a hierarchical multiscale framework for problems with multiscale source terms this paper presents a hierarchical multiscale framework for problems that involve multiscale source terms an assumption on the additive decomposition of the source function results in consistent decoupling of the fully coupled system and constitutes the new method the structure of this decomposition is investigated and its mathematical implications are delineated this method results in variational embedding of fine scale information that is derived from the fine scale equations in the corresponding coarse scale equations it therefore provides a mathematically consistent way of bridging information between disparate spatial scales in the response function that are induced by multiscale forcing functions

a 3d non newtonian fluid structure interaction model for blood flow in arteries the mathematical modelling and numerical simulation of the human cardiovascular system is playing nowadays an important role in the comprehension of the genesis and development of cardiovascular diseases in this paper we deal with two problems of 3d modelling and simulation in this field which are very often neglected in the literature on the one hand blood flow in arteries is characterized by travelling pressure waves due to the interaction of blood with the vessel wall on the other hand blood exhibits non newtonian properties like shear thinning viscoelasticity and thixotropy the present work is concerned with the coupling of a generalized newtonian fluid accounting for the shear thinning behaviour of blood with an elastic structure describing the vessel wall to capture the pulse wave due to the interaction between blood and the vessel wall we provide an energy estimate for the coupling and compare the numerical results with those obtained with an equivalent fluid structure interaction model using a newtonian fluid

the finite difference streamline diffusion methods for sobolev equations with convection dominated term in this paper we give two finite difference streamline diffusion fdsd schemes for solving linear sobolev equations with convection dominated term stability and optimal error estimates for them are derived in suitable norms

interior penalty variational multiscale method for the incompressible navier stokes equation monitoring artificial dissipation in this paper we apply the interior penalty method analyzed in e burman and m a fernndez numer math 107 2007 no 1 39 77 mr2317827 2008c 65317 to flows at high reynolds number as a possible measure of solution quality we propose to monitor the ratio between the artificial dissipation induced by the numerical method and the computed physical dissipation for smooth flows we prove that for our method the artificial dissipation serves as an a posteriori error estimator and also that it vanishes at an optimal rate in the case of flows with multiscale features we discuss a heuristic approach relating the decay of the artificial dissipation to the decay rate of the power spectrum some numerical results in two space dimensions are presented examining the relation between the numerical dissipation and solution quality

a velocity pressure streamline diffusion finite element method for navier stokes equations a streamline diffusion finite element method is introduced for the time dependent incompressible navier stokes equations in a bounded domain in r squared and r cubed in the case of a flow with a high reynolds number an error estimate is proved and numerical results are given the method is based on a mixed velocity pressure formulation using the same finite element discretization of space time for the velocity and the pressure spaces which consist of piecewise linear functions together with certain least squares modifications of the galerkin variational formulation giving added stability without sacrificing accuracy

on a multiscale approach to the transient stokes problem dynamic subscales and anisotropic space time discretization abstract in this article we analyze some residual based stabilization techniques for the transient stokes problem when considering anisotropic time space discretizations we define an anisotropic time space discretization as a family of time space partitions that does not satisfy the condition h 2 c t with c uniform with respect to h and t standard residual based stabilization techniques are motivated by a multiscale approach approximating the effect of the subscales onto the large scales one of the approximations is to consider the subscales quasi static neglecting their time derivative it is well known that these techniques are unstable for anisotropic time space discretizations we show that the use of dynamic subscales where the subscales time derivatives are not neglected solves the problem and prove optimal convergence and stability results that are valid for anisotropic time space discretizations also the improvements related to the use of orthogonal subscales are addressed

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

orthogonal laurent polynomials and strong moment theory a survey these topics are found in many parts of 20th century mathematics and its applications in mathematical physics chemistry statistics and engineering historically the analytic theory of continued fractions has played a central role in both the origin and the development of the other topics continued fractions are intimately related to pad e approximants and special functions emphasis is given to the development of strong moment theory and orthogonal laurent polynomials and to the related continued fractions quadrature formulas integral transforms and linear functionals by a strong moment problem we mean the following for a given bisequence n n of real numbers does there exist a distribution function such that

convergence analyses of galerkin least squares methods for symmetric advective diffusive forms of the stokes and incompressible navier stokes equations abstract symmetric advective diffusive forms of the stokes and incompressible navier stokes equations are presented the galerkin least squares method for advective diffusive equations is used for both systems and is related to other stabilized methods previously studied the presentation reveals that the convergence analysis for advective diffusive equations as applied before to a linearized form of the compressible navier stokes equations carries over in a straightforward manner to the stokes problem and to a linearized form of the incompressible navier stokes equations

stabilised finite element methods for steady incompressible flow abstract we give a brief overview of frequently used stabilised finite element schemes for steady incompressible flow we derive taylor galerkin schemes for the flow equations and show how supg type and taylor galerkin methods can be interpreted within the same framework

a two fluid spectral element method abstract a spectral element formulation for two fluid flows is presented which uses arbitrary lagrangian eulerian mesh movement with an unstructured mesh the main advantage of this approach is that the spectral elements provide a high order of accuracy while the unstructured mesh allows geometric flexibility the accuracy of this approach is demonstrated for several relatively simple configurations with and without moving interfaces another unique feature of the formulation as compared to previous single fluid spectral element methods is that a fully implicit time advancement scheme is used this is made possible by the development of a spectral multigrid iteration which solves the implicit governing equations in a fixed number of iterations insensitive to both the polynomial degree of the spectral elements and the number of elements in the mesh by using this approach solutions for both stiff unsteady problems and steady state problems can be obtained efficiently

hnn extensions of leibniz algebras abstract in this paper we construct hnn extensions of diassociative algebras and leibniz algebras and prove that every leibniz algebra embeds into any of its hnn extensions we also prove that every leibniz algebra with at most countable dimension embeds into a two generator leibniz algebra

adaptive streamline diffusion finite element methods for stationary convection diffusion problems adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed the underlying discretization scheme is the shock capturing streamline diffusion method the adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed a priori error estimates are used to show that the algorithms are efficient in a certain sense

a new projection based stabilized method for steady convection dominated convection diffusion equations abstract we propose a new projection based stabilized method for the steady convection dominated convection diffusion equations this method directly increases the l 2 stability instead of the h 1 stability which the variational multiscale vms methods do numerical analysis and numerical experiments illustrate and confirm that our new method has effective numerical performances on convection dominated convection diffusion problems

ordered olps and cf nth numerators abstract definitions theorems and examples are established for a general model of laurent polynomial spaces and ordered orthogonal laurent polynomial sequences ordered with respect to ordered bases and orthogonal with respect to inner products l decomposed into transition functional and strong moment functional or more generally sample functional l couplings under this formulation that is shown to subsume those in the existing literature new fundamental results are produced including necessary and sufficient conditions for ordered olps to be sequences of nth numerators of continued fractions in contrast to the classical result concerning nth denominators which is shown to hold only in special cases

some cohomologically rigid solvable leibniz algebras abstract in this paper we describe solvable leibniz algebras whose quotient algebra by one dimensional ideal is a lie algebra with rank equal to the length of the characteristic sequence of its nilpotent radical we prove that such leibniz algebra is unique and centerless also it is proved that the first and the second cohomology groups of the algebra with coefficients in the adjoint representation is trivial

a finite element method for fluid structure interaction with surface waves using a finite calculus formulation abstract a stabilized semi implicit fractional step finite element method fem for solving coupled fluid structure interaction problems involving free surface waves is presented the stabilized governing equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus fic procedure a mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described examples of the efficiency of the stabilized semi implicit algorithm for the analysis of fluid structure interaction problems in totally or partially submerged bodies is presented

a space time coupled p version least squares finite element formulation for unsteady two dimensional navier stokes equations this paper presents a p version least squares finite element formulation for two dimensional unsteady fluid flow described by navier stokes equations where the effects of space and time are coupled the dimensionless form of the navier stokes equations are first cast into a set of first order differential equations by introducing auxiliary variables this permits the use of c0 element approximation the element properties are derived by utilizing the p version approximation functions in both space and time and then minimizing the error functional given by the space time integral of the sum of squares of the errors resulting from the set of first order differential equations this results in a true space time coupled least squares minimization procedure the application of least squares minimization to the set of coupled first order partial differential equations results in finding a solution vector which makes gradient of error functional with respect to a null vector this is accomplished by using newton s method with a line search a time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step equilibrium iterations are carried out for each time step until the error functional and each component of the gradient of the error functional with respect to nodal degrees of freedom are below a certain prespecified tolerance the space time coupled p version approximation functions provide the ability to control truncation error which in turn permits very large time steps what literally requires hundreds of time steps in uncoupled conventional time marching procedures can be accomplished in a single time step using the present space time coupled approach the generality success and superiority of the present formulation procedure is demonstrated by presenting specific numerical examples for transient couette flow and transient lid driven cavity the results are compared with the analytical solutions and those reported in the literature the formulation presented here is ideally suited for space time adaptive procedures the element error functional values provide a mechanism for adaptive h p or hp refinements

on stable equal order finite element formulations for incompressible flow problems in this work we discuss stable equal order finite element formulations for incompressible flow problems based on petrov galerkin methods constructed by adding to the classical galerkin formulation least squares of the governing equations continuous and discontinuous pressure interpolations are considered numerical results are presented reinforcing the numerical analysis

a mixed hybrid dirichlet formulation for wall bounded flow problems including turbulent flow abstract in this study a new method for the weak imposition of dirichlet boundary conditions in convection dominated convection diffusion and wall bounded turbulent flow problems is developed it is based on an embedded dirichlet formulation which utilises an additional discontinuous stress field for imposing boundary conditions values at outflow boundaries may not be sufficiently controllable on underresolved meshes e g when using nitsche s method for weak enforcement of dirichlet boundary conditions hence a consistent modification of an earlier proposed constant parameter embedded dirichlet formulation that allows to regain control if required is introduced a separate treatment of boundary conditions in wall normal and tangential direction is enabled this split is physically motivated and it turns out to be crucial for a successful application of the method on the one hand it allows for including a formulation based on the law of the wall in tangential direction on the other hand a consistent modification derived from theoretical considerations for convection diffusion problems is applied in wall normal direction preventing unphysical penetration of walls numerical results obtained for turbulent channel flow at modest friction reynolds number re 395 employing meshes with and without adequate resolution of the boundary layer are presented superior performance of the proposed method compared to strongly imposed boundary conditions is demonstrated by an error reduction of up to 50 for mean velocity results in the core of the channel on coarse discretisations

local projection stabilization of equal order interpolation applied to the stokes problem the local projection stabilization allows us to circumvent the babuska brezzi condition and to use equal order interpolation for discretizing the stokes problem the projection is usually done in a two level approach by projecting the pressure gradient onto a discontinuous finite element space living on a patch of elements we propose a new local projection stabilization method based on possibly enriched finite element spaces and discontinuous projection spaces defined on the same mesh optimal order of convergence is shown for pairs of approximation and projection spaces satisfying a certain inf sup condition examples are enriched simplicial finite elements and standard quadrilateral hexahedral elements the new approach overcomes the problem of an increasing discretization stencil and thus is simple to implement in existing computer codes numerical tests confirm the theoretical convergence results which are robust with respect to the user chosen stabilization parameter

grad div stabilization and subgrid pressure models for the incompressible navier stokes equations in this paper the grad div stabilization for the incompressible navier stokes finite element approximations is considered from two different viewpoints i as a variational multiscale approach for the pressure subgrid modeling and ii as a stabilization procedure of least square type some new error estimates for the linearized problem with the grad div stabilization are proved with the help of norms induced by the pressure schur complement operator we discuss the stabilization parameter choice arising in the frameworks of least square and multiscale methods and consider assumptions which allow to relate both approaches

fluid structure interactions of a parachute crossing the far wake of an aircraft abstract in this paper we describe a computational technique for simulation of the fluid structure interactions of a parachute crossing the far wake of an aircraft this technique relies on using the long wake flow data already computed in our case with the multi domain method mdm we developed earlier the fluid structure interaction computations are carried out over a domain enclosing the parachute and moving with the payload this domain functions as one of the subdomains of the mdm designed specifically for the parachute fluid structure interactions considered here the boundary conditions for this subdomain are extracted from the long wake flow data at locations corresponding to the positions of those boundaries in the subdomain over which the wake flow data were computed the navier stokes equations of incompressible flows governing the fluid dynamics are solved with the deforming spatial domain stabilized space time dsd sst formulation which can handle changes in the spatial domain occupied by the fluid this formulation is coupled to the finite element formulation used for solving the membrane equations governing the structural mechanics of the parachute canopy and the equations governing the mechanics of the suspension lines the numerical example included demonstrates how the technique described here functioning as a component of the mdm enables us to simulate the fluid structure interactions of a parachute crossing an aircraft wake

continuous interior penalty finite element method for the time dependent navier stokes equations space discretization and convergence this paper focuses on the numerical analysis of a finite element method with stabilization for the unsteady incompressible navier stokes equations incompressibility and convective effects are both stabilized adding an interior penalty term giving l 2 control of the jump of the gradient of the approximate solution over the internal faces using continuous equal order finite elements for both velocities and pressures in a space semi discretized formulation we prove convergence of the approximate solution the error estimates hold irrespective of the reynolds number and hence also for the incompressible euler equations provided the exact solution is smooth

a multiscale finite element method for the incompressible navier stokes equations this paper presents a new multiscale finite element method for the incompressible navier stokes equations the proposed method arises from a decomposition of the velocity field into coarse resolved scales and fine unresolved scales modeling of the unresolved scales corrects the lack of stability of the standard galerkin formulation and yields a method that possesses superior properties like that of the streamline upwind petrov galerkin supg method and the galerkin least squares gls method the multiscale method allows arbitrary combinations of interpolation functions for the velocity and the pressure fields specifically the equal order interpolations that are easy to implement but violate the celebrated babuska brezzi condition a significant feature of the present method is that the structure of the stabilization tensor s appears naturally via the solution of the fine scale problem a family of 2 d elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed convergence studies for the method on uniform skewed as well as composite meshes are presented numerical simulations of the nonlinear steady and transient flow problems are shown that exhibit the good stability and accuracy properties of the method 2005 elsevier b v all rights reserved

possibilities of finite calculus in computational mechanics abstract the expression finite calculus refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes forces etc in a domain of finite size the governing equations resulting from this approach are different from those of infinitessimal calculus theory and they incorporate new terms depending on the dimensions of the balance domain the new modified equations allow to derive naturally stabilized numerical schemes using finite element finite difference finite volume or meshless methods the paper briefly discusses the possibilities of the modified governing equations derived via the finite calculus technique for the numerical solution of convection diffusion problems incompressible flow and incompressible solid mechanic problems and strain localization problems

quadrature on the half line and two point pade approximants to stieltjes functions part i algebraic aspects abstract let f z be a stieltjes function with asymptotic expansions l0 and l at z 0 and z respectively let k n denote the two point pade approximant of type m n which matches k of the coefficients of the series l0 and which takes its remaining interpolation conditions from l we discuss in this paper the algebraic aspects of this problem we shall emphasize the relation between quadrature formulas and two point pade approximants and derive expressions for the error in a subsequent paper we shall consider the convergence aspects of these approximants for example the positivity of the error which is obtained here will result in the monotonic convergence of certain sequences of two point pade approximants a property which is well known in the case of classical pade approximants

a space time galerkin least squares finite element formulation of the navier stokes equations for moving domain problems a space time galerkin least squares finite element formulation of the navier stokes equations is presented for the analysis of free surface flows moving spatial configurations and deforming fluid structure interfaces the variational equation is based on the time discontinuous galerkin method employing the physical entropy variables the space time elements are oriented in time to accommodate the spatial deformations if the elements are oriented along the particle paths the formulation is lagrangian and if they are fixed in time it is eulerian consequently this formulation is analogous to the arbitrary lagrangian eulerian ale technique a novel mesh rezoning strategy is presented to orient the elements in time and adapt the fluid mesh to the changing spatial configuration numerical results are presented to show the performance of the method

time dependent subgrid scales in residual based large eddy simulation of turbulent channel flow the present study investigates the effect of taking into account the time dependency of the fine subgrid scales in a residual based variational multiscale approach for large eddy simulation the residual based variational multiscale method with time dependent dynamic subgrid scales is presented and the impact of the time dependency is studied for the well known test case of turbulent channel flow results are presented from computations for various values of the reynolds number namely ret 180 ret 395 and ret 590 and several time step sizes a generalized a time integration scheme is employed results from our numerical experiments with dynamic subgrid scales are compared to results obtained with an approximation not explicitly taking the time dependency of the subgrid scales into account for all re t values and time step sizes under consideration results for resolved quantities computed by both approaches are very similar this statement applies to both mean streamwise velocity and root mean square velocity fluctuations however it provides a model for the subgrid scales not depend ing on the time step size and enabling a more robust representation of unresolved scales thus we conclude that the time dependent subgrid scale approximation is not capable of producing more accurate results for this type of flow if the time step size is chosen within an optimal range however we expect it to be more advantageous for more complex problems since our results indicate that it provides a more reliable representation of unresolved scales

streamline diffusion finite element method for quasilinear elliptic problems we extend the analysis of the streamline diffusion finite element method to quasilinear elliptic problems of second order an existence theorem and error estimates are given in the case of branches of nonsingular solutions following a recent abstract approach in 12 13 26