuities occur fos subdivides a spectral element of order p into p 2 subcells and then uses 1st order basis functions and integration rules on every subcell of the element the algorithms are assessed with the solution of classical steady and transient 1d 2d and pseudo 3d problems using spectral elements up to order 16

global existence and asymptotic behavior of solutions for a semi linear wave equation abstract in this paper we investigate the initial value problem for a semi linear wave equation in n dimensional space based on the decay estimate of solutions to the corresponding linear equation we define a set of time weighted sobolev spaces under small condition on the initial value we prove the global existence and asymptotic behavior of the solution in the corresponding sobolev spaces by the contraction mapping principle

response of two degree of freedom systems to multifrequency parametric excitations abstract the method of multiple scales is used to analyze the response of two degree of freedom systems to multifrequency parametric excitations the equations describing the modulation of the amplitudes with time are derived for the case of four simultaneous resonances main resonances of the two modes combination resonance of the difference type and combination resonance of the summed type when only two simultaneous resonances exist the modulation equations can be transformed into a system of four real first order differential equations with constant coefficients whose solution depends on the eigenvalues of a four by four constant coefficient matrix when three or more simultaneous resonances exist the modulation equations cannot be made autononous in general and hence one may not be able to solve them except numerically

a multi step transversal linearization mtl method in non linear structural dynamics an implicit family of multi step transversal linearization mtl methods is proposed for efficient and numerically stable integration of nonlinear oscillators of interest in structural dynamics the presently developed method is a multi step extension and further generalization of the locally transversal linearization ltl method proposed earlier by roy proceedings of the academy of the royal society london 457 2001 539 566 roy and ramachandra journal of sound and vibration 41 2001a 653 679 international journal for numerical methods in engineering 51 2001b 203 224 and roy international journal of numerical methods in engineering 61 2004 764 the mtl based linearization is achieved through a non unique replacement of the nonlinear part of the vector field by a conditionally linear interpolating expansion of known accuracy whose coefficients contain the discretized state variables defined at a set of grid points in the process the nonlinear part of the vector field becomes a conditionally determinable equivalent forcing function the mtl based linearized differential equations thus become explicitly integrable based on the linearized solution a set of algebraic constraint equations are so formed that transversal intersections of the linearized and nonlinearized solution manifolds occur at the multiple grid points the discretized state vectors are thus found as the zeros of the constraint equations simple error estimates for the displacement and velocity vectors are provided and in particular it is shown that the formal accuracy of the mtl methods as a function of the time step size depends only on the error of replacement of the nonlinear part of the vector field presently only two different polynomial based interpolation schemes are employed for transversal linearization viz the taylor like interpolation and the lagrangian interpolation while the taylor like interpolation leads to numerical ill conditioning as the order of interpolation increases the lagrangian interpolation is shown to overcome this numerical problem finally the family of mtl methods is illustrated through limited numerical results for a couple of harmonically driven workhorse oscillators viz the hardening duffing and the duffing holmes oscillators comparisons with results obtained via a sixth order runge kutta method with adaptive time step sizes are also provided

asymptotic profile of solutions to the double dispersion equation abstract in this paper we investigate the initial value problem for the double dispersion equation in r n decay estimate and asymptotic profile of solutions to the corresponding linear problem are established the asymptotic profile of solutions to the corresponding linear problem is given by the convolution of the fundamental solutions of heat and free wave equations moreover the asymptotic profile of solutions shows the decay estimate of solutions to the corresponding linear problem obtained in this paper is optimal under some conditions finally global existence and optimal decay estimate of solutions to the nonlinear problem are also established

global existence and nonexistence of solution for cauchy problem of multidimensional double dispersion equations abstract in this paper we consider the cauchy problem of multidimensional generalized double dispersion equations u t t u u t t 2 u f u where f u a u p by potential well method we prove the existence and nonexistence of global weak solution without establishing the local existence theory and we derive some sharp conditions for global existence and lack of global existence solution

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

numerical multiscale methods for a reaction dominated model a galerkin enriched finite element method gem is proposed for the singularly perturbed reaction diffusion equation this new method is an improvement on the petrov galerkin enriched method pgem where now the standard piecewise bi linear test space incorporates fine scales this appears as the fundamental ingredient for suppressing oscillations in the numerical solutions also new parameter free stabilized finite element methods derived from both the gem and the pgem are driven by local generalized eigenvalue problems in the process jump stabilizing terms belonging to the class of cip methods emerge as a result of the enriching procedure interestingly numerical results indicate that jump based stabilizations are unnecessary and sometimes undesirable when treating reaction dominated problems finally we establish relationships with more standard enriched and stabilized methods and show that the proposed methods outperform them numerically

global attractor for a nonlinear wave equation arising in elastic waveguide model abstract the paper studies the longtime behavior of solutions to the initial boundary value problem ibvp for a nonlinear wave equation arising in an elastic waveguide model u t t u u t t 2 u u t g u f x it proves that when the space dimension n 5 under rather mild conditions the dynamical system associated with the above mentioned ibvp possesses a global attractor which is connected and has finite fractal and hausdorff dimension

decay property of regularity loss type for nonlinear hyperbolic elliptic system in multi dimensions abstract in this paper we study the asymptotic behavior of solutions for a hyperbolic elliptic system with a 2m order elliptic part in multi dimensional space this system is a modified version of the simplest radiating gas model and it verifies l p decay property of regularity loss type in r n the global existence and l p estimates of the solution to the cauchy problem for the hyperbolic elliptic system are obtained since the dissipative property of this system is so weak in high frequency region the usual energy method does not work well in deriving the a priori estimates for global solutions to the nonlinear problem our analysis is based on a frequency decomposition and the method of combining the green function with some time weight energy estimates

stabilized finite element methods for steady advection diffusion with production abstract finite element methods for solving equations of steady advection diffusion with production are constructed employing a linear source to model production the galerkin method requires relatively fine meshes to retain an acceptable degree of accuracy for wide ranges of values of the physical coefficients numerous criteria for improved accuracy via galerkin least squares are proposed and examined in the entire parameter space of these several provide the lowest error in nodal amplification factors each in a certain range of ratios of physical coefficients guidelines for required mesh resolutions are presented for galerkin and galerkin least squares showing that in large parts of the parameter space substantial savings may be obtained by employing galerkin least squares galerkin least squares gradient least squares a new variation of the galerkin method is designed to provide exact nodal amplification factors offering accurate solutions at any resolution numerical tests validate these conclusions

a high resolution petrov galerkin method for the 1d convection diffusion reaction problem abstract we present the design of a high resolution petrov galerkin hrpg method using linear finite elements for the problem defined by the residual r t u x k 2 x 2 s f where k s 0 the structure of the method in 1d is identical to the consistent approximate upwind petrov galerkin cau pg method a c galeao e g dutra do carmo a consistent approximate upwind petrov galerkin method for the convection dominated problems comput methods appl mech engrg 68 1988 83 95 except for the definitions of the stabilization parameters such a structure may also be attained via the finite calculus fic procedure e onate derivation of stabilized equations for numerical solution of advective diffusive transport and fluid flow problems comput methods appl mech engrg 151 1998 233 265 e onate j miquel g hauke stabilized formulation for the advection diffusion absorption equation using finite calculus and linear finite elements comput methods appl mech engrg 195 2006 3926 3946 by an appropriate definition of the characteristic length the prefix high resolution is used here in the sense popularized by harten i e second order accuracy for smooth regular regimes and good shock capturing in nonregular regimes the design procedure embarks on the problem of circumventing the gibbs phenomenon observed in l 2 projections next we study the conditions on the stabilization parameters to circumvent the global oscillations due to the convective term a conjuncture of the two results is made to deal with the problem at hand that is usually plagued by gibbs global and dispersive oscillations in the numerical solution it is shown that the method indeed reproduces stabilized high resolution numerical solutions for a wide range of values of u k s and f finally some remarks are made on the extension of the hrpg method to multidimensions

global existence and asymptotic behavior of the solutions to the three dimensional bipolar euler poisson systems abstract in this paper the global existence of smooth solutions for the three dimensional bipolar hydrodynamic model is studied when the initial data are close to a constant state the l 2 decay rate of the solutions is also obtained our approach is based on the detailed analysis of the green function of the linearized system and the elaborate energy estimates as far as we known it is the first result about the existence and l 2 decay rate of global smooth solutions to the multi dimensional bipolar hydrodynamic model

a positivity preserving variational method for multi dimensional convectiondiffusionreaction equation a new positivity preserving variational ppv procedure is proposed to solve the convectiondiffusionreaction cdr equation through the generalization of stabilized finite element methods the present variational procedure offers minimal phase and amplitude errors for different regimes associated with convection diffusion and reaction effects by means of fourier analysis we first review the shortcomings of the galerkin least squares gls and the subgrid scale sgs methods during the change in sign of the reaction coefficient that motivates us for the present linear stabilization as a combined gls sgs methodology discrete upwind operator with a solution dependent nonlinear term is then introduced in high gradient regions which enables the positivity preserving property in the variational formulation direct extension to multi dimensions is carried out by considering the principle streamline and crosswind directions the efficacy of the method is demonstrated by the systematic accuracy and stability analyses in one and two dimensions results show the reduction of oscillations in the solution in one and two dimensional cases and a remarkable reduction in the phase error is observed for the cases with negative reaction coefficient the proposed formulation provides a superior solution in the reaction dominated as well as the convection dominated regimes due to the minimization of spurious oscillations and accurate capturing of the high gradient regions

numerical aspects of a real time sub structuring technique in structural dynamics a time domain coupling technique involving combined computational and experimental modelling for vibration analysis of structures built up of linear non linear substructures is developed the study permits in principle one or more of the substructures to be modelled experimentally with measurements being made only on the interfacial degrees of freedom the numerical and experimental substructures are allowed to communicate in real time within the present framework the proposed strategy involves a two stage scheme the first is iterative in nature and is implemented at the initial stages of the solution in a non real time format the second is non iterative employs an extrapolation scheme and proceeds in real time issues on time delays during communications between different substructures are discussed an explicit integration procedure is shown to lead to solutions with high accuracy while retaining path sensitivity to initial conditions the stability of the integration scheme is also discussed and a method for numerically dissipating the temporal growth of high frequency errors is presented for systems with non linear substructures the integration procedure is based on a multi step transversal linearization method and to account for time delays we employ a multi step extrapolation scheme based on the reproducing kernel particle method numerical illustrations on a few low dimensional vibrating structures are presented and these examples are fashioned after problems of seismic qualification testing of engineering structures using real time substructure testing techniques

derivation of stabilized equations for numerical solution of advective diffusive transport and fluid flow problems abstract the concept of the so called artificial or balancing diffusion used to stabilize the numerical solution of advective diffusive transport and fluid flow problems is revised in this paper it is shown that the standard forms of the balancing diffusion terms usually chosen in a heuristic manner can be naturally found by introducing higher order approximations in the derivation of the governing differential equations via standard conservation or equilibrium principles this allows us to reinterpret many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter

the decay rate of solution for the bipolar navier stokes poisson system in this paper the cauchy problem for the bipolar navier stokes poisson system is studied we obtain the global existence and the hs decay rate of classical solutions for this problem our approach is mainly based on the analysis of the green s function of the linearized system and some elaborate energy estimates it should be mentioned that with the help of long wave short wave decomposition the decay rate of the higher order derivatives of the solutions is obtained furthermore based on the hs decay rate of the solutions we also give the lp estimate of the solution

a high resolution petrov galerkin method for the convection diffusion reaction problem part ii a multidimensional extension abstract a multidimensional extension of the hrpg method doi 10 1016 j cma 2009 10 009 using the lowest order block finite elements is presented first we design a nondimensional element number that quantifies the characteristic layers which are found only in higher dimensions this is done by matching the width of the characteristic layers to the width of the parabolic layers found for a fictitious 1d reaction diffusion problem the nondimensional element number is then defined using this fictitious reaction coefficient the diffusion coefficient and an appropriate element size next we introduce anisotropic element length vectors li and the stabilization parameters i i are calculated along these li except for the modification to include the new dimensionless number that quantifies the characteristic layers the definitions of i i are a direct extension of their counterparts in 1d using i i and li objective characteristic tensors associated with the hrpg method are defined the numerical artifacts across the characteristic layers are manifested as the gibbs phenomenon hence we treat them just like the artifacts formed across the parabolic layers in the reaction dominant case several 2d examples are presented that support the design objective stabilization with high resolution

chaos in numerical analysis of ordinary differential equations abstract the discretisation of the ordinary nonlinear differential equation d y d t y 1 y by the entral difference scheme is studied for fixed mesh size in the usual numerical computation this method produces some ghost solution for the long range calculation regarding this discretisation as a dynamical system in r2 these pathological behaviors are shown to be a kind of chaos in the dynamical system for any mesh size moreover some combination of the central difference scheme and the euler s scheme is studied for the above equation it gives some motivation for henon s model the usual discretisation of a second order differential equation are studied also it gives some chaotic behaviors numerically which is similar to the behavior of the orbits of the system of differential equations proposed by henon heiles

lp convergence rate to nonlinear diffusion waves for p system with damping abstract in this paper we study the p system with frictional damping and show that the solutions time asymptotically tend to the nonlinear diffusion waves governed by the classical darcy s law by introducing an approximate green function we obtain the optimal l p 2 p convergence rate of the solution which is a perturbation of the nonlinear diffusion wave to the hyperbolic system

the pointwise estimates of solutions for euler equations with damping in multi dimensions we study the time asymptotic behavior of solutions for the isentropic euler equations with damping in multi dimensions the global existence and pointwise estimates of the solutions are obtained furthermore we obtain the optimal lp 1 p convergence rate of the solution when it is a perturbation of a constant state our approach is based on a detailed analysis of the green function of the linearized system and some energy estimates

a multistep transversal linearization mtl method in non linear dynamics through a magnus characterization a new form of a multi step transversal linearization mtl method is developed and numerically explored in this study for a numeric analytical integration of non linear dynamical systems under deterministic excitations as with other transversal linearization methods the present version also requires that the linearized solution manifold transversally intersects the non linear solution manifold at a chosen set of points or cross section in the state space however a major point of departure of the present method is that it has the flexibility of treating non linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system even though these linearized terms become explicit functions of time from this perspective the present development is closely related to the popular practice of tangent space linearization adopted in finite element fe based solutions of non linear problems in structural dynamics the only difference is that the mtl method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an fe framework the resulting time varying linearized system matrix is then treated as a lie element using magnus characterization w magnus on the exponential solution of differential equations for a linear operator commun pure appl math vii 1954 649 673 and the associated fundamental solution matrix fsm is obtained through repeated lie bracket operations or nested commutators an advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non linear problem yet another advantage of the transversal linearization lies in the non unique representation of the linearized vector field an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors a simple analysis of the formal orders of accuracy is provided within a finite dimensional framework only a limited numerical exploration of the method is presently provided for a couple of popularly known non linear oscillators viz a hardening duffing oscillator which has a non linear stiffness term and the van der pol oscillator which is self excited and has a non linear damping term

pointwise estimates of solutions for the cahn hilliard equation with inertial term in multi dimensions abstract in this paper we study the pointwise estimates of solutions for the cahn hilliard equation with inertial term in multi dimensions by the green function method furthermore we obtain the l p convergence rate of the solution

revisiting stabilized finite element methods for the advective diffusive equation we give a brief overview of stabilized finite element methods and illustrate the developments applied to the advection diffusion equation this article presents a concise perspective of the developments emanated from the works started in the 1980s through today 2005 elsevier b v all rights reserved pacs 47 11 j

fic fem formulation for the multidimensional transient advection diffusion absorption equation abstract in this paper we present a stabilized fic fem formulation for the multidimensional transient advection diffusion absorption equation the starting point is the non local form of the governing equations for the multidimensional transient advection diffusion absorption problems obtained via the finite increment calculus fic procedure the fic governing equations have a residual form that introduces a characteristic length vector that depends on streamline absorption and shock capturing stabilization parameters as well as on a characteristic element size that ensures a stabilized numerical solution using a standard galerkin fem the value of the stabilization parameters is obtained as an extension of the steady state form the accuracy of the fic fem formulation is verified in the solution of several transient advection diffusion absorption problems using regular meshes of 3 noded triangles and 4 noded quadrilaterals

a variational multiscale higher order finite element formulation for turbomachinery flow computations abstract the variational multiscale approach for finite elements addresses the inclusion of the effect of fine scales of the solution in the coarse problem in this framework advective diffusive reactive equations modelling turbomachinery flows feature both advection and reaction induced instabilities to be tackled to this end this work deals with a new method called v sgs variable subgrid scale designed for quadratic elements with a variable intrinsic time parameter two dimensional tests have been considered to compare v sgs against supg and other stabilization devices including the flow around a naca 4412 airfoil to assess its reliability in the handling of advanced turbulence closures on cruder meshes

phase space linearization for non linear oscillators deterministic and stochastic systems abstract a new and efficient semi analytical phase space linearization psl scheme for a class of non linear oscillators is developed in this paper the method is based on replacement of the non linear vector field by a set of linear ones each valid over a short segment of the evolving trajectory or over sufficiently small interval of time based on this concept a few explicit and implicit integration schemes are first proposed and applied to a class of low dimensional non linear dynamical systems to accurately determine their response trajectories this approach of local linearization is further extended to non linear oscillators excited by formal derivatives of one or a combination of gauss markov processes since the present methodology reduces the non linear operator by a set of linear operators it is also demonstrated that the principles of linear random vibration may be suitable exploited to arrive at a faster and semi analytical monte carlo scheme for computing the response statistics both in stationary and non stationary regimes limited examples are presented and compared with exact solutions whenever available to illustrate the efficiency and versatility of the proposed schemes

extensions of the phase space linearization psl technique for non linear oscillators abstract this paper is devoted to further exploration of the psl technique developed earlier in its companion paper to start with it is shown that the method is not only applicable for obtaining one periodic orbits but can be made use of for obtaining every conceivable orbit including subharmonic or periodic doubled orbits quasi periodic orbits and even chaotic orbits this is numerically illustrated by constructing various orbits of ueda s duffing holmes and van der pol s oscillators next the separatrix that separates the basins of attraction of the stable limit cycles of duffing holmes oscillator is constructed using the psl procedure a possibility of predicting the chaotic diffusion of trajectories based on a heuristic argument of a near tangency of stable and unstable limit cycles of duffing holmes oscillator is also discussed finally the psl scheme is made use of to compute various characteristic quantities such as fourier spectra liapunov characteristic exponents and probability density functions many new results are presented to establish the versatility of the psl method

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

initial boundary value problem of the generalized cubic double dispersion equation in this paper the existence and the uniqueness of the global generalized solution and the global classical solution for the initial boundary value problem of the generalized cubic double dispersion equation are proved the nonexistence of global solution for the initial boundary value problem of the generalized cubic double dispersion equation is discussed

stabilized formulation for the advection diffusion absorption equation using finite calculus and linear finite elements abstract a stabilized finite element method fem for the steady state advection diffusion absorption equation is presented the stabilized formulation is based on the modified governing differential equations derived via the finite calculus fic method the basis of the method is detailed for the 1d problem it is shown that the stabilization terms act as a non linear additional diffusion governed by a single stabilization parameter a critical constant value of this parameter ensuring a stabilized solution using two node linear elements is given more accurate numerical results can be obtained by using a simple expression of the non linear stabilization parameter depending on the signs of the numerical solution and of its derivatives a straightforward two steps algorithm yielding a stable and accurate solution for all the range of physical parameters and boundary conditions is described the extension to the multi dimensional case is briefly described numerical results for 1d and 2d problems are presented showing the efficiency and accuracy of the new stabilized formulation

a stabilized finite element method for generalized stationary incompressible flows abstract in this paper we describe a finite element formulation for the numerical solution of the stationary incompressible navier stokes equations including coriolis forces and the permeability of the medium the stabilized method is based on the algebraic version of the sub grid scale approach we first describe this technique for general systems of convection diffusion reaction equations and then we apply it to the linearized flow equations the important point is the design of the matrix of stabilization parameters that the method has this design is based on the identification of the stability problems of the galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix this together with the convergence analysis of the linearized problem leads to a simple expression for the stabilization parameters in the general situation considered in the paper the numerical analysis of the linearized problem also shows that the method has optimal convergence properties

finite element analysis of contaminant transport in groundwater in this paper we focus on the development of a finite element model for predicting the contaminant concentration governed by the advective dispersive equation in this study we take into account the first order degradation of the contaminant to realistically model the transport phenomenon in groundwater to solve the resulting unsteady advection diffusion equation with production a finite element model is constructed which employs a quadratic basis function to approximate the contaminant concentration the development of a weighted residuals finite element model involves constructing a biased test function to retain the scheme stability for wide ranges of values of the physical coefficients in the process of constructing the petrov galerkin finite element model for stability reasons it is desirable to obtain an acceptable degree of accuracy the method used to retain stability without loss of accuracy is to approximate the differential equation within the semi discretization framework after discretizing the time derivative term using the euler time stepping scheme the resulting ordinary differential equation which involves only the spatial derivative terms is solved using the nodally exact finite element model for better control of the user s specified time step and mesh size full analysis of the discretization scheme is conducted in this study both modified equation analysis and fourier stability analysis are employed to better understand the proposed semi discretized petrov galerkin finite element model validation of the newly proposed model is accomplished through analysis of the results obtained for several test problems some of them are amenable to analytic solutions the rate of convergence of the employed finite element model then can be obtained

a simple subgrid scale stabilized method for the advection diffusion reaction equation abstract a subgrid scale method has been developed for the advection diffusion reaction equation with a simple intrinsic time scale parameter the proposed formulation combines very good accuracy and stability in all the physical regimes of the equation that is in the exponential regime for both negative and positive source terms and in the propagation regime numerical examples confirm the robustness and accuracy of the method

variational subgrid scale formulations for the advection diffusion reaction equation abstract the exact variational multiscale vms and the subgrid scale sgs methods have been developed for the advection reaction and the advection diffusion reaction equations from the element green s function approximate intrinsic time scale parameters have been derived for these cases and are shown to be similar to other expressions obtained in the literature out of the maximum principle and convergence error analysis the methods have been compared with typical stabilized finite element methods as expected the vms is nodally exact for the one dimensional case

asymptotic profiles for wave equations with strong damping abstract we consider the cauchy problem in r n for strongly damped wave equations we derive asymptotic profiles of these solutions with weighted l 1 1 r n data by using a method introduced in 9 and or 10

a multiscale a posteriori error estimate we introduce a hierarchic a posteriori error estimate for singularly perturbed reaction diffusion problems the estimator is based on a petrov galerkin method in which the trial space is enriched with nonpolynomial functions or multiscale functions we study the equivalence between the a posteriori estimate and the exact error in the energy norm moreover we prove a relationship between the hierarchic estimator and an explicit residual estimator the approach provides accurate estimates for the boundary layer regions which is confirmed by numerical experiments 2004 elsevier b v all rights reserved

cauchy problem of the generalized double dispersion equation abstract in this paper the existence and the uniqueness of the global solution for the cauchy problem of the generalized double dispersion equation are proved the blow up of the solution for the cauchy problem of the generalized double dispersion equation is discussed by the concavity method under some conditions

on the natural stabilization of convection dominated problems using high order bubnovgalerkin finite elements in the case of dominating convection standard bubnovgalerkin finite elements are known to deliver oscillating discrete solutions for the convectiondiffusion equation this paper demonstrates that increasing the polynomial degree p extension limits these artificial numerical oscillations this is contrary to a widespread notion that an increase of the polynomial degree destabilizes the discrete solution this treatise also provides explicit expressions as to which polynomial degree is sufficiently high to obtain stable solutions for a given peclet number at the nodes of a mesh

a new stabilized finite element method for reaction diffusion problems the source stabilized petrov galerkin method this paper proposes a new stabilized finite element method to solve singular diffusion problems described by the modified helmholtz operator the galerkin method is known to produce spurious oscillations for low diffusion and various alternatives were proposed to improve the accuracy of the solution the mostly used methods are the well known galerkin least squares and galerkin gradient least squares ggls the ggls method yields the exact nodal solution in the one dimensional case and for a uniform mesh however the behavior of the method deteriorates slightly in the multi dimensional case and for non uniform meshes in this work we propose a new stabilized finite element method that leads to improved accuracy for multi dimensional problems for the one dimensional case the new method leads to the same results as the ggls method and hence provides exact nodal solutions to the problem on uniform meshes the proposed method is a galerkin discretization used to solve a modified equation that includes a term depending on the gradient of the original partial differential equation copyright 2008 john wiley sons ltd

large time behavior for the system of compressible adiabatic flow through porous media in r3 abstract the cauchy problem of the system of compressible adiabatic flow through porous media in r 3 is considered we obtain the global existence and large time behavior of the solution when the initial data is close to its equilibrium in h 3 norm this is a continuing work of 31 where due to non dissipative property of the entropy s an additional assumption that the initial data is bounded in l 1 norm plays a key role in closing the a priori energy estimates and hence establishing the global existence of the solution in this paper to remove this assumption we first decompose the solution u into high frequency part u h and low frequency part u l then by constructing delicate energy functionals for u h and optimal decay rates for u l we can get the desired energy estimates to close the a priori assumption furthermore we get the optimal l 2 l 2 decay rate of the solution and show that the velocity decays faster than the density

accurate fic fem formulation for the multidimensional steady state advection diffusion absorption equation abstract in this paper we present an accurate stabilized fic fem formulation for the multidimensional steady state advection diffusion absorption equation the stabilized formulation is based on the galerkin fem solution of the governing differential equations derived via the finite increment calculus fic method using two stabilization parameters the value of the two stabilization parameters ensuring an accurate nodal fem solution using uniform meshes of linear elements is obtained from the optimal values for the 1d problem the accuracy of the new fic fem formulation is demonstrated in the solution of 2d steady state advection diffusion absorption problems for a range of physical parameters and boundary conditions

modeling of steep layers in singularly perturbed diffusion reaction equation via flexible fine scale basis abstract we present a new stabilized method for the diffusion reaction equation which develops sharp boundary and or internal layers for the reaction dominated case i e singularly perturbed case the method relies on an improved expression for the stabilization parameter that is derived via the fine scale variational formulation facilitated by the variational multiscale vms framework the proposed fine scale basis consists of enrichment functions which may be nonzero at element edges the derived stabilization parameter enjoys spatial variation over element interiors and along inter element boundaries that helps model the rapid variation of the residual of the euler lagrange equations over the domain this feature also facilitates consistent stabilization across boundary and internal layers as well as capturing anisotropic refinement effects the method is able to better satisfy the maximum principle as compared to other existing methods we present a priori mathematical analysis of the stability and convergence of the method for the diffusion reaction equation optimal convergence on meshes comprised of linear triangles and bilinear quadrilateral elements are presented for smooth problems as well as for problems with steep boundary layers stability and accuracy features of the method for problems with discontinuous forcing function internal layers and boundary layers are shown and its performance on unstructured and distorted meshes comprised of quadrilateral and triangular elements is highlighted

fourier analysis of semi discrete and space time stabilized methods for the advective diffusive reactive equation i supg abstract in this paper the work initiated in part one and two is extended to the transient subgrid scale gradient subgrid scale sgs gsgs stabilized method temporal accuracy and stability of semi discrete and time discontinuous space time versions of the method are examined for transient advection diffusion reaction problems also for the above methods predictor multi corrector algorithms are analyzed with special emphasis on mass and source lumping which has been shown to enhance both stability and accuracy of explicit stabilized methods it will be shown that the parent supg sgs and sgs gsgs methods perform very similarly and that explicit predictor multi corrector mass source lumping practically retains the accuracy of the parent method while gaining stability

implementation of a one equation turbulence model within a stabilized finite element formulation of a symmetric advective diffusive system the success of stabilized finite element methods for symmetric advective diffusive formulations of the laminar navier stokes equations has motivated extension of these concepts to turbulent flows a one equation model which preserves the symmetry of the system s advective and diffusive matrices has been developed this model is based on the work of norris and reynolds and utilizes a transport equation for the turbulent velocity scale q and an algebraic relation for the turbulent length scale l from these two quantities an eddy viscosity can be calculated this model has been implemented by way of a galerkin least squares finite element method solutions are presented which verify the good behavior of the formulation

pointwise estimates of global small solutions to the generalized double dispersion equation abstract in this paper we investigate the initial value problem for the generalized double dispersion equation in r n under suitable conditions global classical solutions are proved for n 3 and n 1 respectively moreover pointwise estimates of global classical solutions are established when n 3 and n is an odd integer by fourier splitting frequency technique

pointwise convergence to shock waves for viscous conservation laws we are interested in the pointwise behavior of the perturbations of shock waves for viscous conservation laws it is shown that besides a translation of the shock waves and of linear and nonlinear diffusion waves of heat and burgers equations a perturbation also gives rise to algebraically decaying terms which measure the coupling of waves of different characteristic families our technique is a combination of time asymptotic expansion construction of approximate green functions and analysis of nonlinear wave interactions the pointwise estimates yield optimal lp convergence of the perturbation to the shock and diffusion waves 1 p the new approach of obtaining pointwise estimates based on the green functions for the linearized system and the analysis of nonlinear wave interactions is also useful for studying the stability of waves of distinct types and nonclassical shocks these are being explored elsewhere 1997 john wiley sons inc

on the stabilized finite element method for steady convection dominated problems with anisotropic mesh adaptation in this work we combine the use of the streamline upwind petrov galerkin supg method with anisotropic mesh adaptation to obtain accurate solutions for steady convection dominated problems the anisotropic mesh adaptation framework is introduced in the context of a local mesh generation method based on a mesh topology modification and a minimal volume principle a new route to get a metric field directly at the node of the mesh is highlighted using the length distribution tensor and an edge based error analysis an a posteriori error estimation is applied to the stabilized finite element solution detecting automatically all sharp gradients inner and boundary layers the numerical examples show that the use of the anisotropic mesh adaptation algorithm allows the recovery of the global convergence order of the numerical schemes while producing accurate and oscillation free numerical solutions

galerkin generalized least squares finite element methods for time harmonic structural acoustics galerkin generalized least squares ggls finite element methods are developed and implemented for modeling the response of fluid loaded structures a general formalism for the application of this methodology to problems in structural acoustics the vibration of an elastic structure in contact with an acoustic medium is presented a consistent approach for the development and implementation of the design parameters inherent to the ggls methods for coupled problems is given this general methodology is then applied to an exterior problem of a fluid loaded reissner mindlin plate complex wave number dispersion analysis and numerical experiments demonstrate clearly the reduction of storage requirements and solution time of the new ggls methods over standard discretization techniques

large time behavior of solutions for hyperbolic balance laws we study the existence and the large time behavior of global solutions to the initial value problem for hyperbolic balance laws in n space dimensions with n 3 admitting an entropy and satisfying the stable condition we first construct global existence of the solutions to such a system around a steady state if the initial energy is small enough then we show that k order derivatives of these solutions approach a constant state in the lp norm at a rate o t 12 k n2 np with p 2 and 0 n2 provided that initially z0 b 2 where b 2 is a homogeneous besov space these decay results do not impose an additional smallness assumption on lp norm of the initial data and we thus improve the results in 3 19 we also show faster decay results in the sense that if pz0 b 2 i p z0 b 2 1 with n2 n 22 k order derivatives of the solutions approach a constant state in the lp norm at a rate o t 12 k 1 n2 np

the linearization method based on the equivalence of dissipated energies for nonlinearly damped structural systems even though the nonlinear damping characteristics inherently pertain to most structural systems many useful dynamic models are still linear as a consequence a method that is able to equivalently linearize eql the nonlinear damping so that it can be directly applied in these existing linear models is essential in the present paper a novel eql method for nonlinearly damped and single degree of freedom systems is developed the method is theoretically derived by modulating the steady state responses of the original nonlinear system during the linearization the new eql method requires the dissipated energy of the target linear system to equal that of the original nonlinear one in effect this criterion is equivalent to forcing both the phase angles and amplitudes of the two systems to be equal or at least to within a small allowable error furthermore the present paper proves that it is possible for the dissipative energy to be expressed in terms of the fourier coefficients of the modulated signal thus the equivalent viscous damping ratio can be computed from these fourier coefficients this new eql method is numerically tested using examples of bi linear damping models and subjected to experimental measurements both the simulation results and the experimental data verify the validity of the method they also prove that the current method gives the equivalent viscous damping with good accuracy in addition a quality index that signifies how well the eql system reaches is appropriately added

improved finite element methods for elastic waves abstract in this work we develop finite element methods for exterior problems of time harmonic elastic waves we employ dtn exterior boundary conditions on an artificial boundary to obtain a well posed equivalent problem in a bounded region that is suitable for domain based computation galerkin galerkin least squares and galerkin gradient least squares finite element methods are presented in acoustic wave problems the galerkin least squares method counters the numerical difficulties that result from employing the galerkin method but proves to be insufficient for elastic waves a specialization of the galerkin gradient least squares method to problems of elastic waves yields good results numerical tests validate these conclusions

computational chaos a prelude to computational instability abstract chaotic behavior sometimes occurs when difference equations used as approximations to ordinary differential equations are solved numerically with an excessively large time increment in two simple examples we find that as increases chaos first sets in when attractor a acquires two distinct points that map to the same point this happens when a acquires slopes of the same sign in a rectifying coordinate system at two consecutive intersections with the critical curve chaotic and quasi periodic behavior may then alternate within a range of before computational instability finally prevails bifurcations to and from chaos and transitions to computational instability are highly scheme dependent even among differencing schemes of the same order systems exhibiting computational chaos can serve as illustrative examples in more general studies of noninvertible mappings

new approaches for the study of non linear oscillators abstract this paper presents a power series approach to accurately obtain the damped separatrices for a class of unforced non linear oscillators this in turn delineates the basins of attraction of two or more stable attractors in the phase space the method is illustrated by its applications to the unforced duffing holmes and blacklash oscillators next a novel semi analytical integration scheme called the phase space linearization method psl is developed to obtain stable and unstable periodic solutions of forced as well as unforced non linear oscillators and also the damped separatrices the performance of the proposed method has been tested against periodic solutions of three oscillators namely ueda s duffing holmes and van der pol s oscillators obtained using a fourth order runge kutta method with a sufficiently small time step moreover the separatrices obtained using the psl method are compared with those obtained via the power series method as developed earlier the issue of accumulation of error in the psl method as against the fourth order runge kutta scheme is also described numerically through an example of a first order non linear equation having closed form solution

a global attractor for the elastic waveguide model in rn abstract this paper studies the longtime behavior of solutions to the elastic waveguide model in r n u t t u u t t 2 u u t u t u g x u f x it proves that when the space dimension n 5 under rather mild conditions on g and f the related solution semigroup possesses in phase space with low regularity x h 2 h 1 h 2 h with 0 1 a global attractor which is connected

a generalized local linearization principle for non linear dynamical systems tangent spaces in non linear dynamical systems are state dependent hence it is generally not possible to exactly represent a non linear dynamical system by a linear one over finite segments of the evolving trajectories in the phase space it is known from the well known theorem of hartman and grobman that a non linear oscillator admits a linearization within a neighbourhood of any hyperbolic fixed point in the sense that the linearized flow bears a topological conjugacy to the non linear flow within the same neighbourhood this linearization is based on the construction of the tangent space to the non linear vector field at the hyperbolic fixed point even though useful in bifurcation analysis such a linearization procedure cannot be successfully applied to identically simulate the non linear flow over the phase space because the functional form of the topological conjugacy is not known with this in mind an implicit approach to local linearization is evolved in this paper such that the tangent space of the linearized equation transversally intersects the tangent space to the non linear dynamical system at that point in the state space where the solution vector is desired several numerical schemes for the implementation of this implicit and local linearization procedure are explored and illustrated with several numerical results it is shown that the locally transversal linearization ltl procedure finally reduces the given set of non linear ordinary differential equations odes to a set of transcendental algebraic equations with the desired solution vector as the unknown the variables in the state space appear as unknown quantities in this approach finally one arrives at non linear poincare maps for the non linear oscillator in this scheme the characteristic time interval for the map is arbitrarily fixed the methodology is found to be quite versatile for handling non linear dynamical systems in particular it is verified that these schemes are capable of accurately predicting a wide spectrum of typically non linear response characteristics such as limit cycles multi periodicity almost periodicity and chaos for a limited class of response patterns the principle proposed has another advantage in that the time step for integrating the non linear odes need not be small an improved and a more general higher order version of the ltl method is also considered a distinct advantage of this higher version is in its improved ability for a closer simulation of phase dependent time histories where a difference in the initial conditions leads to a phase difference in the realized solution history

global solution and large time behavior of the 3d compressible euler equations with damping national natural science foundation of china nsaf 10976026 national natural science foundation of china 11271305

global attractor for the generalized double dispersion equation abstract the paper studies the existence of global attractor for the generalized double dispersion equation arising in elastic waveguide model u t t u u t t 2 u u t g u f x the main result is concerned with nonlinearities g u with supercritical growth in that case we construct a subclass g of the limit solutions and show that it has a weak global attractor especially in non supercritical case the weak topology becomes strong the further regularity of the global attractor is obtained and the exponential attractor is established in natural energy space

a fourth order compact scheme for the helmholtz equation alpha interpolation of fem and fdm stencils we propose a fourth order compact scheme on structured meshes for the helmholtz equation given by r f x 2 0 the scheme consists of taking the alpha interpolation of the galerkin finite element method and the classical central finite difference method in 1d this scheme is identical to the alpha interpolation method j comput appl math 1982 8 1 15 19 and in 2d making the choice 0 5 we recover the generalized fourth order compact pade approximation j comput phys 1995 119 252 270 comput meth appl mech engrg 1998 163 343 358 therein using the parameter 2 we follow siam rev 2000 42 3 451 484 comput meth appl mech engrg 1995 128 325 359 for the analysis of this scheme and its performance on square meshes is compared with that of the quasi stabilized fem comput meth appl mech engrg 1995 128 325 359 in particular we show that the relative phase error of the numerical solution and the local truncation error of this scheme for plane wave solutions diminish at the rate o l 4 where l represent the wavenumber and the mesh size respectively an expression for the parameter is given that minimizes the maximum relative phase error in a sense that will be explained in section 4 5 convergence studies of the error in the l2 norm the h1 semi norm and the l euclidean norm are done and the pollution effect is found to be small copyright 2010 john wiley sons ltd

the lp decay estimates for the chemotaxis shallow water system abstract in this paper we consider the large time behavior of solution for the chemotaxis shallow water system in two dimension by the method of frequency decomposition first we construct the green s function of the linearized system and get the corresponding estimates for low frequency part then we introduce an energy method we named double cycle method to get the decay rate for high frequency part due to the dissipative mechanism of this system the high frequency part decays faster than the low frequency part

a space time finite element method for structural acoustics in infinite domains part 1 formulation stability and convergence abstract a space time finite element method for solution of the exterior structural acoustics problem involving the interaction of vibrating elastic structures submerged in an infinite acoustic fluid is formulated in particular time discontinuous galerkin and galerkin least squares gls variational formulations for coupled structural acoustics in unbounded domains are developed and analyzed for stability and convergence the formulation employs a finite computational fluid domain surrounding the structure and incorporates time dependent non reflecting boundary conditions on the fluid truncation boundary energy estimates are obtained which allow us to prove the unconditional stability of the method for the coupled fluid structure problem with absorbing boundaries the methods developed are especially useful for the application of adaptive solution strategies for transient acoustics in which unstructured space time meshes are used to track waves propagating along space time characteristics an important feature of the space time formulation is the incorporation of temporal jump operators which allow for finite element interpolations that are discontinaous in time for additional stability least squares operators based on local residuals of the structural acoustics equations including the non reflecting boundary conditions are incorporated the energy decay estimates and high order accuracy predicted by our a priori error estimates are demonstrated numerically in a simple canonical example

a new finite element formulation for computational fluid dynamics x the compressible euler and navier stokes equations a space time element method is presented for solving the compressible euler and navier stokes equations the proposed formulation includes the variational equation predictor multi corrector algorithms and boundary conditions the variational equation is based on the time discontinuous galerkin method in which the physical entropy variables are employed a least squares operator and a discontinuity capturing operator are added resulting in a high order accurate and unconditionally stable method implicit explicit predictor multi corrector algorithms applicable to steady as well as unsteady problems are presented techniques are developed to enhance their efficiency implementation of boundary conditions is addressed in particular a technique is introduced to satisfy nonlinear essential boundary conditions and a consistent method is presented to calculate boundary fluxes numerical results are presented to demonstrate the performance of the method

asymptotic behavior of solutions to conservation laws with diffusion type terms of regularity gain and regularity loss abstract in this paper we study asymptotic behaviors of solutions to the cauchy problem of nonlinear conservation laws with a diffusion type source term related to an index s r for s 1 and s 1 the diffusion type term takes on a characteristic of regularity gain and regularity loss on the high frequency domain respectively by combining the green function method with the energy method we overcome the weakly dissipative structure of the equation for the case of s 1 and obtain the global existence and optimal l p norm time decay rates of solutions in the case of regularity gain pointwise estimates of solutions are shown by using the refined analysis on the green function

existence and asymptotic stability of time periodic solutions to the generalized double dispersion equation with periodic external force abstract in this paper we investigate the generalized double dispersion equation with periodic external force in r n we prove the existence and uniqueness of time periodic solutions that have the same period as the external force in some suitable function space for the space dimension n 3 the proof is based on the spectral analysis for the solution operator and the contraction mapping theorem in addition we also discuss the time asymptotic stability of the time periodic solutions by continuous argument

global existence of solution for cauchy problem of multidimensional generalized double dispersion equations abstract we study the cauchy problem of a class of multidimensional generalized double dispersion equations u t t u u t t 2 u k u t f u we prove the global existence of weak solution under some assumptions on the nonlinear term and the initial data