on stabilized finite element methods for linear systems of convection diffusion reaction equations abstract a stabilized finite element method for solving systems of convection diffusion reaction equations is studied in this paper the method is based on the subgrid scale approach and an algebraic approximation to the subscales after presenting the formulation of the method it is analyzed how it behaves under changes of variables showing that it relies on the law of change of the matrix of stabilization parameters associated to the method an expression for this matrix is proposed for the case of general coupled systems of equations that is an extension of the expression proposed for a one dimensional 1d model problem applications of the stabilization technique to the stokes problem with convection and to the bending of reissner mindlin plates are discussed next the design of the matrix of stabilization parameters is based on the identification of the stability deficiencies of the standard galerkin method applied to these two problems

a natural derivation of discontinuity capturing operator for convection diffusion problems abstract the concept of effective transport velocity is introduced to derive a discontinuity capturing operator for convection diffusion problems the effective transport velocity which depends both on the flow velocity and on the local solution gradient is used to modify the classical representation of the convective term at the continuum level as a result a discontinuity capturing operator arises naturally in the derivation of lax wendroff taylor galerkin and least squares type approximations of the convection diffusion equation the numerical examples presented demonstrate the effectiveness of the proposed approach these include the classical problem of the advection of a steep profile skew to the mesh and the computation of the temperature field in a free convection problem

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

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

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

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

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

on the stabilization parameter in the subgrid scale approximation of scalar convection diffusion reaction equations on distorted meshes abstract in this paper we revisit the definition of the stabilization parameter in the finite element approximation of the convection diffusion reaction equation the starting point is the decomposition of the unknown into its finite element component and a subgrid scale that needs to be approximated in order to incorporate the distortion of the mesh into this approximation we transform the equation for the subgrid scale within each element to the shape regular reference domain the expression for the subgrid scale arises from an approximate fourier analysis and the identification of the wave number direction where instabilities are most likely to occur the final outcome is an expression for the stabilization parameter that accounts for anisotropy and the dominance of either convection or reaction terms in the equation

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

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

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

modeling incompressible flows at low and high reynolds numbers via a finite calculus finite element approach we present a formulation for incompressible flows analysis using the finite element method fem the necessary stabilization for dealing with convective effects and the incompressibility condition is modeled via the finite calculus fic method the stabilization terms introduced by the fic formulation allow to solve a wide range of fluid flow problems for low and high reynolds numbers flows without the need for a turbulence model examples of application of the fic fem formulation to the analysis of 2d and 3d incompressible flows with moderate and large reynolds numbers are presented

the smale conjecture for seifert fibered spaces with hyperbolic base orbifold let m be a closed orientable 3 manifold admitting an mathbb h 2 times mathbb r or widetilde mathrm sl 2 mathbb r geometry or equivalently a seifert fibered space with a hyperbolic base 2 orbifold our main result is that the connected component of the identity map in the diffeomorphism group mathrm diff m is either contractible or homotopy equivalent to s 1 according as the center of pi 1 m is trivial or infinite cyclic apart from the remaining case of non haken infranilmanifolds this completes the homeomorphism classifications of mathrm diff m and of the space of seifert fiberings mathrm sf m for compact orientable aspherical 3 manifolds we also prove that when m has an mathbb h 2 times mathbb r or widetilde mathrm sl 2 mathbb r geometry and the base orbifold has underlying manifold the 2 sphere with three cone points the inclusion mathrm isom m to mathrm diff m is a homotopy equivalence

bubble functions prompt unusual stabilized finite element methods a second order linear scalar differential equation including a zero th order term is approximated using first the standard galerkin method enriched with bubble functions static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations the method is generalized to allow for a convection operator in the equation this work may be employed as a starting point for simulation of nonlinear equations governing turbulence phenomena flows with chemical reactions and other important problems

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

on the convergence of shock capturing streamline diffusion finite element methods for hyperbolic conservation laws we extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the meh size with this term present we prove a maximum norm bound for finite element solutionsof burgers equation an thus complete an earlier convergence proof for this equation we further prove using entropy variables that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality asociated with the entropy variables results of some numerical experiments for the time dependent compressible euler equations in two dimensions are also reported

finite element formulation for convective diffusive problems with sharp gradients using finite calculus abstract a finite element method fem for steady state convective diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary layers is presented the necessary stabilization of the numerical solution is provided by the finite calculus fic approach the fic method is based in the solution by the galerkin fem of a modified set of governing equations which include characteristic length parameters it is shown that the fic balance equation for the multidimensional convection diffusion problem written in the principal curvature axes of the solution introduces an orthotropic diffusion which stabilizes the numerical solution both in smooth regions as well in the vicinity of sharp gradients the dependence of the stabilization terms with the principal curvature directions of the solution makes the method non linear details of the iterative scheme to obtain stabilized results are presented together with examples of application which show the efficiency and accuracy of the approach

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

on an improved unusual stabilized finite element method for theadvective reactive diffusive equation an improved unusual finite element method is studied herein for a second order linear scalar differential equation including a zero order term the method consists in subtracting from the standard galerkin method a mesh dependent term suggested by static condensation of the bubbles based on this idea a new stabilized parameter is constructed which improves accuracy of the solution several numerical tests attest the efficiency of the present method and an error analysis is perfomed

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 stabilized finite point method for analysis of fluid mechanics problems in this paper a meshless procedure termed the finite point method for solving convection diffusion and fluid flow type problems is presented the method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals special emphasis is given to the stabilization of the convective terms and the neumann boundary condition which has been found to be essential to obtain accurate results some examples of application to diffusive and convective transport and compressible flow problems using quadratic fp interpolations are presented

distance enumerator analysis for interleave division multi user codes consider an interleave division multi user coding model for a gaussian multiple access channel mac each user s message is encoded by a separate channel encoder followed by a user interleaver which is employed for user separation all the users codewords are jointly regarded as one multi user codeword and the distance between two multi user codewords is defined as the euclidean distance after the inter user superposition caused by the mac a distance enumerator analysis estimates the multi user maximum likelihood decoding performance by introducing user scramblers a multi user code ensemble is defined and its distance enumerator is calculated as concatenated multiple single user codes and a superposition code both finite length and asymptotic analyses are given and it is shown that interleave division multi user codes have much better distance properties than conventional random direct sequence code division multiple access in fact the codes achieve almost the same asymptotic uniquely decodable performance as a multi user random code