adaptive poromechanics computations based on a posteriori error estimates for fully mixed formulations of biot s consolidation model abstract this paper is concerned with the analysis of coupled mixed finite element methods applied to the biot s consolidation model we consider two mixed formulations that use the stress tensor and darcy velocity as primary variables as well as the displacement and pressure the first formulation is with a symmetric stress tensor while the other enforces the symmetry of the stress weakly through the introduction of a lagrange multiplier the well posedness of the two formulations is shown through galerkin s method and suitable a priori estimates the two formulations are then discretized with the backward euler scheme in time and with two mixed finite elements in space we present next a general and unified a posteriori error analysis which is applicable for any flux and stress conforming discretization our estimates are based on h 1 conforming reconstruction of the pressure and a suitable h 1 d conforming reconstruction of the displacement both are continuous and piecewise affine in time these reconstructions are used to infer a guaranteed and fully computable upper bound on the energy type error measuring the differences between the exact and the approximate pressure and displacement the error components resulting from the spatial and the temporal discretization are distinguished they are then used to design an adaptive space time algorithm numerical experiments illustrate the efficiency of our estimates and the performance of the adaptive algorithm

local discontinuous galerkin methods for the stokes system in this paper we introduce and analyze local discontinuous galerkin methods for the stokes system for a class of shape regular meshes with hanging nodes we derive a priori estimates for the l2 norm of the errors in the velocities and the pressure we show that optimal order estimates are obtained when polynomials of degree k are used for each component of the velocity and polynomials of degree k 1 for the pressure for any k ge1 we also consider the case in which all the unknowns are approximated with polynomials of degree k and show that although the orders of convergence remain the same the method is more efficient numerical experiments verifying these facts are displayed

existence of periodic solutions for ordinary differential systems in musielak orlicz sobolev spaces abstract in this paper we study the periodic solutions for the ordinary differential systems in musielak orlicz sobolev spaces we get some propositions of the musielak orlicz sobolev space w t 1 which are used to get the existence results using variational methods we have some existence results of the periodic solutions for the ordinary differential systems in musielak orlicz sobolev spaces

multivalued periodic lienard systems abstract we consider a nonlinear multivalued periodic lienard system driven by a general strictly monotone nonhomogeneous homeomorphism which includes as a special case the vector p laplacian the reaction has also a maximal monotone map which need not be defined on all of r n we prove existence theorems for both the convex and nonconvex problems we also show the existence of extremal trajectories that is solutions moving through the extremal points of the multivalued perturbation we also show that every solution of the convexified system can be obtained as the c 1 t r n limit of a sequence of certain extremal trajectories finally as an illustration we examine a nonlinear control system with a priori feedback

diffusion in poro elastic media existence uniqueness and regularity theory is developed for a general initial boundary value problem for a system of partial differential equations which describes the biot consolidation model in poro elasticity as well as a coupled quasi static problem in thermoelasticity additional effects of secondary consolidation and pore fluid exposure on the boundary are included this quasi static system is resolved as an application of the theory of linear degenerate evolution equations in hilbert space and this leads to a precise description of the dynamics of the system

nonlinear systems with singular vector φ laplacian under the hartman type condition based on a continuation principle we give some existence results of solutions for the nonlinear problem u f t u u 0 u t u 0 u t involving singular vector laplacian with b a rn 0 a or rn b a 0 a a homeomorphism under the hartman type condition or the modified hartman type condition

discontinuous galerkin methods for incompressible and nearly incompressible elasticity by nitsche s method we propose and analyze a discontinuous finite element method for nearly incompressible linear elasticity on triangular meshes we show optimal error estimates that are uniform with respect to poisson s ratio the method is thus locking free we also introduce an equivalent mixed formulation allowing for completely incompressible elasticity problems numerical results are presented

on some techniques for approximating boundary conditions in the finite element method we discuss the stabilization of finite element methods in which essential boundary conditions are approximated by babuska s method of lagrange multipliers and we show that there is a close connection with this technique and a classical method by nitsche

fully discrete stabilized multiphysics finite element method for the polymer gel model abstract in this paper we propose a fully discrete stabilized multiphysics finite element method by the pressure projection method to solve the polymer gel model to reveal the multi physical process of the polymer gel model we reformulate the polymer gel model by introducing a new variable to get a new multi field problem then we propose the fully discrete stabilized multiphysics finite element method using the simplest equal order element of p 1 p 1 p 1 without the discrete inf sup condition to solve the new reformulated system and we prove that the new method not only has no locking phenomenon but also preserves some energy conservation laws also we prove that the stabilized multiphysics finite element method has optimal convergence order finally we give the numerical example to verify the theoretical results

coupling biot and navier stokes equations for modelling fluid poroelastic media interaction the interaction between a fluid and a poroelastic structure is a complex problem that couples the navier stokes equations with the biot system the finite element approximation of this problem is involved due to the fact that both subproblems are indefinite in this work we first design residual based stabilization techniques for the biot system motivated by the variational multiscale approach then we state the monolithic navier stokes biot system with the appropriate transmission conditions at the interface for the solution of the coupled system we adopt both monolithic solvers and heterogeneous domain decomposition strategies different domain decomposition methods are considered and their convergence is analyzed for a simplified problem we compare the efficiency of all the methods on a test problem that exhibits a large added mass effect as it happens in hemodynamics applications

weak galerkin method for the biot s consolidation model abstract we develop a weak galerkin wg finite element method for the biot s consolidation model in the classical displacement pressure two field formulation weak galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations backward euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme we study the well posedness of the linear system at each time step and also derive the overall optimal order convergence of the wg formulation such wg scheme is designed on general shape regular polytopal meshes and provides stable and oscillation free approximation for the pressure without special treatment numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak galerkin finite element method

existence of periodic solutions for a class of second order p laplacian systems abstract in this paper the existence of periodic solutions are obtained for a class of non autonomous second order p laplacian systems by the least action principle

strongly nonlinear multivalued boundary value problems in this paper we study nonlinear second order differential inclusions involving the differential operator depending on both unknown function x and its derivative x a multivalued maximal monotone operator and nonlinear multivalued boundary conditions our framework is general and can be applied to the classical boundary value problems namely the dirichlet the neumann and the periodic problems using notions and techniques from the nonlinear operator theory and from multivalued analysis we obtain solutions for both the convex and nonconvex problems finally we present the cases of special interest which fit into our framework illustrating the generality of our results

existence of infinitely many periodic solutions for ordinary p laplacian systems abstract in this paper we study the existence and multiplicity of non trivial periodic solutions of ordinary p laplacian systems by using the minimax technique in critical point theory we also give an example to illustrate that the obtained results are new even in the case p 2

hartman type results for p t laplacian systems consider the weighted p t laplacian ordinary system w t u t p t 2u t w t f t u t 0 in a b u a u b 0 where f c a b rn rn w c a b r p c a b r and p t 1 for t a b it is proved that if r 0 such that f t u u 0 t a b u rn with u r then the problem has a solution u such that u t r for t a b as a corollary of this result taking w t tn 1 we obtain the existence of the radial solutions for the elliptic systems our result generalized the corresponding results obtained by hartman and mawhin

analysis and application of finite volume element methods to a class of partial differential equations abstract the finite volume element fve methods for a class of partial differential equations are discussed and analyzed in this paper the new initial values are introduced in the finite volume element schemes and we obtain optimal error estimates in l p and w 1 p 2 p as well as some superconvergence estimates in w 1 p 2 p the main results in this paper perfect the theory of the finite volume element methods

discontinuous galerkin methods for the helmholtz equation with large wave number this paper develops and analyzes some interior penalty discontinuous galerkin ipdg methods using piecewise linear polynomials for the helmholtz equation with the first order absorbing boundary condition in two and three dimensions it is proved that the proposed discontinuous galerkin methods are stable hence well posed without any mesh constraint for each fixed wave number k optimal order with respect to h error estimate in the broken h 1 norm and suboptimal order estimate in the l 2 norm are derived without any mesh constraint the latter estimate improves to optimal order when the mesh size h is restricted to the preasymptotic regime i e k 2 h gtrsim 1 numerical experiments are also presented to gauge the theoretical result and to numerically examine the pollution effect with respect to k in the error bounds the novelties of the proposed ipdg methods include the following first the methods penalize not only the jumps of the function values across the element edges but also the jumps of the normal and tangential derivatives second the penalty parameters are taken as complex numbers of positive imaginary parts so essentially and practically no constraint is imposed on the penalty parameters since the helmholtz problem is a non hermitian and indefinite linear problem as expected the crucial and the most difficult part of the whole analysis is to establish the stability estimates i e a priori estimates for the numerical solutions to this end the cruxes of our analysis are to establish and to make use of a local version of the rellich identity for the laplacian and to mimic the stability analysis for the pde solutions given in p cummings analysis of finite element based numerical methods for acoustic waves elastic waves and fluid solid interactions in the frequency domain ph d thesis the university of tennessee knoxville tn 2001 p cummings and x feng math models methods appl sci 16 2006 pp 139 160 u hetmaniuk commun math sci 5 2007 pp 665 678

stabilized finite element methods for the velocity pressure stress formulation of incompressible flows abstract formulated in terms of velocity pressure and the extra stress tensor the incompressible navier stokes equations are discretized by stabilized finite element methods the stabilized methods proposed are analyzed for a linear model and extended to the navier stokes equations the numerical tests performed confirm the good stability characteristics of the methods these methods are applicable to various combinations of interpolation functions including the simplest equal order linear and bilinear elements

a posteriori analysis and adaptive error control for operator decomposition solution of coupled semilinear elliptic systems summary in this paper we develop an a posteriori error analysis for operator decomposition iteration methods applied to systems of coupled semilinear elliptic problems the goal is to compute accurate error estimates that account for the combined effects arising from numerical approximation discretization and operator decomposition iteration in an earlier paper 1 we considered triangular systems that can be solved without iteration in contrast operator decomposition iterative methods for fully coupled systems involve an iterative solution technique we construct an error estimate for the numerical approximation error that specifically addresses the propagation of error between iterates and provide a computable estimate for the iteration error arising due to the decomposition of the operator finally we extend the adaptive discretization strategy in 1 to systematically reduce the discretization error copyright c 2010 john wiley sons ltd

a taxonomy of consistently stabilized finite element methods for the stokes problem stabilized mixed methods can circumvent the restrictive inf sup condition without introducing penalty errors for properly chosen stabilization parameters these methods are well posed for all conforming velocity pressure pairs however their variational forms have widely varying properties first stabilization offers a choice between weakly or strongly coercive bilinear forms that give rise to linear systems with identical solutions but very different matrix properties second coercivity may be conditional upon a proper choice of a stabilizing parameter here we focus on how these two aspects of stabilized methods affect their accuracy and efficient iterative solution we present results that indicate a preference of krylov subspace solvers for strongly coercive formulations stability criteria obtained by finite element and algebraic analyses are compared with numerical experiments while for two popular classes of stabilized methods sufficient stability bounds correlate well with numerical stability our experiments indicate the intriguing possibility that the pressure stabilized galerkin method is unconditionally stable

a mixed finite element method for nearly incompressible multiple network poroelasticity in this paper we present and analyze a new mixed finite element formulation of a general family of quasi static multiple network poroelasticity mpet equations the mpet equations describe flow a

homoclinic solutions for ordinary p laplacian systems abstract a new result for the existence of homoclinic orbits is obtained for ordinary p laplacian system d dt u t p 2 u t v t u t f t where p 1 t r u r n and v c 1 r r n r v t x k t x w t x is t periodic with respect to t t 0 and f r r n is a continuous and bounded function this result generalizes and improves some known results in the previous literature

stabilized discontinuous finite element approximations for stokes equations in this paper we derive two stabilized discontinuous finite element formulations symmetric and nonsymmetric for the stokes equations and the equations of the linear elasticity for almost incompressible materials these methods are derived via stabilization of a saddle point system where the continuity of the normal and tangential components of the velocity displacements are imposed in a weak sense via lagrange multipliers for both methods almost all reasonable pair of discontinuous finite element spaces can be used to approximate the velocity and the pressure optimal error estimate for the approximation of both the velocity of the symmetric formulation and pressure in l2 norm are obtained as well as one in a mesh dependent norm for the velocity in both symmetric and nonsymmetric formulations

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

solutions and multiple solutions for periodic systems with nonhomogeneous differential operators abstract in this paper we consider nonlinear periodic systems driven by the nonhomogeneous vector p laplacian differential operator and with a nonsmooth potential using variational techniques based on the nonsmooth critical point theory we prove existence and multiplicity results finally we obtain an existence result for systems driven by the ordinary vector p laplacian and we show that it is still true in the more general framework of the previous results

infinitely many periodic solutions for second order p q laplacian differential systems abstract some existence theorems are obtained for infinitely many periodic solutions for second order p q laplacian differential systems by using a general variational principle due to b ricceri

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

a unified stabilized method for stokes and darcy s equations we use the lowest possible approximation order piecewise linear continuous velocities and piecewise constant pressures to compute solutions to stokes equation and darcy s equation applying an edge stabilization term to avoid locking we prove that the formulation satisfies the discrete inf sup condition we prove an optimal a priori error estimate for both problems the formulation is then extended to the coupled case using a nitsche type weak formulation allowing for different meshes in the two subdomains finally we present some numerical examples verifying the theoretical predictions and showing the flexibility of the coupled approach

shannon theoretic approach to a gaussian cellular multiple access channel with fading shannon theoretic limits on the achievable throughput for a simple infinite cellular multiple access channel mac model wyner 1994 in the presence of fading are presented in this model which is modified to account for flat fading the received signal at a given cell site s antenna is the sum of the faded signals transmitted from all users within that cell plus an attenuation factor spl alpha spl isin 0 1 times the sum of the faded signals received from the adjacent cells accompanied by gaussian additive noise this model serves as a tractable model providing considerable insight into complex and analytically intractable real world cellular communications both linear and planar cellular arrays are considered with exactly k active users in each cell we assume a hyper receiver jointly decoding all of the users incorporating the received signals from all of the active cell sites the hyper receiver is assumed to be aware of the codebooks and realizations of the fading processes of all the users in the system in this work we consider the intracell time division multiple access tdma and the wideband wb protocols we focus on the maximum reliably transmitted equal rate bounds to this rate are found for the intracell tdma protocol by incorporating information theoretic inequalities and the chebyshev markov moment theory as applied to the limiting distribution of the eigenvalues of a quadratic form of tridiagonal random matrices we demonstrate our results for the special case where the amplitudes of the fading coefficients are drawn from a rayleigh distribution i e rayleigh fading for this special case we observe the rather surprising result that fading may increase the maximum equal rate for a certain range of spl alpha as compared to the nonfaded case in this setting the wb strategy which achieves the maximum reliable equal rate of the model is proved to be superior to the tdma scheme an upper bound to the maximum equal rate of the wb scheme is also obtained this bound is asymptotically tight when the number of users is large k spl gt 1 the asymptotic bound shows that the maximum equal rate of the wb scheme in the presence of fading is higher than the rate which corresponds to the nonfaded case for any intercell interference factor spl alpha spl isin 0 1 signal to noise ratio snr values this result is found to be independent of the statistics of the fading coefficients

analysis of a pressure stabilized finite element approximation of the stationary navier stokes equations the purpose of this paper is to analyze a finite element approximation of the stationary navier stokes equations that allows the use of equal velocity pressure interpolation the idea is to introduce as unknown of the discrete problem the projection of the pressure gradient multiplied by suitable algorithmic parameters onto the space of continuous vector fields the difference between these two vectors pressure gradient and projection is introduced in the continuity equation the resulting formulation is shown to be stable and optimally convergent both in a norm associated to the problem and in the l 2 norm for both velocities and pressure this is proved first for the stokes problem and then it is extended to the nonlinear case all the analysis relies on an inf sup condition that is much weaker than for the standard galerkin approximation in spite of the fact that the present method is only a minor modification of this

ordinary p laplacian systems with nonlinear boundary conditions abstract this paper is concerned with the existence of solutions for the boundary value problem u p 2 u u p 2 u f t u in 0 t u p 2 u 0 u p 2 u t j u 0 u t where 0 p 1 are fixed j r n r n is a proper convex and lower semicontinuous function and f 0 t r n r is a caratheodory mapping continuously differentiable with respect to the second variable and satisfies some usual growth conditions our approach is a variational one and relies on szulkin s critical point theory a szulkin minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems ann inst h poincare anal non lineaire 3 1986 77 109 we obtain the existence of solutions in a coercive case as well as the existence of nontrivial solutions when the corresponding euler lagrange functional has a mountain pass geometry

periodic solutions of non autonomous second order systems with a p laplacian abstract in this paper we investigate non autonomous second order systems with a p laplacian and obtain existence results for periodic solutions with the dual least action principle

absolutely stable local discontinuous galerkin methods for the helmholtz equation with large wave number two local discontinuous galerkin ldg methods using some non standard numerical uxes are developed for the helmholtz equation with the rst order absorbing boundary condition in the high frequency regime it is shown that the proposed ldg methods are absolutely stable hence well posed with respect to both the wave number and the mesh size optimal order with respect to the mesh size error estimates are proved for all wave numbers in the preasymptotic regime to analyze the proposed ldg methods they are recasted and treated as non conforming mixed nite element methods the crux of the analysis is to establish a generalized inf sup condition which holds without any mesh constraint for each ldg method the generalized inf sup conditions then easily infer the desired absolute stability of the proposed ldg methods in return the stability results not only guarantee the well posedness of the ldg methods but also play a crucial role in the derivation of the error estimates numerical experiments which conrm the theoretical results and compare the proposed two ldg methods are also presented in the paper

nonlinear boundary value problems for second order differential inclusions abstract in this paper we study a class of nonlinear value boundary problems for second order differential inclusions with nonlinear perturbations which satisfy the generalized hartman condition weaker than that considered in some papers using techniques from multivalued analysis theory of monotone operators and fixed points we prove the existence of solutions in both convex and nonconvex cases our framework can be incorporated with dirichlet neumann and mixed boundary problems

a posteriori error estimators for convection diffusion equations we derive a posteriori error estimators for convection diffusion equations with dominant convection the estimators yield global upper and local lower bounds on the error measured in the energy norm such that the ratio of the upper and lower bounds only depends on the local mesh peclet number the estimators are either based on the evaluation of local residuals or on the solution of discrete local dirichlet or neumann problems

fully discrete finite element approximations of a polymer gel model this paper proposes and analyzes some fully discrete multiphysics finite element methods for a displacement pressure model which describes swelling dynamics of polymer gels under mechanical constraints by introducing an elastic pressure we first present a reformulation of the original model we then propose a time stepping scheme which decouples the pde system at each time step into two subproblems one of which is a stokes like problem for the displacement vector field of the solid network of the gel and the other is a diffusion problem for a pseudopressure field of the solvent of the gel to make such a multiphysics approach feasible it is vital to find admissible constraints to resolve the uniqueness issue for the stokes like problem and to construct a good boundary condition for the diffusion equation so that it also becomes uniquely solvable the key to the first difficulty is to discover certain conserved quantities for the pde solution and the solution to the second difficulty is to use the stokes like problem to generate a boundary condition for the diffusion problem the time stepping scheme allows one to use any convergent stokes solver and its code together with any convergent diffusion equation solver and its code to solve the polymer gel model in the paper the taylor hood mixed finite element method combined with the continuous linear finite element method are chosen as an example to present the ideas and to demonstrate the viability of the proposed multiphysics approach it is proved that under a mesh constraint both the semidiscrete in space and fully discrete methods enjoy some discrete energy laws which mimic the differential energy law satisfied by the pde solution optimal order error estimates in various norms are established for both semidiscrete and fully discrete methods numerical experiments are also presented to show the performance of the proposed approach and methods

shannon theoretic approach to a gaussian cellular multiple access channel we obtain shannon theoretic limits for a very simple cellular multiple access system in our model the received signal at a given cell site is the sum of the signals transmitted from within that cell plus a factor spl alpha 0 spl les spl alpha spl les 1 times the sum of the signals transmitted from the adjacent cells plus ambient gaussian noise although this simple model is scarcely realistic it nevertheless has enough meat so that the results yield considerable insight into the workings of real systems we consider both a one dimensional linear cellular array and the familiar two dimensional hexagonal cellular pattern the discrete time channel is memoryless we assume that n contiguous cells have active transmitters in the one dimensional case and that n sup 2 contiguous cells have active transmitters in the two dimensional case there are k transmitters per cell most of our results are obtained for the limiting case as n spl rarr spl infin the results include the following 1 we define c sub n c spl circ sub n as the largest achievable rate per transmitter in the usual shannon theoretic sense in the one and two dimensional cases respectively assuming that all signals are jointly decoded we find expressions for limn spl rarr spl infin c sub n and limn spl rarr spl infin c spl circ sub n 2 as the interference parameter spl alpha increases from 0 c sub n and c spl circ sub n increase or decrease according to whether the signal to noise ratio is less than or greater than unity 3 optimal performance is attainable using tdma within the cell but using tdma for adjacent cells is distinctly suboptimal 4 we suggest a scheme which does not require joint decoding of all the users and is in many cases close to optimal

existence of positive and of multiple solutions for nonlinear periodic problems abstract in this paper we consider a scalar periodic problem driven by the ordinary p laplacian differential operator and having a nonsmooth potential using a variational method based on nonsmooth critical point theory first we prove the existence of a strictly positive solution then by strengthening our hypotheses on the nonsmooth potential we prove the existence of a second periodic solution

periodic problems with asymmetric nonlinearities and nonsmooth potentials abstract we consider a nonlinear periodic boundary value problem driven by the ordinary scalar p laplacian and with a nonsmooth locally lipschitz potential which exhibits an asymmetric behaviour at and at using the fucik spectrum and a variational approach based on the nonsmooth critical point theory we obtain a solution for the problem using a general minimax principle concerning linking sets

stabilized lowest order finite element approximation for linear three field poroelasticity a stabilized conforming mixed finite element method for the three field displacement fluid flux and pressure poroelasticity problem is developed and analyzed we use the lowest possible approximation order namely piecewise constant approximation for the pressure and piecewise linear continuous elements for the displacements and fluid flux by applying a local pressure jump stabilization term to the mass conservation equation we ensure stability and avoid pressure oscillations importantly the discretization leads to a symmetric linear system for the fully discretized problem we prove existence and uniqueness an energy estimate and an optimal a priori error estimate including an error estimate for the divergence of the fluid flux numerical experiments in two and three dimensions illustrate the convergence of the method show its effectiveness in overcoming spurious pressure oscillations and evaluate the added mass effect of the stabilization term

periodic solutions for semi linear evolution inclusions in this paper we study the periodic problem for semi linear evolution inclusion using techniques from multivalued analysis and fixed point theorems we establish existence theorems under the one sided lipschitz condition first we prove existence theorems for nonconvex and convex problem second we look for extremal periodic solutions and prove the relaxation theorem

on the existence of solutions of p laplacian m point boundary value problem at resonance abstract by using the theory of coincidence degree we study a kind of solutions of p laplacian m point boundary value problem at resonance in the following form p u t f t u u 0 t 1 u 0 0 u 1 i 1 m 2 a i u i where m 3 a i 0 i 1 2 m 2 0 1 2 m 2 1 such that i 1 m 2 a i 1 a result on the existence of solutions is obtained the degrees of two variables x 1 x 2 in the function f t x 1 x 2 are allowable to be bigger than 1

some existence results on periodic solutions of euler lagrange equations in an orlicz sobolev space setting abstract in this paper we consider the problem of finding periodic solutions of certain euler lagrange equations we employ the direct method of the calculus of variations i e we obtain solutions minimizing certain functional i we give conditions which ensure that i is finitely defined and differentiable on certain subsets of orlicz sobolev spaces w 1 l associated to an n function we show that in some sense it is necessary for the coercivity that the complementary function of satisfy the 2 condition we conclude by discussing conditions for the existence of minima of i

spectral efficiency of cdma with random spreading the cdma channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods furthermore its analysis provides a comparison baseline for cdma channels with deterministic signature waveforms spanning one symbol period we analyze the spectral efficiency total capacity per chip as a function of the number of users spreading gain and signal to noise ratio and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading white gaussian background noise and equal power synchronous users are assumed the following receivers are analyzed a optimal joint processing b single user matched filtering c decorrelation and d mmse linear processing

stability and convergence of sequential methods for coupled flow and geomechanics fixed stress and fixed strain splits abstract we analyze stability and convergence of sequential implicit methods for coupled flow and geomechanics in which the flow problem is solved first we employ the von neumann and energy methods for linear and nonlinear problems respectively we consider two sequential methods with the generalized midpoint rule for tn where is the parameter of time discretization namely the fixed strain and fixed stress splits the von neumann method indicates that the fixed strain split is only conditionally stable and that its stability limit is a coupling strength less than unity if 0 5 on the other hand the fixed stress split is unconditionally stable when 0 5 the amplification factors of the fixed stress split are different from those of the undrained split and are identical to the fully coupled method unconditional stability of the fixed stress split is also obtained from the energy method for poroelastoplasticity we show that the fixed stress split is contractive and b stable when 0 5 we also estimate the convergence behaviors for the two sequential methods by the matrix based and spectral analyses for the backward euler method in time from the estimates the fixed strain split may not be convergent with a fixed number of iterations particularly around the stability limit even though it is stable the fixed stress split however is convergent for a fixed number of iterations showing better accuracy than the undrained split even when we cannot obtain the exact local bulk modulus or exact rock compressibility at the flow step a priori due to complex boundary conditions or the nonlinearity of the materials the fixed stress split can still provide stability and convergence by an appropriate estimation of the local bulk modulus such as the dimension based estimation by which the employed local bulk modulus is less stiff than the exact local bulk modulus we provide numerical examples supporting all the estimates of stability and convergence for the fixed strain and fixed stress splits

existence and multiplicity results for nonlinear nonautonomous second order systems in this paper we consider nonlinear periodic systems driven by the ordinary p laplacian and having a nonsmooth potential function under minimal and natural hypotheses on the nonsmooth potential and using variational methods based on the nonsmooth critical point theory we prove four existence theorems and a multiplicity theorem we conclude the paper with an existence theorem for the scalar problem in which the energy functional is indefinite i e it is unbounded both above and below

a high order hdg method for the biot s consolidation model abstract we propose a novel high order hdg method for the biot s consolidation model in poroelasticity we present optimal h version error analysis for both the semi discrete and full discrete combined with temporal backward differentiation formula schemes numerical tests are provided to demonstrate the performance of the method

notes on periodic solutions of subquadratic second order systems some existence theorems are obtained for periodic solutions of the subquadratic second order systems by the minimax methods in critical point theory

a stabilized finite element method based on two local gauss integrations for the stokes equations this paper considers a stabilized method based on the difference between a consistent and an under integrated mass matrix of the pressure for the stokes equations approximated by the lowest equal order finite element pairs i e the p 1 p 1 and q 1 q 1 pairs this method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf sup condition optimal error estimates are obtained by applying the standard galerkin technique finally the numerical illustrations agree completely with the theoretical expectations

second order periodic problem with φ laplacian and impulses abstract existence principles for the bvp u t f t u t u t a e on 0 t u t i j i u t i u t i m i u t i i 1 2 m u 0 u t u 0 u t are presented they are based on the method of lower upper functions which need not be well ordered

existence of periodic solutions for p t laplacian systems abstract in this paper by using minimax methods in critical point theory we obtain some existence theorems for periodic solutions of p t laplacian system u t p t 2 u t f t u t 0 u 0 u t u 0 u t 0 and our results generalize some existed theorems

on the existence of periodic solutions for a class of p laplacian system by using generalized borsuk theorem in coincidence degree theory some criteria to guarantee the existence of periodic solutions for a class of p laplacian system are derived

periodic solutions of a class of non autonomous second order systems some existence theorems are obtained by the least action principle for periodic solutions of nonautonomous second order systems with a potential which is the sum of a subconvex function and a subquadratic function

spectral efficiency of joint multiple cell site processors for randomly spread ds cdma systems a chip interleaved randomly spread direct sequence code division multiple access ds cdma scheme is considered employed in two variants of wyner s infinite linear cell array model with flat fading focusing on the asymptotic setup in which both the number of users per cell and the processing gain go to infinity while their ratio the ldquocell loadrdquo goes to some finite constant the spectral efficiencies of the optimum and linear minimum mean squared error mmse joint multicell receivers are investigated a dramatic performance enhancement as compared to single cell site processing is demonstrated the asymptotic behavior of the two receivers in extreme signal to noise ratio snr regimes and in a high cell load regime are analyzed as well the impact of chip interleaving versus symbol interleaving is also investigated chip level interleaving is found beneficial in several cases of interests and is conjectured to be beneficial in general

a knobloch type result for p t laplacian systems we consider the periodic boundary value problem of ordinary differential systems with p t laplacian of the form u p t 2u f t u u 0 u t u 0 u t 0 where p c r r is a t periodic function and p t 1 for t r f c r rn rn and f t u is t periodic with respect to t we prove that if there exists some r 0 such that f t u u 0 for t r and u rn with u r then the problem has at least one solution u satisfying u t r for t r this is a generalization of the results obtained by knobloch and mawhin under the case of p t 2 and p t p 1 respectively

three periodic solutions for p hamiltonian systems abstract the existence of at least three periodic solutions is established for a class of p hamiltonian systems our technical approach is based on two general three critical points theorems obtained by ricceri and averna bonanno

ergodic sum capacity of macrodiversity mimo systems in flat rayleigh fading the prospect of base station cooperation leading to joint combining at widely separated antennas has led to increased interest in macrodiversity systems where both sources and receive antennas are geographically distributed in this scenario analytical investigation of channel capacity is extremely challenging for finite size systems since the channel matrices have a very general form where each path may have a different power hence in this paper we consider the ergodic sum capacity of a macrodiversity multiple input multiple output system with arbitrary numbers of sources and receive antennas operating over rayleigh fading channels for this system we compute the exact ergodic capacity for a system with at most two transmit antennas and a compact approximation for the general system which is shown to be very accurate over a wide range of cases finally we compare our results with previous asymptotic results and bounds results are verified by monte carlo simulations and the impact on capacity of various channel power profiles is investigated

some existence results on periodic solutions of ordinary p laplacian systems some existence theorems are obtained for periodic solutions of ordinary p laplacian systems by the minimax methods in critical point theory

some existence uniqueness results for a class of one dimensional nonlinear biot models abstract the wave propagation in a poro elastic medium is generally described by a biot model this model couples the displacement in the solid structure with the fluid pressure and the most complete system involves coupled equations which are mixed hyperbolic parabolic in this paper we are interested in including nonlinearities in the displacement equation we restrict our study to the one dimensional case and we establish existence and uniqueness results in sobolev spaces using galerkin approximants the quasi static case is also investigated the hyperbolic character is then suppressed and we get the well posedness of the system with data less regular than the complete model but we also prove that the complete model may be considered as an approximation of the quasi static model

a coupling of weak galerkin and mixed finite element methods for poroelasticity abstract in this paper we present a coupling of a weak galerkin method for the displacement of the solid phase with a standard mixed finite method for the pressure and velocity of the fluid phase in poroelasticity equation because our method provides a stable element combination for the mixed linear elasticity problem it can avoid the poroelasticity locking mathematically indeed uniform in time error estimates of all the unknowns are obtained for both semidiscrete scheme and fully discrete scheme without assuming that the constrained specific storage coefficient is uniformly positive compared with the method proposed by jeonghun j lee our method can get the arbitrary convergence order by changing degree of the polynomial as for the computational cost we can use the modified weak galerkin method to eliminate the boundary term and reduce the number of unknowns in addition we do not use gronwall inequality in the error analysis finally the numerical experiments verify the theoretical analysis and show the effectiveness to overcome spurious pressure oscillations

mountain pass type periodic solutions for euler lagrange equations in anisotropic orlicz sobolev space abstract using the mountain pass theorem we establish the existence of periodic solution for euler lagrange equation lagrangian consists of kinetic part an anisotropic g function potential part k w and a forcing term we consider two situations g satisfying 2 2 at infinity and globally we give conditions on the growth of the potential near zero for both situations

periodic solutions of second order differential inclusions systems with p laplacian some existence results are obtained for periodic solutions of nonautonomous second order differential inclusions systems with p laplacian

multiphysics discontinuous galerkin method for a poroelasticity model abstract in this paper we develop and analyze a multiphysics discontinuous galerkin method for a poroelasticity model which describes the dynamics of poro elastic materials under an applied mechanical force on the boundary and we prove that the multiphysics discontinuous galerkin method is absolutely stable for all positive mesh size h also we propose a time stepping algorithm which decouples the reformulated poroelasticity model at each time step into two sub problems one of which is a generalized stokes problem for the displacement vector field along with a pseudo pressure and the other is a diffusion problem for the pseudo pressure field and we give the optimal order error estimates in the energy norm finally we give the numerical examples to verify the theoretical results

homoclinic solutions for ordinary p laplacian systems with a coercive potential abstract a result for the existence of homoclinic orbits is obtained for p laplacian systems d d t u t p 2 u t f t u t f t where p 1 u r n f c 1 r r n r is t periodic with respect to t and f r r n is a continuous and bounded function such that f t x f t 0 b x and r f t 1 d t for some b 0 and 1

stabilized finite element method for the transient navier stokes equations based on a pressure gradient projection abstract in this paper we present a stabilized finite element formulation for the transient incompressible navier stokes equations the main idea is to introduce as a new unknown of the problem the projection of the pressure gradient onto the velocity space and to add to the incompresibility equation the difference between the laplacian of the pressure and the divergence of this new vector field this leads to a pressure stabilization effect that allows the use of equal interpolation for both velocities and pressures in the case of the transient equations we consider the possibility of treating the pressure gradient projection either implicitly or explicity in the first case the number of unknowns of the problem is substantially increased with respect to the standard galerkin formulation nevertheless iterative techniques may be used in order to uncouple the calculation of the pressure gradient projection from the rest of unknowns velocity and pressure when this vector field is treated explicitly the increment of computational cost of the stabilized formulation with respect to the galerkin method is very low we provide a stability estimate for the case of the simple backward euler time integration scheme for both the implicit and the explicit treatment of the pressure gradient projection

on stability and convergence of finite element approximations of biot s consolidation problem stability and convergence analysis of finite element approximations of biot s equations governing quasistatic consolidation of saturated porous media are discussed a family of decay functions parametrized by the number of time steps is derived for the fully discrete backward euler galerkin formulation showing that the pore pressure oscillations arising from an unstable approximation of the incompressibility constraint on the initial condition decay in time error estimates holding over the unbounded time domain for both semidiscrete and fully discrete formulations are presented and a post processing technique is employed to improve the pore pressure accuracy

a nonconforming finite element method for the biot s consolidation model in poroelasticity a stable finite element scheme that avoids pressure oscillations for a three field biot s model in poroelasticity is considered the involved variables are the displacements fluid flux darcy velocity and the pore pressure and they are discretized by using the lowest possible approximation order crouzeix raviart finite elements for the displacements lowest order raviart thomas nedelec elements for the darcy velocity and piecewise constant approximation for the pressure mass lumping technique is introduced for the raviart thomas nedelec elements in order to eliminate the darcy velocity and therefore reduce the computational cost we show convergence of the discrete scheme which is implicit in time and use these types of elements in space with and without mass lumping finally numerical experiments illustrate the convergence of the method and show its effectiveness to avoid spurious pressure oscillations when mass lumping for the raviart thomas nedelec elements is used

stabilization of low order mixed finite elements for the stokes equations we present a new family of stabilized methods for the stokes problem the focus of the paper is on the lowest order velocity pressure pairs while not lbb compliant their simplicity and attractive computational properties make these pairs a popular choice in engineering practice our stabilization approach is motivated by terms that characterize the lbb deficiency of the unstable spaces the stabilized methods are defined by using these terms to modify the saddle point lagrangian associated with the stokes equations the new stabilized methods offer a number of attractive computational properties in contrast to other stabilization procedures they are parameter free do not require calculation of higher order derivatives or edge based data structures and always lead to symmetric linear systems furthermore the new methods are unconditionally stable achieve optimal accuracy with respect to solution regularity and have simple and straightforward implementations we present numerical results in two and three dimensions that showcase the excellent stability and accuracy of the new methods

the picard boundary value problem for nonlinear second order vector differential equations the existence of solutions is studied for the picard boundary value problem b x b f b t b x b x 0 b x b a b x b b 0 where b b b a and b f b a b b b r sup n b r sup n rarr b r sup n is a continuous function

a discontinuous galerkin finite element method for swelling model of polymer gels abstract an attractive feature of discontinuous galerkin dg finite element schemes is that this concept offers a unified and versatile discretization platform for various types of partial differential equations the locality of the trial functions not only supports local mesh refinements but also offers a framework for comfortably varying the order of the discretization in this paper we propose and analyze a mixed dg finite element method for a displacement pressure model which describes swelling dynamics of polymer gels under mechanical constraints by introducing a flux variable we first present a reformulation of the governing equations of polymer gels we then approximate the pressure and flux variables by a mixed finite element space and the displacement by dg finite element method existence and uniqueness are proved and error estimates are derived for mixed dg finite element scheme finally numerical experiments are presented to show the performance of the mixed dg approximation of polymer gels

impact of antenna correlation on the capacity of multiantenna channels this paper applies random matrix theory to obtain analytical characterizations of the capacity of correlated multiantenna channels the analysis is not restricted to the popular separable correlation model but rather it embraces a more general representation that subsumes most of the channel models that have been treated in the literature for arbitrary signal to noise ratios snr the characterization is conducted in the regime of large numbers of antennas for the low and high snr regions in turn we uncover compact capacity expansions that are valid for arbitrary numbers of antennas and that shed insight on how antenna correlation impacts the tradeoffs among power bandwidth and rate

multiplicity theorems for periodic systems with a p laplacian like operator abstract in this paper we study the existence of multiple solutions for nonlinear periodic systems with a p laplacian like operator using an abstract local linking result a two solution theorem is obtained in both resonant and nonresonant cases

a reduced order energy stability preserving finite difference iterative scheme based on pod for the allen cahn equation abstract we focus on proposing and analyzing a reduced order finite difference rofd iterative scheme based on a proper orthogonal decomposition pod technique for allen cahn equations with a small perturbation parameter and strong nonlinearity we prove the discrete maximum principle dmp preserving and discrete energy stability des preserving of the rofd iterative solutions under a reasonable restriction on the time step size we also analyze the convergence of the rofd iterative solutions for allen cahn equations numerical tests are presented to verify our proposed rofd method such as error estimates convergence rates dmp preserving and des preserving moreover it is shown that the computing time of rofd iterative schemes with very few unknowns is much less than that of usual finite difference fd iterative schemes

periodic solutions of non autonomous second order systems with γ quasisubadditive potential abstract the existence of periodic solutions to non autonomous second order systems with quasisubadditive potential is proved with classical theorems of variational calculus