explicit residual based a posteriori error estimation for finite element discretizations of the helmholtz equation computation of the constant and new measures of error estimator quality abstract this paper continues the study of an explicit residual based a posteriori error estimator developed for finite element discretizations of the helmholtz equation in the context of time harmonic exterior acoustics problems in previous papers 1 3 the error estimator was derived and subsequently applied to h adaptive computations of model problems in two dimensions in the present paper a methodology is established for computing error estimates these error estimates are then analyzed in detail the error estimates are made possible by computing the scaling constant which exists in error estimators of this type in our case this constant is difficult to obtain an algorithm for computing the constant is described it is noted that the error indicators used for adaptive computations do not require knowledge of this constant several measures are used to analyze the quality of the error estimates providing a complete description of the error estimator in the context of these problems we compute global effectivity indices and utilize the local element wise effectivity index in computing three additional measures the first of these is the robustness index the others are the modified robustness index and the distribution index which are introduced for the first time it is found that the global effectivity index varies with problem parameters in particular the wave number robustness indices also vary due to the local error definition and wave number values of the distribution index are much better however indicating the suitability of the error estimator in guiding efficient adaptive mesh refinement the analysis of the error estimator is carried out on relatively coarse meshes typical of those used in practical engineering computations

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

a symmetric formulation for computing transient shallow water flows abstract the shallow water equations fall into the category of symmetric advective diffusive systems with source terms these types of equations can be very effectively solved using stabilized methods such as supg and gls a semi discrete finite element method based on these ingredients is presented for the computation of transient shallow water flows special care has been taken in the design of the operators in order to improve the performance for unsteady calculations the solution is advanced in time via a predictor multi corrector algorithm which includes as special cases the second order trapezoidal rule a first order explicit method and a first order implicit method equivalent to the constant in time element of the space time formulation

a grassmann calculus for infinite spin groups the correlation functions of the two dimensional ising model satisfy nonlinear equations both on the lattice discovered by mccoy and wu nucl phys b 180 89 1981 and perk phys lett a1 79 3 1980 and in a continuum limit discovered by wu mccoy tracy and barouch and generalized by sato miwa and jimbo publ rims 14 223 1978 in this paper results are presented for infinite spin groups that extend results of sato miwa and jimbo publ rims 14 223 1978 and lead to normal ordered product formulas for the difference of adjacent ising spin fields these product formulas are shown to lead directly to the lattice difference equations for the correlations and are also a key ingredient in the scaling limit analysis

a variational multiscale method with bubble stabilization for the oseen problem based on two local gauss integrations abstract we present a variational multiscale method for the oseen equation with higher reynolds number based on the mini element discretization the stabilization term only depends on bubble functions and the best algorithmic feature of our method is using two local gauss integrations to replace projection operator without adding any extra storage a priori error estimate is proved and the effectiveness of the method is illustrated through several numerical experiments

enforcement of constraints and maximum principles in the variational multiscale method abstract we present a new theoretical framework for the enforcement of constraints in variational multiscale vms analysis the theory is first presented in an abstract operator format and subsequently specialized for the steady advection diffusion equation the approach borrows heavily from results in constrained and convex optimization an exact expression for the fine scales is derived in terms of variational derivatives of the constraints lagrange multipliers and a fine scale green s function the methodology described enables the development of numerical methods which satisfy predefined attributes a practical and effective procedure for solving the steady advection diffusion equation is presented based on a vms inspired stabilized method weakly enforced dirichlet boundary conditions and enforcement of a maximum principle and conservation constraint

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

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

the universal regular quotient of the chow group of points on projective varieties let x be a projective variety of dimension n de ned over an algebraically closed eld k for x irreducible and non singular matsusaka ma constructed an abelian variety alb x and a morphism a x alb x called the albanese variety and mapping respectively depending on the choice of a base point on x which is universal among the morphisms to abelian varieties see lang la serre se for other constructions over the eld of complex numbers the existence of alb x and a was known before and has a purely hodge theoretic description see igusa i for the hodge theoretic construction incidentally the terminology albanese variety was introduced by a weil for reasons explained in his commentary on the article 1950a of volume i of his collected works see w one of which is that the paper alb of albanese de nes it for a surface as a quotient of the group of 0 cycles of degree 0 modulo an equivalence relation let chn x deg 0 denote the chow group of 0 cycles of degree 0 on x modulo rational equivalence when x is irreducible and non singular a remarkable feature of the albanese morphism a is that it factors through a regular homomorphism u chn x deg 0 alb x that is a homomorphism which when composed with the cycle map c x chn x deg 0 gives an algebraic morphism this follows immediately from the fact that an abelian variety does not contain any rational curve thus one can reformulate matsusaka s theorem as the invent math 135 595 664 1999 doi 10 1007 s002229900890

a two level variational multiscale method for convection dominated convection diffusion equations this paper studies the error in the efficient implementation of and time stepping methods for a variational multiscale method vms for solving convection dominated problems the vms studied uses a fine mesh c0 finite element space xh to approximate the concentration and a coarse mesh discontinuous vector finite element space lh for the large scales of the flux in the two scale discretization our tests show that these choices lead to an efficient vms whose complexity is further reduced if a locally l2 orthogonal basis for lh is used a fully implicit and a semi implicit treatment of the terms which link effects across scales are tested and compared the semi implicit vms was much more efficient the observed global accuracy of the most straightforward vms implementation was much better than the artificial diffusion stabilization and comparable to a streamline diffusion finite element method in our tests

a new stabilized finite element method for the transient navier stokes equations abstract this paper is concerned with the development and analysis of a new stabilized finite element method based on two local gauss integrations for the two dimensional transient navier stokes equations by using the lowest equal order pair of finite elements this new stabilized finite element method has some prominent features parameter free avoiding higher order derivatives or edge based data structures and stabilization being completely local at the element level an optimal error estimate for approximate velocity and pressure is obtained by applying the technique of the galerkin finite element method under certain regularity assumptions on the solution compared with other stabilized methods using the same pair of mixed finite elements for the two dimensional transient navier stokes equations through a series of numerical experiments it is shown that this new stabilized method has better stability and accuracy results

towards connectivity for codimension 2 cycles infinitesimal deformations abstract let x be a smooth projective variety over an algebraically closed field k c of characteristic zero and y x a smooth complete intersection the weak lefschetz theorem states that the natural restriction map h i x c q h i y c q on singular cohomology is an isomorphism for all i dim y the bloch beilinson conjectures on the existence of certain filtrations on chow groups combined with standard conjectures in the theory of motives imply that a similar result should be true for chow groups and more generally for motivic cohomology in this note we prove a consequence of the motivic weak lefschetz conjecture see conjecture 1 2 for codimension 2 cycles

critical scaling for monodromy fields the large scale asymptotics of the correlations for a family of two dimensional lattice field theories is calculated at the critical temperature

a connection between subgrid scale eddy viscosity and mixed methods we consider a new mixed method related to the evss method in computational viscoelasticity for the convection dominated convection diffusion equation in which stabilization is added then removed through the extra mixed variables this consistent stabilization is equivalent to an artificial viscosity operator acting only on the fluctuations in u h by suitable choice of the mixed spaces a method of guermond is recovered exactly we show that for a different natural choice a new method results with global error estimates similar to both guermond s method and the streamline diffusion supg method

murthy s conjecture on 0 cycles we show that the levine weibel chow group of 0 cycles mathrm ch d a of a reduced affine algebra a of dimension d ge 2 over an algebraically closed field is torsion free among several applications it implies an affirmative solution to an old conjecture of murthy in classical k theory

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

a finite element formulation of compressible flows using various sets of independent variables abstract this paper presents a finite element method for the simulation of compressible flows the navier stokes and euler equations are solved in the conservation form using various sets of independent variables a variational formulation is developed based upon a variant of the petrov galerkin method and uses a shock capturing operator an adaptive algorithm based on a particular residual norm is proposed several numerical examples are presented to demonstrate the performances of each set of variables in solving compressible high speed flows

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

an arbitrary lagrangian eulerian finite element method for solving three dimensional free surface flows abstract this paper discusses numerical solution of unsteady three dimensional free surface flows the governing equilibrium equations are written in the framework of the arbitrary lagrangian eulerian kinematic description the corresponding variational formulation is established afterwards since the variational problems are nonlinear with respect to the moving coordinates a second order approximate variational problem is derived after a consistent linearization of the referential motion stability of the discrete formulations is ensured with the help of a new stabilization method a robust preconditioned gmres algorithm is then used to solve the resulting set of nonlinear equations finally the computational algorithms are assessed through numerical studies of various problems a large sloshing flow in a three dimensional reservoir a discharge flow from a reservoir simulation of a liquid vortex produced inside a cylindrical container with a disk rotating at the bottom and a three dimensional practical hydraulic problem

an anisotropic gls stabilized finite element method for incompressible flow problems abstract we consider a stabilized finite element approximation of incompressible flow problems in primitive velocity pressure variables which is based on a gls formulation equal order interpolation for the velocity and the pressure can be employed with this formulation the method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios rather than using a single stabilization parameter within each element the jacobian matrix of the affine transformation from the reference element is employed for stabilization purposes stability and anisotropic error estimates in a suitable mesh dependent norm are proved for the linear stokes problem numerical results confirm the accuracy and robustness of the proposed method compared to similar previous stabilized schemes

a variational multiscale method based on bubble functions for convection dominated convection diffusion equation this work presents a variational multiscale method based on polynomial bubble functions as subgrid scale and a numerical implementation based on two local gauss integrations this method can be implemented easily and efficiently for the convection dominated problem static condensation of the bubbles suggests the stability of the method and we establish its global convergence representative numerical tests are presented

adaptive spacetime discontinuous galerkin method for hyperbolic advection diffusion with a non negativity constraint summary applications where the diffusive and advective time scales are of similar order give rise to advection diffusion phenomena that are inconsistent with the predictions of parabolic fickian diffusion models non fickian diffusion relations can capture these phenomena and remedy the paradox of infinite propagation speeds in fickian models in this work we implement a modified frame invariant form of cattaneo s hyperbolic diffusion relation within a spacetime discontinuous galerkin advection diffusion model an h adaptive spacetime meshing procedure supports an asynchronous patch by patch solution procedure with linear computational complexity in the number of spacetime elements this localized solver enables the selective application of optimization algorithms in only those patches that require inequality constraints to ensure a non negative concentration solution in contrast to some previous methods we do not modify the numerical fluxes to enforce non negative concentrations thus the element wise conservation properties that are intrinsic to discontinuous galerkin models are defined with respect to physically meaningful riemann fluxes on the element boundaries we present numerical examples that demonstrate the effectiveness of the proposed model and we explore the distinct features of hyperbolic advection diffusion response in subcritical and supercritical flows copyright 2015 john wiley sons ltd

duality via cycle complexes we show that bloch s complex of relative zero cycles can be used as a dualizing complex over perfect fields and number rings this leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over algebraically closed fields finite fields local fields of mixed characteristic and rings of integers in number rings generalizing results which so far have only been known for smooth schemes or in low dimensions and unifying the p adic and l adic theory as an application we generalize rojtman s theorem to normal projective schemes

a nonlinear subgrid method for advection diffusion problems abstract this work presents a general framework for approximating advection diffusion equations based on principles of scale separation a two level decomposition of the discrete approximation space is performed and the local problem is modified to capture both local and nonlocal discontinuities the new feature is the local control resulting from decomposing the velocity field into the resolved and unresolved scales and requiring the satisfaction of the discrete model problem at the element level for a minimum kinetic energy associated to the unresolved scales this procedure leads to a nonlinear subgrid model that acts only on the unresolved scales but does not require any tuned up parameter it can be considered a self adaptive method such that the amount of the subgrid viscosity is automatically introduced according to the residual of the resolved scale at element level

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

a space time coupled p version least squares finite element formulation for unsteady fluid dynamics problems this paper presents a p version least squares finite element formulation for unsteady fluid dynamics problems where the effects of space and time are coupled the dimensionless form of the differential equations describing the problem are first cast into a set of first order differential equations by introducing auxiliary variables this permits the use of c element approximation the element properties are derived by utilizing 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 a time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step 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 for non linear problems the non linear algebraic equations resulting from the least squares process are solved using newton s method with a line search this procedure results in a symmetric hessian matrix 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 generality success and superiority of the present formulation procedure is demonstrated by presenting specific formulations and examples for the advection diffusion and burgers equations 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 the work presented in this paper provides the basis for the extension of the space time coupled least squares minimization concept to two and three dimensional unsteady fluid flow

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

a new family of stable elements for nearly incompressible elasticity based on a mixed petrov galerkin finite element formulation adding to the classical hellinger reissner formulation another residual form of the equilibrium equation a new petrov galerkin finite element method is derived it fits within the framework of a mixed finite element method and is proved to be stable for rather general combinations of stress and displacement interpolations including equal order discontinuous stress and continuous displacement interpolations which are unstable within the galerkin approach error estimates are presented using the babuska brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method

streamline upwind petrov galerkin method supg vs residual free bubbles rfb abstract the purpose of this paper is to present the residual free bubbles rfb method and to show its relationship with the streamline upwind petrov galerkin method supg the paper is organized as follows after the introduction we show how the failure of classical finite element methods for convection dominated convection diffusion problem can be explained by energy considerations then we describe the residual free bubbles ideas and in the last section we show the equivalence of rfb and supg in a simple case

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

periodic ising correlations in this paper we first rework b kaufman s 1949 paper phys rev 76 1232 1949 by using representation theory our approach leads to a simpler and more direct way of deriving the spectrum of the transfer matrix for the finite periodic ising model we then determine formulas for the spin correlation functions that depend on the matrix elements of the induced rotation associated with the spin operator in a basis of eigenvectors for the transfer matrix the representation of the spin matrix elements is obtained by considering the spin operator as an intertwining map we exhibit the new elements v and v in the bugrij lisovyy formula phys lett a 319 390 2003 as part of a holomorphic factorization of the periodic and antiperiodic summability kernels on the spectral curve associated with the induced rotation for the transfer matrix

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

zero cycles and k theory on normal surfaces in this paper we prove a formula conjectured by bloch and srinivas s2 which describes the chow group of zero cycles of a normal quasi projective surface x over a field as an inverse limit of relative chow groups of a desingularisation x relative to multiples of the exceptional divisor we then give several applications of this result a relative version of the famous bloch conjecture on 0 cycles the triviality of the chow group of 0 cycles for any 2 dimensional normal graded q algebra analogue of the bloch beilinson conjecture and the analogue of the roitman theorem for torsion 0 cycles in characteristic p 0 for normal varieties including the case of p torsion

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

a fic based stabilized finite element formulation for turbulent flows abstract we present a new stabilized finite element fem formulation for incompressible flows based on the finite increment calculus fic framework onate 1998 in comparison to existing fic approaches for fluids this formulation involves a new term in the momentum equation which introduces non isotropic dissipation in the direction of velocity gradients we also follow a new approach to the derivation of the stabilized mass equation inspired by recent developments for quasi incompressible flows onate et al 2014 the presented fic fem formulation is used to simulate turbulent flows using the dissipation introduced by the method to account for turbulent dissipation in the style of implicit large eddy simulation

a finite element variational multiscale method for the navier stokes equations this paper presents a variational multiscale method vms for the incompressible navier stokes equations which is defined by a large scale space lh for the velocity deformation tensor and a turbulent viscosity nu t the connection of this method to the standard formulation of a vms is explained the conditions on lh under which the vms can be implemented easily and efficiently into an existing finite element code for solving the navier stokes equations are studied numerical tests with the smagorinsky large eddy simulation model for nu t are presented

on the stability of residual free bubbles for convection diffusion problemsand their approximation by a two level finite element method we consider the galerkin finite element method for partial diffferential equations in two dimensions where the finite dimensional space used consists of piecewise isoparametric polynomials enriched with bubble functions writing l for the differential operator we show that for elliptic convection diffusion problems the component of the bubble enrichment that stabilizes the method is essentially equivalent to a petrov galerkin method with an l spline exponentially fitted trial space and piecewise polynomial test space the remaining component of the bubble influences the accuracy of the method a stability inequality recently obtained by brezzi franca and russo for a limiting case of bubbles applied to convection diffusion problems is shown to be slightly weaker than the standard stability inequality that is obtained for the sdfem supg method thereby demonstrating that the bubble approach is in general slightly less stable than the streamline diffusion method when the trial functions are piecewise linear we show that residual free bubbles are as stable as sdfem supg and we extend this stability inequality to include positive mesh peclet numbers in the convection dominated regime approximate computations of the residual free bubbles are performed using a two level finite element method

on the roles of minimization and linearization in least squares finite element models of nonlinear boundary value problems in this paper we examine the roles of minimization and linearization in the least squares finite element formulations of nonlinear boundary values problems the least squares principle is based upon the minimization of the least squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations in the present case we consider l 2 norms since the least squares method is independent of the discretization procedure and the solution scheme the least squares principle suggests that minimization should be performed prior to linearization where linearization is employed in the context of either the picard or newton iterative solution procedures however in the least squares finite element analysis of nonlinear boundary value problems it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations the main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged the assessment is performed mathematically through an examination of the variational setting for the least squares formulation of an abstract nonlinear boundary value problem and also computationally through the numerical simulation of the least squares finite element solutions of both a nonlinear form of the poisson equation and also the incompressible navier stokes equations the assessment suggests that although the least squares principle indicates that minimization should be performed prior to linearization such an approach is often impractical and not necessary

local enhancement of functional evaluation and adjoint error estimation for variational multiscale formulations abstract we develop superconvergent postprocessing techniques and accurate a posteriori error estimators for variational multiscale formulations vms of partial differential equations we show that including vms fine scale information in the quantity of interest qoi approximation can provide a superior rate of convergence including exact recovery for a non trivial class of qois further improved postprocessing is achieved by reinterpreting the standard vms fine scale approximation via a local bubble function projection decomposing the error in this modified qoi evaluation into an element local component which depends only on the stabilization and a non local dual weighted residual component allows us to obtain accurate qoi error estimates this analysis also leads to a new adjoint based expression for the classic stabilization parameter the intrinsic time numerical experiments on challenging boundary layer problems demonstrate the superior convergence of the modified qoi evaluation and the reliability of the adjoint error estimator for various qois we also provide computational confirmation of exact recovery of an average value qoi using our estimator with the canonical hughes 1995 as predicted by our analysis

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

a stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation abstract a stabilized finite element formulation for incompressible viscous flows is derived the starting point are the modified navier stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus fic procedure application of the standard finite element galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields the fic method also provides a natural explanation for the stabilization terms appearing in all equations for both the navier stokes and the simpler stokes equations transient solution schemes with enhanced stabilization properties are also proposed finally a procedure for computing the stabilization parameters is presented

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100