stabilized finite element schemes with lbb stable elements for incompressible flows we study stabilized fe approximations of supg type to the incompressible navier stokes problem revisiting the analysis for the linearized model we show that for conforming lbb stable elements the design of the stabilization parameters for many practical flows differs from that commonly suggested in literature and initially designed for the case of equal order approximation then we analyze a reduced supg scheme often used in practice for lbb stable elements to provide the reduced scheme with appropriate stability estimates we introduce a modified lbb condition which is proved for a family of fe approximations the analysis is given for the linearized equations numerical experiments for some linear and nonlinear benchmark problems support the theoretical results

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

on stable representations of bell elements abstract the paper is concerned with the space of c 1 continuous polynomial splines of degree 5 on general triangulations such that the restriction to each triangle corresponds to a bell element it is investigated how the standard construction of bell elements which is based on prescribing values and derivatives up to order two at the vertices of the triangulation can be used to define different bases the most straightforward one is the nodal basis which lacks stability but it is shown that this can be improved by scaling the interpolation data however the prime focus of the paper is on the construction of b spline like bases that depend on the choice of special domain triangles associated with the vertices of the triangulation a b spline like basis consists of functions that are locally supported and form a partition of unity if the triangulation satisfies certain geometric constraints e g is acute and the domain triangles are chosen suitably the basis is also non negative the stability analysis of the derived bases is addressed theoretically as well as numerically the latter with the examples of least square fitting and pde solving

isogeometric collocation methods with generalized b splines we introduce isogeometric collocation methods based on generalized b splines and we analyze their performance through numerical examples for univariate and multivariate scalar and vector valued problems in particular advection diffusion and linear elasticity model problems are addressed the resulting method combines the favorable properties of isogeometric collocation and the geometrical and analytical problem oriented advantages of generalized b splines

geometry independent field approximation cad analysis integration geometrical exactness and adaptivity in isogeometric analysis iga the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain this identity of the geometry and field approximation spaces was put forward in the now classic 2005 paper 20 as a key advantage on the way to the integration of computer aided design cad and subsequent analysis in computer aided engineering cae 20 claims indeed that any change to the geometry of the domain is automatically inherited by the approximation of the field variables without requiring the regeneration of the mesh at each change of the domain geometry yet in finite element versions of iga a parameterization of the interior of the domain must still be constructed since cad only provides information about the boundary the identity of the boundary and field representation decreases the flexibility in which this parameterization can be generated and somewhat constrains the modeling and simulation process because an approximation able to represent the domain geometry accurately need not be adequate to also approximate the field variables accurately in particular when the solution is not smooth we propose here a new paradigm called geometry independent field approximation gift where the spline spaces used for the geometry and the field variables can be chosen and adapted independently while preserving geometric exactness and tight cad integration gift has the following features 1 it is possible to flexibly

a hierarchical approach to adaptive local refinement in isogeometric analysis abstract adaptive local refinement is one of the key issues in isogeometric analysis in this article we present an adaptive local refinement technique for isogeometric analysis based on extensions of hierarchical b splines we investigate the theoretical properties of the spline space to ensure fundamental properties like linear independence and partition of unity furthermore we use concepts well established in finite element analysis to fully integrate hierarchical spline spaces into the isogeometric setting this also allows us to access a posteriori error estimation techniques numerical results for several different examples are given and they turn out to be very promising

a stabilized powell sabin finite element method for the 2d euler equations in supersonic regime in this paper a powell sabin finite element ps fem scheme is presented for the solution of the 2d euler equations in supersonic regime the spatial discretization is based on ps splines that are piecewise quadratic polynomials with a global continuity defined on conforming triangulations some geometrical issues related to the practical construction of the ps elements are discussed in particular the generation of the control triangles and the imposition of the boundary conditions a stabilized formulation is considered and a novel shock capturing technique in the context of continuous finite elements is proposed to reduce oscillations around the discontinuity and compared with the classical technique proposed by tezduyar and senga 2006 the code is verified using manufactured solutions and validated using two challenging numerical examples which allows to evaluate the performance of the ps discretization in capturing the shocks

local discontinuous galerkin numerical solutions of non newtonian incompressible flows modeled by p navier stokes equations we present a local discontinuous galerkin ldg method for solving non newtonian incompressible flow problems the problems are modeled by p type navier stokes equations the extra stress tensor follows a p power rule p ns the aim of this paper is to present an efficient way for discretizing the governing equations by an ldg method choosing both equal and mixed order local polynomial space for velocity and pressure the velocity gradient is introduced as an auxiliary variable and the p ns system is decomposed into a first order system including the projection of the nonlinear stress tensor components to the local discontinuous space every equation resulting from the splitting of the extra stress tensor is discretized under the dg element by element technique in the divergence constraint equation an artificial compressibility term time derivative of the pressure with a small parameter is added and the first order terms are expressed in a divergence form and are discretized by utilizing the lax friedrichs numerical fluxes an upwind wave analysis is applied on the outflow boundary for constructing artificial outflow boundary conditions for the time discretization s stage diagonally implicit runge kutta schemes are applied numerical experiments on problems with known exact solutions are performed for verifying the expected convergence rates of the method benchmark problems are considered in order to check the performance of the method for solving flow problems described by p ns systems

on approximation of non newtonian fluid flow by the finite element method in this paper the problem of numerical approximation of non newtonian fluid flow with free surface is considered namely the flow of fresh concrete is addressed industrial mixtures often behaves like non newtonian fluids exhibiting a yield stress that needs to be overcome for the flow to take place cf r b bird r c armstrong o hassager dynamics of polymeric liquids vol 1 fluid mechanics wiley new york 1987 r p chhabra j f richardson non newtonian flow in the process industries butterworth heinemann london 1999 the main interest is paid to the mathematical formulation of the problem and to discretization with the aid of finite element method the described numerical procedure is applied onto the solution of several problems

surface fitting using convex powell sabin splines abstract convexity conditions for powell sabin splines are derived and an algorithm is presented for fitting a convex powell sabin spline to a set of scattered data part of this algorithm deals with the elimination of as many redundant conditions as possible the powell sabin splines are defined in terms of basis functions b splines with local support making use of their bernstein bezier representation leads to an easy handling of and an efficient calculating with these b splines numerical examples are supplied to illustrate the usefulness of surface fitting by means of convex powell sabin splines

adaptive isogeometric analysis with hierarchical box splines abstract isogeometric analysis is a recently developed framework based on finite element analysis where the simple building blocks in geometry and solution space are replaced by more complex and geometrically oriented compounds box splines are an established tool to model complex geometry and form an intermediate approach between classical tensor product b splines and splines over triangulations local refinement can be achieved by considering hierarchically nested sequences of box spline spaces since box splines do not offer special elements to impose boundary conditions for the numerical solution of partial differential equations pdes we discuss a weak treatment of such boundary conditions along the domain boundary an appropriate domain strip is introduced to enforce the boundary conditions in a weak sense the thickness of the strip is adaptively defined in order to avoid unnecessary computations numerical examples show the optimal convergence rate of box splines and their hierarchical variants for the solution of pdes

some computational aspects of the stability analysis of nonlinear structures abstract the perturbation method and the continuation method are the two most popular techniques for the solution of finite element equations that describe instability phenomena this paper presents a summary of the principles involved and describes some trends in the development of these techniques

nonlinear complementarity problem and galerkin method etude du probleme de complementarite non lineaire dans des espaces de dimensions infinies en utilisant l approximation de galerkin et une generalisation de l hypothese de karamardian on obtient plusieurs resultats d existence pour une forme speciale du probleme ou f x x l x t x l etant un operateur lineaire et t un operateur non lineaire

discontinuous galerkin method for the solution of a transport level set problem the subject of the paper is the numerical analysis of the transport level set problem discretized by the discontinuous galerkin method without the assumption that the first order nonstationary transport equation contains a reaction term which is used in a standard literature we prove error estimates in the l l 2 norm in the case of the space semidiscretization method of lines and in the case of the space time discontinuous galerkin method in the l 2 l 2 norm numerical experiments support the derived error estimates and show that they are not sharp in the case of the space time discontinuous galerkin method

on finite element approximation in the l norm of variational inequalities we are interested in the approximation in thel norm of variational inequalities with non linear operators and somewhat irregular obstacles we show that the order of convergence will be the same as that of the equation associated with the non linear operator if the discrete maximum principle is verified

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

bezier projection a unified approach for local projection and quadrature free refinement and coarsening of nurbs and t splines with particular application to isogeometric design and analysis abstract we introduce bezier projection as an element based local projection methodology for b splines nurbs and t splines this new approach relies on the concept of bezier extraction and an associated operation introduced here spline reconstruction enabling the use of bezier projection in standard finite element codes bezier projection exhibits provably optimal convergence and yields projections that are virtually indistinguishable from global l 2 projection bezier projection is used to develop a unified framework for spline operations including cell subdivision and merging degree elevation and reduction basis roughening and smoothing and spline reparameterization in fact bezier projection provides a quadrature free approach to refinement and coarsening of splines in this sense bezier projection provides the fundamental building block for h p k r adaptivity in isogeometric analysis

optimizing domain parameterization in isogeometric analysis based on powell sabin splines we address the problem of constructing a high quality parameterization of a given planar physical domain defined by means of a finite set of boundary curves we look for a geometry map represented in terms of powell sabin b splines powell sabin splines are c 1 quadratic splines defined on a triangulation and thus the parameter domain can be any polygon the geometry map is generated by the following three step procedure first the shape of the parameter domain and a corresponding triangulation are determined in such a way that its number of corners matches the number of corners of the physical domain second the boundary control points related to the powell sabin b spline representation are chosen so that they parameterize the boundary curve of the physical domain third the remaining inner control points are obtained by solving a nimble optimization problem based on the winslow functional the proposed domain parameterization procedure is illustrated numerically in the context of isogeometric galerkin discretizations based on powell sabin splines it turns out that the flexibility rising from the generality of the parameter domain has a beneficial effect on the quality of the parameterization and also on the accuracy of the computed approximate solution

laminar unsteady flows of bingham fluids a numerical strategy and some benchmark results we propose a numerical method to calculate unsteady flows of bingham fluids without any regularization of the constitutive law the strategy is based on the combination of the characteristic galerkin method to cope with convection and of the fortin glowinsky decomposition coordination method to deal with the non differentiable and non linear terms that derive from the constitutive law for the spatial discretization we use low order finite elements with in particular linear discretization for the velocity and the pressure stabilized by a brezzi pitkaranta perturbation term we illustrate this numerical strategy through two well known problems namely the hydrodynamic benchmark of the lid driven cavity and the natural convection benchmark of the differentially heated cavity for both we assess our numerical scheme against previous publications for newtonian flow or in the creeping flow regime and propose novel results in the case of bingham fluid non creeping flows

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

on c 2 quintic spline functions over triangulations of powell sabin s type abstract given a triangulation of a polygonal domain we find a refinemet of of by choosing t in a neighborhood of the center of the inscribed circle of each triangle of t connecting t to the vertices of the triangle t and connecting t to t if t shares an interior edge with t or to the midpoint e of any boundary edge e of t the resulting triangulation is a triangulation of powell sabin s type we investigate a c 2 quintic spline space s 5 2 whose elements are c 3 only at t s we give a dimension formula for this spline space show how to construct a locally supported basis display an interpolation scheme and prove that this spline space has the full approximation order

a mechanical model for the buckling of unilaterally constrained rectangular plates a mechanical model is described for the problem of buckling of unilaterally constrained finite rectangular plates due to the nature of the imposed constraint on the plate s lateral deflection w solving for the buckling load required the solution of a nonlinear partial differential equation in w while the plates were modeled along the lines of classical plate theory the nonlinearity arose from the fact that the plates were attached to nonlinear elastic foundations exhibiting a deformation sign dependent force displacement relationship this feature was introduced to model the unilateral constraint the influence of different boundary conditions material orthotropy and transverse load distributions was investigated for each case the weak form of the governing differential equation was solved via the galerkin s method investigations of the buckling loads of rectangular plates attached to such foundations and subjected to a uniform inplane stress field showed the validity of this approach for the cases investigated and compared to some previous exact results reported in the literature

parameterization of computational domain in isogeometric analysis methods and comparison parameterization of computational domain plays an important role in isogeometric analysis as mesh generation in finite element analysis in this paper we investigate this problem in the 2d case i e how to parametrize the computational domains by planar b spline surface from the given cad objects four boundary planar b spline curves firstly two kinds of sufficient conditions for injective b spline parameterization are derived with respect to the control points then we show how to find good parameterization of computational domain by solving a constraint optimization problem in which the constraint condition is the injectivity sufficient conditions of planar b spline parametrization and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of planar b spline parameterization by using this method the resulted parameterization has no self intersections and the isoparametric net has good uniformity and orthogonality after introducing a posteriori error estimation for isogeometric analysis we propose r refinement method to optimize the parameterization by repositioning the inner control points such that the estimated error is minimized several examples are tested on isogeometric heat conduction problem to show the effectiveness of the proposed methods and the impact of the parameterization on the quality of the approximation solution comparison examples with known exact solutions are also presented

from nurbs to nurps geometries abstract quadratic powell sabin splines and their rational extension the so called nurps surfaces are an interesting alternative for classical tensor product nurbs in the context of isogeometric analysis because they allow the use of local refinements while retaining a b spline like representation and exact description of conic sections in this paper we present a simple and effective strategy to convert a given planar geometry defined by a quadratic nurbs representation into a nurps representation suitable for the analysis

generalized b splines as a tool in isogeometric analysis the concept of isogeometric analysis has been proposed in 13 where nurbs are considered as basis of the analysis thanks to their ability to construct an exact geometric model in several practical applications and to their popularity in commercial cad systems in this paper we propose an alternative to the rational model presenting an isogeometric analysis approach based on generalized b splines geometric models exactly represented by generalized b splines include those generated by nurbs moreover generalized b splines possess all fundamental properties of algebraic b splines and nurbs including classical refinement processes as h p k refinements finally since generalized b splines are not confined to rational functions they behave completely similar to algebraic b splines with respect to differentiation and integration this seems to be of interest in the treatment of some relevant problems

enhancing isogeometric analysis by a finite element based local refinement strategy abstract while isogeometric analysis has the potential to close the gap between computer aided design and finite element methods the underlying structure of nurbs non uniform rational b splines is a weakness when it comes to local refinement we propose a hybrid method that combines a globally c 1 continuous piecewise polynomial finite element basis with rational nurbs mappings in such a way that an isoparametric setting and exact geometry representation are preserved we define this basis over t meshes with a hierarchical structure that allows locally restricted refinement combined with a state of the art a posteriori error estimator we present an adaptive refinement procedure this concept is successfully demonstrated with the laplace equation advection diffusion problems and linear elasticity problems

stabilization of low order cross grid pkql mixed finite elements abstract in this paper we analyze a low order family of mixed finite element methods for the numerical solution of the stokes problem and a second order elliptic problem in two space dimensions in these schemes the pressure is interpolated on a mesh of rectangular elements while the velocity is approximated on a triangular mesh obtained by dividing each rectangle into four triangles by its diagonals for the lowest order p 1 q 0 a global spurious pressure mode is shown to exist and so this element as p 1 q 1 case analyzed in armentano and blasco 2010 is unstable however following the ideas given in bochev et al 2006 a simple stabilization procedure can be applied when we approximate the solution of the stokes problem such that the new p 1 q 0 and p 1 q 1 methods are unconditionally stable and achieve optimal accuracy with respect to solution regularity with simple and straightforward implementations moreover we analyze the application of our p 1 q 1 element to the mixed formulation of the elliptic problem in this case by introducing the modified mixed weak form proposed in brezzi et al 1993 optimal order of accuracy can be obtained with our stabilized p 1 q 1 elements numerical results are also presented which confirm the existence of the spurious pressure mode for the p 1 q 0 element and the excellent stability and accuracy of the new stabilized methods

approximation of obstacle problems by continuation methods nonlinear variational inequalities associated with obstacle problems are considered which may exhibit multiple solutions and turning points a predictor corrector continuation method for following a solution branch is presented essentially it is shown that regular or simple singular solutions of the nonlinear eigenvalue problem are regular for an augmented problem the main difficulty here is due to the fact that the equations are not differentiable in the frechet sense the numerical schemes that are used in the implementation of the method are developed for the predictor step a deflated block algorithm is used and for the corrector step algorithms are set up using projected sor projected newton and projected preconditioned conjugate gradients the efficiency of the various algorithms is compared by applying the continuation method to a finite element discretization of a two dimensional problem numerical results are presented

multi patch nonsingular isogeometric boundary element analysis in 3d abstract a multi patch nonsingular isogeometric boundary element method igabem for 3d problems is presented that provides accurate solutions for multi patch igabem in order to conveniently implement this method based on the greville abscissae a new collocation method moves the first and the last collocation points of each parametric direction inside of their patches and a simple method for merging equations handles the extra equations the numerical results verify the accuracy and efficiency of the present method by comparing it to the conventional igabem

numerical solution of partial differential equations with powell sabin splines powell sabin splines are piecewise quadratic polynomials with global c 1 continuity they are defined on conforming triangulations of two dimensional domains and admit a compact representation in a normalized b spline basis recently these splines have been used successfully in the area of computer aided geometric design for the modelling and fitting of surfaces in this paper we discuss the applicability of powell sabin splines for the numerical solution of partial differential equations defined on domains with polygonal boundary a galerkin type pde discretization is derived for the variable coefficient diffusion equation special emphasis goes to the treatment of dirichlet and neumann boundary conditions finally an error estimator is developed and an adaptive mesh refinement strategy is proposed we illustrate the effectiveness of the approach by means of some numerical experiments

powell sabin b splines and unstructured standard t splines for the solution of the kirchhoff love plate theory exploiting bezier extraction the equations that govern kirchhoff love plate theory are solved using quadratic powell sabin b splines and unstructured standard t splines bezier extraction is exploited to make the formulation computationally efficient because quadratic powell sabin b splines result in inline image continuous shape functions they are of sufficiently high continuity to capture kirchhoff love plate theory when cast in a weak form unlike non uniform rational b splines nurbs which are commonly used in isogeometric analysis powell sabin b splines do not necessarily capture the geometry exactly however the fact that they are defined on triangles instead of on quadrilaterals increases their flexibility in meshing and can make them competitive with respect to nurbs as no bending strip method for joined nurbs patches is needed this paper further illustrates how unstructured t splines can be modified such that they are inline image continuous around extraordinary points and that the blending functions fulfil the partition of unity property the performance of quadratic nurbs unstructured t splines powell sabin b splines and nurbs to nurps non uniform rational powell sabin b splines which are obtained by a transformation from a nurbs patch is compared in a study of a circular plate

multilevel continuation techniques for nonlinear boundary value problems with parameter dependence a new technique is described to continue along solution branches of parameter dependent nonlinear boundary value problems in order to obtain accurate multigrid solutions at specified points in particular the implementation for a general class of second order equations in divergence form in the program pltmg is described and analyzed this method has proven to be very robust and efficient as is illustrated by several examples

adaptive isogeometric analysis by local h refinement with t splines isogeometric analysis based on non uniform rational b splines nurbs as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space which renders a purely local refinement impossible this paper demonstrates how this difficulty can be overcome by using t splines instead t splines allow the introduction of so called t junctions which are related to hanging nodes in the standard fem obeying a few straightforward rules rectangular patches in the parameter space of the t splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry furthermore it is shown how state of the art a posteriori error estimation techniques can be combined with refinement by t splines numerical examples underline the potential of isogeometric analysis with t splines and give hints for further developments

stable and unstable cross grid pkql mixed finite elements for the stokes problem in this paper we develop and analyze a family of mixed finite element methods for the numerical solution of the stokes problem in two space dimensions in these schemes the pressure is interpolated on a mesh of rectangular elements while the velocity is approximated on a triangular mesh obtained by dividing each rectangle into four triangles by its diagonals continuous interpolations of degrees k for the velocity and l for the pressure are considered so the new finite elements are called cross grid p kq l a stability analysis of these approximations is provided based on the macroelement technique of stenberg the lowest order p 1q 1 and p 2q 1 cases are analyzed in detail in the first case a global spurious pressure mode is shown to exist so this element is unstable in the second case however stability is rigorously proved numerical results obtained in these two cases are also presented which confirm the existence of the spurious pressure mode for the p 1q 1 element and the stability of the p 2q 1 element

finite dimensional approximation for a class of elliptic obstacle problems in this paper we study the finite dimensional approximation for a class of elliptic obstacle problems involving unbounded domains by using the galerkin method the convergence of the approximation is deduced

algorithms for refining triangular grids suitable for adaptive and multigrid techniques two general algorithms for refining triangular computational meshes based on the bisection of triangles by the longest side are presented and discussed the algorithms can be applied globally or locally for selective refinement of any conforming triangulation and always generate a new conforming triangulation after a finite number of interactions even when locally used the algorithms also ensure that all angles in subsequent refined triangulations are greater than or equal to half the smallest angle in the original triangulation the shape regularity of all triangles is maintained and the transition between small and large triangles is smooth in a natural way proofs of the above properties are presented the second algorithm is a simpler improved version of the first which retains most of the properties of the latter the algorithms can be used either for constructing irregular computational meshes or for locally refining any given triangulation in this sense they can be adequately combined with adaptive and or multigrid techniques for solving finite element systems examples of the application of the algorithms are given and two possible generalizations are pointed out

on continuation for variational inequalities while many continuation methods for the numerical solution of nonlinear eigenvalue problems for ordinary and partial differential equations have been proposed and successfully applied little has b

isogeometric analysis with bezier tetrahedra abstract this paper presents an approach for isogeometric analysis of 3d objects using rational bezier tetrahedral elements in this approach both the geometry and the physical field are represented by trivariate splines in bernstein bezier form over the tetrahedrangulation of a 3d geometry given a nurbs represented geometry either untrimmed or trimmed we first convert it to a watertight geometry represented by rational triangular bezier splines rtbs for trimmed geometries a compatible subdivision scheme is developed to guarantee the watertightness the rtbs geometry preserves exactly the original nurbs surfaces except for an interface layer between trimmed surfaces where controlled approximation occurs from the watertight rtbs geometry a bezier tetrahedral partition is generated automatically by imposing continuity constraints on bezier ordinates of the elements we obtain a set of global c r smooth basis functions and use it as the basis for analysis numerical examples demonstrate that our method achieves optimal convergence in c r spaces and can handle complicated geometries

continuity and convergence in rational triangular bezier spline based isogeometric analysis abstract this paper presents a method for isogeometric analysis using rational triangular bezier splines rtbs where optimal convergence rates are achieved in this method both the geometry and the physical field are represented by bivariate splines in bernstein bezier form over the triangulation of a domain from a given physical domain bounded by nurbs curves a parametric domain and its triangulation are constructed by imposing continuity constraints on bezier ordinates we obtain a set of global c r smooth basis functions convergence analysis shows that isogeometric analysis with such c r rtbs basis can deliver the optimal rate of convergence provided that the c r geometric map remains unchanged during the refinement process this condition can be satisfied by constructing a pre refinement geometric map that is sufficiently smooth numerical experiments verify that optimal rates of convergence are achieved for poisson and linear elasticity problems

stabilization of incompressibility and convection through orthogonal sub scales in finite element methods two apparently different forms of dealing with the numerical instability due to the incompressibility constraint of the stokes problem are analyzed in this paper the first of them is the stabilization through the pressure gradient projection which consists of adding a certain least squares form of the difference between the pressure gradient and its l2 projection onto the discrete velocity space in the variational equations of the problem the second is a sub grid scale method whose stabilization effect is very similar to that of the galerkin least squares gls method for the stokes problem it is shown here that the first method can also be recast in the framework of sub grid scale methods with a particular choice for the space of sub scales this leads to a new stabilization procedure whose applicability to stabilize convection is also studied in this paper

numerical simulations of flow through channels with t junction the paper deals with numerical solution of laminar and turbulent flows of newtonian and non newtonian fluids in branched channels with two outlets mathematical model of the flow is based on the reynolds averaged navier stokes equations for the incompressible fluid in the turbulent case the closure of the system of equations is achieved by the explicit algebraic reynolds stress earsm turbulence model generalized non newtonian fluids are described by the power law model the governing equations are solved by cell centered finite volume schemes with the artificial compressibility method dual time scheme is applied for unsteady simulations channels considered in presented calculations are of constant square or circular cross sections numerical results for laminar flow of non newtonian fluid are presented further turbulent flow through channels with perpendicular branch is simulated possible methods for setting the flow rate are discussed and numerical results presented for two flow rates in the branch

isogeometric analysis with powell sabin splines for advection diffusion reaction problems abstract this paper presents the use of powell sabin splines in the context of isogeometric analysis for the numerical solution of advection diffusion reaction equations powell sabin splines are piecewise quadratic c 1 functions defined on a given triangulation with a particular macro structure we discuss the galerkin discretization based on a normalized powell sabin b spline basis we focus on the accurate detection of internal and boundary layers and on local refinements we apply the approach to several test problems and we illustrate its effectiveness by a comparison with classical finite element and recent isogeometric analysis procedures

isogeometric analysis in advection diffusion problems tension splines approximation we present a novel approach within the new paradigm of isogeometric analysis introduced by hughes et al 2005 6 to deal with advection dominated advection diffusion problems the key ingredient is the use of galerkin approximating spaces of functions with high smoothness as in iga based on classical b splines but particularly well suited to describe sharp layers involving very strong gradients