a new mixed finite element for the stokes and elasticity problems the stokes problem is approximated by a mixed finite element method using a new finite el ement which has properties analogous to the finite volume methods namely the local conservation of the momentum and the mass estimates of optimal order are derived for the errors in the velocity the pressure and the gradient of the velocity this new finite element also works for the elasticity problem and all estimates are valid uniformly with respect to the compressibility finally some numerical results for the incompressible navier stokes equations are presented

corrections and additions to error recovery for variable length codes by j c maxted and j p robinson an error in the subject article is corrected additionally a method of calculating the standard deviation of the expected span of errors is presented for four example codes the standard deviation of the subject article s reduced model is compared to the standard deviation of the subject article s complete model

a unary error correction code for the near capacity joint source and channel coding of symbol values from an infinite set a novel joint source and channel code jscc is proposed which we refer to as the unary error correction uec code unlike existing jsccs our uec facilitates the practical encoding of symbol values that are selected from a set having an infinite cardinality conventionally these symbols are conveyed using separate source and channel codes ssccs but we demonstrate that the residual redundancy that is retained following source coding results in capacity loss this loss is found to have a value of 1 11 db in a particular practical scenario where quaternary phase shift keying qpsk modulation is employed for transmission over an uncorrelated narrowband rayleigh fading channel by contrast the proposed uec code can eliminate this capacity loss or reduce it to an infinitesimally small value furthermore the uec code has only a moderate complexity facilitating its employment in practical low complexity applications

on some mixed finite element methods with numerical integration in this paper a new family of mixed finite volume methods is analyzed for the approximation of a reaction diffusion problem all the methods are obtained starting from the dual mixed formulation of the problem and then employing the lowest order raviart thomas finite element spaces plus a suitable quadrature formula for the mass matrix this allows for the use of different averages of the inverse diffusion coefficient to enforce the constitutive law for the fluxes at the interelement boundary in a finite volume fashion the soundness of the methods is supported by an error analysis which shows optimal cal o h convergence rate with respect to the standard mixed finite element norm in the case of both smooth and piecewise smooth coefficients numerical results on test problems with both smooth and nonsmooth coefficients support the theoretical estimates

a discontinuous petrov galerkin method with lagrangian multipliers for second order elliptic problems we present a discontinuous petrov galerkin dpg method for the finite element discretization of second order elliptic boundary value problems the novel approach emanates from a one element weak formulation of the differential problem this procedure which is typical of discontinuous galerkin dg methods is based on introducing variables defined in the interior and on the boundary of the element the interface variables are suitable lagrangian multipliers that enforce interelement continuity of the solution and of its normal derivative thus providing the proper connection between neighboring elements the internal variables can be eliminated in favor of the interface variables using static condensation to end up with a system of reduced size in the sole lagrangian multipliers a stability and convergence analysis of the novel formulation is carried out and its connection with mixed hybrid and dg methods is explored numerical tests on several benchmark problems are included to validate the convergence performance and the flux conservation properties of the dpg method

a pde constrained optimization approach to the discontinuous petrov galerkin method with a trust region inexact newton cg solver abstract we propose a partial differential equation constrained pde constrained approach to the discontinuous petrov galerkin dpg of demkowicz and gopalakrishnan 2010 2011 this view opens the door to invite all the state of the art pde constrained techniques to be part of the dpg framework and hence enabling one to solve large scale and difficult nonlinear problems efficiently that is our proposed method preserves all the attractive features of the dpg framework while enjoying all advances from the pde constrained optimization community the proposed approach can be considered as a rayleigh ritz method for the dpg minimum residual statement it is equipped with a trust region inexact newton conjugate gradient trincg method which prevents over solving when optimization iterates are far away from the optimal solution but converges quadratically otherwise for sufficiently smooth residual the pde constrained approach together with the trincg solver is therefore a robust iterative method for the dpg framework it is robust in the sense that the approximate solution is improved after each optimization iterate until the algorithm converges to a local minimum of the residual as numerically shown it is also scalable in the sense that the number of newton iterations remains constant as either the mesh or the solution order is refined moreover the proposed approach solves neither the optimal test functions nor the original pde directly though the discretization of the latter is still necessary the gradient and hessian vector product which are required by the trincg solver are explicitly derived for both abstract variational problems and viscous burger equation this reveals a fact that the complexity of each newton iteration scales like o n n c g where n and n c g are the number of unknowns and the number of conjugate iterations respectively optimal h and p convergences of the proposed approach are demonstrated for laplace and helmholtz equations numerical results for the viscous burger equation and the euler equation of gas dynamics are very promising

the synchronization of variable length codes many variable length codes exhibit a tendency for resynchronization to occur automatically following any error however attempts to identify an underlying synchronization mechanism and to accurately predict the expected synchronization delay for even quite specific variable length codes appear to have been largely unsuccessful the present paper explores a novel method for estimating the synchronization performance for a wide variety of variable length codes based on the t codes t codes are a class of self synchronizing codes which typically synchronize within 2 3 codewords by a mechanism that derives from a recursive t augmentation construction it is observed that the t code mechanism for synchronization is followed more or less by other variable length codes wherever substantial numbers of codewords are shared with a t code set t augmentation itself provides a means for assessing the contribution individual codewords make to the overall synchronization process for a t code set thus codeword differences between sets may be specifically evaluated to estimate the synchronization performance of a variable length code set from a closely related t code set

a multiscale formulation of the discontinuous petrov galerkin method for advective diffusive problems abstract we consider the discontinuous petrov galerkin method for the advection diffusion model problem and we investigate the application of the variational multiscale method to this formulation we show the exact modeling of the fine scale modes at the element level for the linear case and we discuss the approximate modeling both in the linear and in the non linear cases furthermore we highlight the existing link between this multiscale formulation and the p version of the finite element method numerical examples illustrate the behavior of the proposed scheme

the continuous galerkin method is locally conservative we examine the conservation law structure of the continuous galerkin method we employ the scalar advection diffusion equation as a model problem for this purpose but our results are quite general and apply to time dependent nonlinear systems as well in addition to global conservation laws we establish local conservation laws which pertain to subdomains consisting of a union of elements as well as individual elements these results are somewhat surprising and contradict the widely held opinion that the continuous galerkin method is not locally conservative

existence uniqueness and approximation for generalized saddle point problems extensions of the well known results of brezzi on saddle point problems are presented the class of problems is generalized to include the unsymmetric case and the known stability and approximation results are strengthened and applied to the generalized problem an application to the solution of certain exterior interface problems is indicated

the discontinuous petrov galerkin method for elliptic problems abstract we propose a novel discontinuous mixed finite element formulation for the solution of second order elliptic problems fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions the discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that on the one hand enforce the weak continuity of the trial functions and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous galerkin methods static condensation is performed at the element level leading to a solution procedure based on the sole interface unknowns the resulting family of discontinuous dual primal mixed dpm finite element methods is presented in the one and two dimensional cases in the one dimensional case we show the equivalence of the method with implicit runge kutta schemes of the collocation type exhibiting optimal behavior and we develop the stability analysis numerical experiments in one and two dimensions demonstrate the order accuracy of the new method confirming the results of the analysis

error recovery for variable length codes when an error occurs in the encoded bit stream produced by a variable length code the decoder may lose synchronization a state model for synchronization recovery is developed and a method for determining the expected span of source symbols lost is presented the performance of various codes with respect to error recovery is discussed two examples are given where equivalent optimal codes have a marked difference in their error recovery characteristics some open problems are indicated

generalized finite element methods their performance and their relation to mixed methods the notion of a generalized finite element method is introduced this class of methods is analyzed and their relation to mixed methods is discussed the class of generalized finite element methods offers a wide variety of computational procedures from which particular procedures can be selected for particular problems a particular generalized finite element method which is very effective for problems with rough coefficients is discussed in detail

unidirectional covering codes a code c spl sube z sup n sub 2 where z sub 2 0 1 has unidirectional covering radius r if r is the smallest integer so that any word in z sup n sub 2 can be obtained from at least one codeword c spl isin c by replacing either 1s by 0s in at most r coordinates or 0s by 1s in at most r coordinates the minimum cardinality of such a code is denoted by e n r upper bounds on this function are here obtained by constructing codes using tabu search lower bounds on the other hand are mainly obtained by integer programming and exhaustive search best known bounds on e n r for n spl les 13 and r spl les 6 are tabulated

a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime we present a discontinuous galerkin method dgm for the solution of the helmholtz equation in the mid frequency regime our approach is based on the discontinuous enrichment method in which the standard polynomial field is enriched within each finite element by a non conforming field that contains free space solutions of the homogeneous partial differential equation to be solved hence for the helmholtz equation the enrichment field is chosen here as the superposition of plane waves we enforce a weak continuity of these plane waves across the element interfaces by suitable lagrange multipliers preliminary results obtained for two dimensional model problems discretized by uniform meshes reveal that the proposed dgm enables the development of elements that are far more competitive than both the standard linear and the standard quadratic galerkin elements for the discretization of helmholtz problems

covering codes with improved density we prove a general recursive inequality concerning spl mu sup r the asymptotic least density of the best binary covering codes of radius r in particular this inequality implies that spl mu sup r spl les e spl middot rlogr logr loglogr 2 which significantly improves the best known density 2 sup r r sup r r 1 r our inequality also holds for covering codes over arbitrary alphabets

synchronization recovery and state model reduction for soft decoding of variable length codes variable length codes vlcs exhibit loss of synchronization problems when transmitted over noisy channels trellis decoding techniques based on maximum a posteriori map estimators are often used to minimize the error rate on the estimated sequence if the number of symbols and or bits transmitted is known by the decoder termination constraints can be incorporated in the decoding process all the paths in the trellis which do not lead to a valid sequence length are suppressed this correspondence presents an analytic method to assess the expected error resilience of a vlc when trellis decoding with a sequence length constraint is used the approach is based on the computation for a given code of the amount of information brought by the constraint it is then shown that this quantity is not significantly altered by appropriate trellis states aggregation this proves that the performance obtained by running a length constrained viterbi decoder on aggregated state models approaches the one obtained with the bit symbol trellis with a significantly reduced complexity it is then shown that the complexity can be further decreased by projecting the state model on two state models of reduced size

error recovery of variable length code over bsc with arbitrary crossover probability the error recovery capability of variable length code vlc has been considered as an important performance and design criterion in addition to its coding efficiency however almost all of the existing methods for evaluating the error recovery capability of vlc assume that the transmission fault is a random single bit inversion in this paper we consider a more generalized problem of precisely evaluating the error recovery capability of vlc in the case that the encoded bit stream is transmitted over a bsc with arbitrary crossover probability by making use of the perron frobenius theorem we derive a very simple expression for the exact mean error propagation rate mepr and show that the variance of error propagation rate vepr is zero we also prove that in the regime of very low crossover probability the mean error propagation length mepl derived for single inversion error case approaches a scaled value of the mepr furthermore we briefly discuss the problem of evaluating the error detection capability of non exhaustive code over bsc

a family of mixed finite elements for the elasticity problem a new mixed finite element formulation for the equations of linear elasticity is considered in the formulation the variables approximated are the displacement the unsymmetric stress tensor and the rotation the rotation act as a lagrange multiplier introduced in order to enforce the symmetry of the stress tensor based on this formulation a new family of both two and three dimensional mixed methods is defined optimal error estimates which are valid uniformly with respect to the poisson ratio are derived finally a new postprocessing scheme for improving the displacement is introduced and analyzed

application of the mixed hybrid finite element approximation in a groundwater flow model luxury or necessity selected groundwater flow scenarios are used in a two way comparison between the mixed hybrid finite element method and the standard finite element method also called the conforming finite element method the simulations presented are performed in the bidimensional case with a triangular space discretization because of its practical interest for hydrogeologists the basic idea of the mixed procedure is to approximate both the hydraulic potential and the velocity simultaneously and to satisfy an exact water balance for each element by contrast the conforming finite element method calculates the potential field everywhere and then calculates the velocity by differentiation of the potential the conventional approach results in an elementwise constant velocity which can be subject to significant problems because of the normal component discontinuity of the velocity the mixed hybrid finite element method provides velocities everywhere in the field as well as potentials at the center of each element and each edge moreover the normal component of the velocity field is continuous between adjacent elements the results of the simulations are presented in the form of streamlines to avoid the problem of velocity discontinuity the method of cordes and kinzelbach 1992 is used it allows the construction of a continuous velocity field from potentials obtained by the conforming finite element method the comparison studies show that the mixed hybrid finite element is superior to the conforming method in terms of accuracy it is also superior to the conforming method in terms of computational effort the potential fields obtained by the mixed hybrid and the conforming finite element methods are the same

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

generalized inf sup conditions for chebyshev spectral approximation of the stokes problem a mixed problem and its approximation in an abstract framework are considered they are proved to be well posed if and only if several inf sup conditions are satisfied these results are applied to the stokes equations in a square formulated in chebyshev weighted sobolev spaces and their approximations two kinds of spectral discretizations are analyzed a galerkin method and a collocation method at the chebyshev nodes

trellis complexity of short linear codes an extended table of shuurman s bounds on the state complexity of short binary linear codes is presented some new lower and upper bounds are obtained most of the newly found codes are based on the so called double zero tail termination dzt construction

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

two dimensional exponential fitting and applications to drift diffusion models a class of methods is introduced that generalizes the so called exponential fitting method to two dimensional problems and more specifically to equations of the type operatorname div underset raise0 3em hbox smash scriptscriptstyle nabla u u underset raise0 3em hbox smash scriptscriptstyle nabla psi f with psi given and underset raise0 3em hbox smash scriptscriptstyle nabla psi big in a part of the domain the basic idea is the following i write the equation as operatorname div e psi underset raise0 3em hbox smash scriptscriptstyle nabla rho f through the change of variables u rho e psi ii discretize the symmetric equation by means of a method that uses some kind of harmonic average for the coefficient e psi mixed hybrid etc iii write the discrete scheme in terms of the nodal values of u e psi rho this produces an m matrix

hierarchical mixed hybridized methods for elliptic problems abstract in this article we propose a computational procedure for the efficient implementation of dual mixed hybridized methods of arbitrary degree the procedure relies on the decomposition of the finite element spaces into a vertical p type hierarchy consisting of a lower order part and a defect correction coupled with an additional horizontal decomposition of the defect correction space for the vector variable based on the helmholtz principle an appropriate definition of the basis function set allows us to obtain a systematic substructuring of the block matrix system this property in turn naturally gives rise to an efficient implementation of the procedure through an approximate fixed point block iteration exploiting the equivalence between the principle of defect correction and the variational multiscale modeling theory we also devise and numerically validate a hierarchical a posteriori error estimator for dual mixed methods in hybridized form

dual hybrid methods for the elasticity and the stokes problems a unified approach a unified approach to construct finite elements based on a dual hybrid formulation of the linear elasticity problem is given in this formulation the stress tensor is considered but its symmetry is relaxed by a lagrange multiplier which is nothing else than the rotation this construction is linked to the approximations of the stokes problem in the primitive variables and it leads to a new interpretation of known elements and to new finite elements moreover all estimates are valid uniformly with respect to compressibility and apply in the incompressible case which is close to the stokes problem