efficient numerical schemes for viscoplastic avalanches part 2 the 2d case abstract this paper deals with the numerical resolution of a shallow water viscoplastic flow model viscoplastic materials are characterized by the existence of a yield stress below a certain critical threshold in the imposed stress there is no deformation and the material behaves like a rigid solid but when that yield value is exceeded the material flows like a fluid in the context of avalanches it means that after going down a slope the material can stop and its free surface has a non trivial shape as opposed to the case of water newtonian fluid the model involves variational inequalities associated with the yield threshold finite volume schemes are used together with duality methods namely augmented lagrangian and bermudez moreno to discretize the problem to be able to accurately simulate the stopping behavior of the avalanche new schemes need to be designed involving the classical notion of well balancing in the present context it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet dry fronts which are encountered in geophysical geometries here we derive such schemes in 2d as the follow up of the companion paper treating the 1d case numerical tests include in particular a generalized 2d benchmark for bingham codes the bingham couette flow with two non zero boundary conditions on the velocity and a simulation of the avalanche path of taconnaz in chamonix mont blanc to show the usability of these schemes on real topographies from digital elevation models dem

finite element solution of the stokes problem with dominating coriolis force abstract the objective of this paper is to present a finite element formulation to solve the stokes problem with coriolis force this force results in a skew symmetric term in the weak formulation of the problem that deteriorates the stability of the standard galerkin finite element method when the viscosity is small we show that the stability is worsened due to the presence of the pressure gradient to enforce the incompressibility of the flow the relevance of this effect depends on the relative importance of the viscous force and the coriolis force which is measured by the ekman number when it is small oscillations occur using the galerkin approach to overcome them we propose two different methods based on a consistent modification of the basic galerkin formulation both methods eliminate the oscillations keeping the accuracy of the formulation and enhancing its numerical stability

an adaptive finite element method for viscoplastic fluid flows in pipes the numerical modelling of the fully developed poiseuille flow of a yield stress fluid in a square section is presented the dead regions in outer corners and the plug region in the center are exhibited numerical computations cover the complete range of the dimensionless number describing the yield stress effect from a newtonian flow to a fully stopped flow the resolution of variational inequalities describing the flow is based on the augmented lagrangian method and a specific mixed finite element method the localization of yield surfaces is approximated by an anisotropic auto adaptive mesh procedure the limit load analysis and the associated limit yield surface are obtained by an extrapolation procedure

quantitative error estimate in modeling the laminar stationary flow of a bingham fluid we present a quantitative a posteriori error estimate when the linear laminar stationary flow of a bingham fluid in a cylindrical pipe is modeled as a newtonian fluid the estimate is proved by using a complementary variational principle for the bingham fluid flow examples show that the estimate is effective

relativistic calogero sutherland model spin generalization quantum affine symmetry and dynamical correlation functions spin generalization of the relativistic calogero sutherland model is constructed by using the affine hecke algebra and shown to possess the quantum affine symmetry the spinless model is exactly diagonalized by means of the macdonald symmetric polynomials the dynamical density density correlation function as well as the one particle green function are evaluated exactly we also investigate the finite size scaling of the model and show that the low energy behaviour is described by the c 1 gaussian theory with a new selection rule the results indicate that the excitations obey the fractional exclusion statistics and also exhibit the tomonaga luttinger liquid behaviour

a generalized auxiliary equation method and its application to the 2 1 dimensional kdv equations abstract in this paper a generalized auxiliary equation method is proposed to construct more general exact solutions of nonlinear partial differential equations as an application of the method the 2 1 dimensional korteweg de vries equations are considered as a result many new and more general non travelling wave and coefficient function solutions are obtained including soliton like solutions trigonometric function solutions exponential solutions and rational solutions

spectral hp least squares finite element formulation for the navier stokes equations we consider the application of least squares finite element models combined with spectral hp methods for the numerical solution of viscous flow problems the paper presents the formulation validation and application of a spectral hp algorithm to the numerical solution of the navier stokes equations governing two and three dimensional stationary incompressible and low speed compressible flows the navier stokes equations are expressed as an equivalent set of first order equations by introducing vorticity or velocity gradients as additional independent variables and the least squares method is used to develop the finite element model high order element expansions are used to construct the discrete model the discrete model thus obtained is linearized by newton s method resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method spectral convergence of the l2 least squares functional and l2 error norms is verified using smooth solutions to the two dimensional stationary poisson and incompressible navier stokes equations numerical results for flow over a backward facing step steady flow past a circular cylinder three dimensional lid driven cavity flow and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation

qualitative and numerical analysis of quasi static problems in elastoplasticity the quasi static problem of elastoplasticity with combined kinematic isotropic hardening is formulated as a time dependent variational inequality vi of the mixed kind that is it is an inequality involving a nondifferentiable functional and is imposed on a subset of a space this vi differs from the standard parabolic vi in that time derivatives of the unknown variable occur in all of its terms the problem is shown to possess a unique solution we consider two types of approximations to the vi corresponding to the quasi static problem of elastoplasticity semidiscrete approximations in which only the spatial domain is discretized by finite elements and fully discrete approximations in which the spatial domain is again discretized by finite elements and the temporal domain is discretized and the time derivative appearing in the vi is approximated in an appropriate way estimates of the errors inherent in the above two types of approximations in suitable sobolev norms are obtained for the quasi static problem of elastoplasticity in particular these estimates express rates of convergence of successive finite element approximations to the solution of the variational inequality in terms of element size h and where appropriate of the time step size k a major difficulty in solving the problems is caused by the presence of the nondifferentiable terms we consider some regularization techniques for overcoming the difficulty besides the usual convergence estimates we also provide a posteriori error estimates which enable us to estimate the error by using only the solution of a regularized problem

on an elastic plastic problem etude d un probleme elastoplastique de valeur limite quasi statique pour des corps pouvant etre discretement heterogenes et elastiquement anisotropes dont le comportement plastique est regi par des fonctions de deformation lineaires par morceaux dependantes de l histoire du materiau et par des lois de durcissement couplees existence unicite et regularite d une solution faible convergence des solutions d elements finis

topology optimization of incompressible media using mixed finite elements abstract we present an alternative formulation for the topology optimization of structures made of incompressible materials a topic that cannot be tackled using most of the approaches of the current literature that are mainly based on displacement finite elements that are well known to be affected by the locking phenomenon a way out of the problem has recently been proposed in sigmund and clausen 2007 o sigmund p m clausen topology optimization using a mixed formulation an alternative way to solve pressure load problems comput methods appl mech engrg 196 13 16 2007 1874 1889 based on a displacement pressure finite element discretization the approach presented here consists in a truly mixed variational formulation coupled to a mixed fem discretization that uses the composite element of johnson and mercier for the discretization of the stress field by so doing the continuous and discrete inf sup conditions of the problem are automatically met even in the presence of incompressible materials a few numerical studies are presented to validate the theoretical framework for which the well known method of moving asymptotes mma is adopted for the numerical optimization of the problem different topologies in plane stress and plane strain conditions are presented with particular attention to the convergence of the last ones to pure 0 1 designs some forthcoming investigations are eventually highlighted including the solution of stress constrained topology optimization problems that find in the truly mixed setting their natural environment and the extension of the present formulation to deal with pressure load structural problems

characteristic stabilized finite element method for the transient navier stokes equations abstract based on the lowest equal order conforming finite element subspace xh mh i e p1 p1 or q1 q1 elements a characteristic stabilized finite element method for transient navier stokes problem is proposed the proposed method has a number of attractive computational properties parameter free avoiding higher order derivatives or edge based data structures and averting the difficulties caused by trilinear terms existence uniqueness and error estimates of the approximate solution are proved by applying the technique of characteristic finite element method finally a serious of numerical experiments are given to show that this method is highly efficient for transient navier stokes problem

an augmented lagrangian approach to bingham fluid flows in a lid driven square cavity with piecewise linear equal order finite elements abstract we study an augmented lagrangian approach to bingham fluid flows in a lid driven square cavity the piecewise linear equal order finite element spaces for both the velocity and the pressure approximations proposed and analyzed by latche and vola 18 are applied based on the resulting regularity of the numerical solutions a mesh adaptive strategy is proposed to render the yield surfaces of desired resolution the corresponding numerical scheme is formulated for general herschel bulkley models and its validity is verified on the benchmark model bingham fluid flows in a lid driven square cavity

analysis of the brezzi pitkaranta stabilized galerkin scheme for creeping flows of bingham fluids in this paper we propose and analyze a finite element scheme for a class of variational nonlinear and nondifferentiable mixed inequalities including balance equations governing incompressible creeping flows of bingham fluids for numerical efficiency reasons equal order piecewise linear approximations are used for both velocity and pressure and the numerical scheme is stabilized by a brezzi pitkaranta perturbation term we obtain error estimates of the same order as for stable discretizations namely h1 2 for velocity and pressure solutions in htwod and hun respectively a decomposition coordination algorithm to solve the discrete nonlinear algebraic system is presented together with its convergence properties finally numerical tests are performed the solution of the problem under consideration presents particular regularity properties that are shown to permit convergence order improvement to h log h 1 2 this estimate is confirmed by numerical results

the decomposition of level 1 irreducible highest weight modules with respect to the level 0 actions of the quantum affine algebra the level 1 irreducible highest weight modules of the quantum affine algebra uq bn are decomposed into irreducible components with respect to the level 0 u 0 q bn action previously defined in 13 the components of the decomposition are found to be the so called tame representations of u 0 q bn parametrized by the skew young diagrams of the border strip type this result verifies a recent conjecture due to kirillov et al

variational principles and convergence of finite element approximations of a holonomic elastic plastic problem it is shown that a boundary value problem based on a holonomic elastic plastic constitutive law may be formulated equivalently as a variational inequality of the second kind a regularised form of the problem is analysed and finite element approximations are considered it is shown that solutions based on finite element approximation of the regularised problem converge

error analysis of some finite element methods for the stokes problem we prove the optimal order of convergence for some two dimensional finite element methods for the stokes equations first we consider methods of the taylor hood type the triangular p3 p2 element and the qk qk 1 i k 2 family of quadrilateral elements then we introduce two new low order methods with piecewise constant approximations for the pressure the analysis is performed using our macroelement technique which is reviewed in a slightly altered form

exp function method exactly solving a kdv equation with forcing term in this paper the exp function method is used to construct generalized solitonary solutions and periodic solutions of a kdv equation with forcing term it is shown that the exp function method with the help of symbolic computation provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations with forcing term in mathematical physics

a new fixed point algorithm for hardening plasticity based on non linear mixed variational inequalities moving from the seminal papers of han and reddy we propose a fixed point algorithm for the solution of hardening plasticity two dimensional problems the continuous problem may be classified as a mixed non linear non differentiable variational inequality of the second type and is discretized by means of a truly mixed finite element scheme one of the main peculiarities of our approach is the use of the composite triangular element of johnson and mercier for the approximation of the stress field the non differentiability is coped with via regularization whereas the non linearity is approached with a fixed point iterative strategy numerical results are proposed that investigate the sensitivity of the approach with respect to the mesh size and the regularization parameter e the simplicity of the proposed fixed point scheme with respect to more classical return mapping approaches seems to represent one of the key features of our algorithm copyright 2003 john wiley sons ltd

a taxonomy of consistently stabilized finite element methods for the stokes problem stabilized mixed methods can circumvent the restrictive inf sup condition without introducing penalty errors for properly chosen stabilization parameters these methods are well posed for all conforming velocity pressure pairs however their variational forms have widely varying properties first stabilization offers a choice between weakly or strongly coercive bilinear forms that give rise to linear systems with identical solutions but very different matrix properties second coercivity may be conditional upon a proper choice of a stabilizing parameter here we focus on how these two aspects of stabilized methods affect their accuracy and efficient iterative solution we present results that indicate a preference of krylov subspace solvers for strongly coercive formulations stability criteria obtained by finite element and algebraic analyses are compared with numerical experiments while for two popular classes of stabilized methods sufficient stability bounds correlate well with numerical stability our experiments indicate the intriguing possibility that the pressure stabilized galerkin method is unconditionally stable

breather type multi solitary waves to the kadomtsev petviashvili equation with positive dispersion abstract in this work kp equation with positive dispersion is studied by virtue of hirota bilinear method and generalized three wave type of ansatz approach we obtain the breather type multi solitary waves with fission and fusion behaviors of kp equation based on the structures of those 2 1 dimensional solutions and show via computer simulation the fission and fusion interactions characteristics of breather type multi solitary waves solutions are discussed which might provide us with the useful information on the dynamics of the relevant physical fields

advances in the simulation of viscoplastic fluid flows using interior point methods abstract we present a primal dual interior point algorithm for the resolution of steady state viscoplastic fluid flows formulated as a conic optimization problem we give a complete description of the algorithm including some advanced aspects such as a predictor corrector and scaling scheme to improve its efficiency our interior point approach is shown to be largely more efficient than augmented lagrangian al approaches which are traditionally used to solve such problems in particular the interior point approach is roughly 5 times faster than the modern accelerated version of al algorithms the yield surfaces are shown to be accurately predicted and various examples ranging from channel flows to three dimensional flows through a porous medium demonstrate its efficiency

an adaptive finite element method for bingham fluid flows around a cylinder the numerical modeling of the steady flow of a yield stress fluid around a cylinder is presented three categories of yielded regions are exhibited the asymptotic behavior when the cylinder gets close to the wall is investigated the resolution of variational inequalities describing the flow is based on the augmented lagrangian method and a mixed finite element method the localization of yield surfaces is approximated by an anisotropic auto adaptive mesh procedure

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

constrained anisotropic elastic materials in unilateral contact with or without friction we consider time independent problems of linear homogeneous anisotropic elasticiy for materials with internal constraints that are in frictional or frictionless contact with a rigid support

level 0 structure of level 1 uq sl2 modules and macdonald polynomials the level 1 integrable highest weight modules of uq sl2 admit a level 0 action of the same algebra this action is defined using the affine hecke algebra and the basis of the level 1 module generated by components of vertex operators each level 1 module is a direct sum of finite dimensional irreducible level 0 modules whose highest weight vector is expressed in terms of macdonald polynomials this decomposition leads to the fermionic character formula for the level 1 modules

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

breather wave solutions for the generalized shallow water wave equation with variable coefficients in the atmosphere rivers lakes and oceans abstract herein a 3 1 dimensional generalized shallow water wave equation with variable coefficients is studied which describes the flow below a pressure surface in a fluid abundant breather wave solutions are constructed via the hirota bilinear form and a novel test function velocity amplitude and shape changes of the breather wave solutions are shown in some 3d graphs and contour plots by selecting different values of the variable coefficients the novel test function is very effective for obtaining the breather wave solutions of the variable coefficient nonlinear partial differential equations

exact three wave solution for higher dimensional kdv type equation a new periodic type of three wave solutions including periodic two solitary solution doubly periodic solitary solution and breather type of two solitary solution for the 1 2 dimensional and 1 3 dimensional kdv type equations are obtained using hirota s bilinear form and generalized three wave type of ansatz approach

cfd shape optimization using an incomplete gradient adjoint formulation a design methodology based on the adjoint approach for flow problems governed by the incompressible euler equations is presented the main feature of the algorithm is that it avoids solving the adjoint equations which saves an important amount of cpu time furthermore the methodology is general in the sense it does not depend on the geometry representation all the grid points on the surface to be optimized can be chosen as design parameters in addition the methodology can be applied to any type of mesh the partial derivatives of the flow equations with respect to the design parameters are computed by finite differences in this way this computation is independent of the numerical scheme employed to obtain the flow solution once the design parameters have been updated the new solid surface is obtained with a pseudo shell approach in such a way that local singularities which can degrade or inhibit the convergence to the optimal solution are avoided some 2d and 3d numerical examples are shown to demonstrate the proposed methodology copyright 2001 john wiley sons ltd

a prange hellinger reissner type finite element formulation for small strain elasto plasticity abstract in this contribution we propose a mixed variational formulation of the prange hellinger reissner type for elasto plasticity at small strains here the displacements and the stresses are interpolated independently which are balanced within the variational functional by the relation of the elastic strains and the partial derivative of the complementary stored energy with respect to the stresses for the elasto plastic material behavior a von mises yield criterion is considered where we restrict ourselves w l o g to linear isotropic hardening in the proposed formulation we enforce the constraints arising from plasticity point wise in contrast to the element wise realization of the plastic return mapping algorithm suggested in simo et al 1989 the performance of the new formulation is demonstrated by the analysis of several benchmark problems here we compare the point wise treatment of elasto plasticity with the original element wise formulation of simo et al 1989 furthermore we derive an algorithmic consistent treatment for plane stress as well as for plane strain condition

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

a family of higher order mixed finite element methods for plane elasticity the dirichler problem for the equations of plane elasticity is approximated by a mixed finite element method using a new family of composite finite elements having properties analogous to those possessed by the raviart thomas mixed finite elements for a scalar second order elliptic equation estimates of optimal order and minimal regularity are derived for the errors in the displacement vector and the stress tensor inl 2 and optimal order negative norm estimates are obtained inh s for a range ofs depending on the index of the finite element space an optimal order estimate inl for the displacement error is given also a quasioptimal estimate is derived in an appropriate space all estimates are valid uniformly with respect to the compressibility and apply in the incompressible case the formulation of the elements is presented in detail

error analysis of some galerkin least squares methods for the elasticity equations the recent technique of stabilizing mixed finite element methods by augmenting the galerkin formulation with least squares terms calculated separately on each element is considered the error analysis is performed in a unified manner yielding improved results for some methods introduced earlier in addition a new formulation is introduced and analyzed method is used within two different contexts the first is in connection with the plain strain or three dimensional problems near the incompressible limit for which the poisson ratio equals one half it is well known that for these problems a standard lower order displacement finite element method will break down by now it is also well known how a working method can be obtained a new unknown the pressure is introduced and discretized with a finite element space different from that used for the displacements the finite element method obtained falls into the class of saddlepoint problems for which there is a general theory developed by brezzi and babuska 5 7 the application of this theory shows that the method converges optimally if the discrete spaces for the displacement and pressure satisfy a stability condition for a particular choice of displacement and pressure approximations it can be a difficult task to verify this babuska brezzi or inf sup condition during the last decade this problem has been intensively studied and the performances of many combinations are now known cf 18 and 23 26 for some recent extensions in addition there exists a general technique utilizing bubble functions by which a stable method can

applications of hta and ehta to ytsf equation new approaches homoclinic test approach hta and extended homoclinic test approach ehta are proposed to seek solitary wave solution of high dimensional nonlinear wave system exact periodic solitary wave periodic soliton cross solitary wave and doubly periodic wave solutions for ytsf equation are obtained using hta and ehta respectively

modeling cohesive crack growth via a truly mixed formulation an alternative approach for cohesive crack growth in elastic media is proposed standard methods move from displacement based formulations that are enriched to handle discontinuities in the inherently continuous displacement field the herein adopted formulation is conversely based on a truly mixed discretization that has stresses as main regular variables while discontinuous displacements play the role of lagrangian multipliers the approach directly handles the analysis of propagating cohesive cracks in elastic media through the appropriate inclusion of interface energy terms that enrich the formulation when a crack is growing notably no edge element is introduced but simply the inherent discontinuity of the displacement field is taken advantage of furthermore the continuity of traction vectors is imposed in an exact fashion within the formulation and not as an additional weak constraint as classically done the work has the main aim of investigating the features of the approach through numerical simulations that refer to well known experimental results on concrete specimens the capability of modeling size effect is firstly tested in case of a pure mode i growth the accuracy of truly mixed stress interpolation is also exploited to recover crack path and to handle energy dissipation in mixed mode simulations

the variational formulation and solution of problems of finite strain elastoplasticity based on the use of a dissipation function the solution of initial boundary value problems involving finite elastoplastic deformations is discussed the formulation considered differs from conventional formulations in that the evolution law is expressed in terms of the dissipation function a generalized midpoint rule is used to obtain an incremental problem a variational form of which is derived the finite element method is used for spatial discretization and an algorithm to solve the resulting discrete problem is developed this algorithm has the predictor corrector structure common to most solution procedures for problems in plasticity methods for imposing the plastic incompressibility constraint are investigated solutions to two axisymmetric examples obtained using the proposed algorithm are presented and compared with those obtained by other authors

on the finite element method for mixed variational inequalities arising in elastoplasticity we analyze the finite element method for a class of mixed variational inequalities of the second kind which arises in elastoplastic problems an abstract variational inequality of which the elast

transient adaptivity applied to two phase incompressible flows an anisotropic adaptation process is applied to a three dimensional incompressible two phase flow solver the solver uses a level set finite element method on unstructured tetrahedral meshes we show how the level set function can be used to build an anisotropic mesh with good properties some computations with a strong transient character and large densities ratios 1 1000 are presented we show that the efficiency of the computations can be deeply enhanced by mesh adaptations

stabilized finite element methods for the generalized oseen problem the numerical solution of the non stationary incompressible navierstokes model can be split into linearized auxiliary problems of oseen type we present in a unique way different stabilization techniques of finite element schemes on isotropic meshes first we describe the state of the art for the classical residual based supg pspg method then we discuss recent symmetric stabilization techniques which avoid some drawbacks of the classical method these methods are closely related to the concept of variational multiscale methods which seems to provide a new approach to large eddy simulation finally we give a critical comparison of these methods

analysis and finite element approximation of compressible and incompressible linear isotropic elasticity based upon a variational principle abstract we propose a variational principle for compressible and incompressible linear isotropic elasticity involving four dependent variables the strain tensor the augmented stress tensor pressure and displacement the variational formulation derived from the principle is analyzed employing a general result due to brezzi finite element methods using the galerkin and sbb methods are shown to converge for a wide family of finite element interpolations

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

on the construction of optimal mixed finite element methods for the linear elasticity problem the mixed finite element method for the linear elasticity problem is considered we propose a systematic way of designing methods with optimal convergence rates for both the stress tensor and the displacement the ideas are applied in some examples

analysis of some mixed finite element methods for plane elasticity equations we analyze some mixed finite element methods based on rectangular elements for solving the two dimensional elasticity equations we prove error estimates for a method proposed by taylor and zienkiewicz and for some new variants of the known equilibrium methods a numerical example is given demonstrating the performance of the various algorithms considered 1 introduction in the numerical solution of problems of continuum mechanics the stresses are normally of primary interest in the elastic region it is therefore natural to design the numerical algorithms so that the stresses can be obtained directly without first computing the displacements such methods can be derived from the dual variational formulation of the elasticity problem the corresponding finite element algorithms are usually formulated as mixed methods where both the displacements and the stresses are first approximated and the displacements are then eliminated from the discrete equations in many cases the elimination can be rather effectively done using penalty perturbation techniques or their iterative variants cf 3 11 12 the best known finite element methods of the above type are the so called equilibrium methods first proposed by fraejis de veubeke 17 cf also 14 16 18 and analyzed theoretically by johnson and mercier 9 cf also 8 in these methods one uses specific composite elements which allow the equilibrium condi tion between the stresses and the volume load to be satisfied exactly in the case where the volume load is zero

anisotropic adaptive simulation of transient flows using discontinuous galerkin methods an anisotropic adaptive analysis procedure based on a discontinuous galerkin finite element discretization and local mesh modification of simplex elements is presented the procedure is applied to transient two and three dimensional problems governed by euler s equation a smoothness indicator is used to isolate jump features where an aligned mesh metric field in specified the mesh metric field in smooth portions of the domain is controlled by a hessian matrix constructed using a variational procedure to calculate the second derivatives the transient examples included demonstrate the ability of the mesh modification procedures to effectively track evolving interacting features of general shape as they move through a domain copyright c 2004 john wiley sons ltd

a class of generalized mixed variational hemivariational inequalities i existence and uniqueness results abstract we investigate a generalized lagrange multiplier system in a banach space called a mixed variational hemivariational inequality mvhvi for short which contains a hemivariational inequality and a variational inequality first we employ the minty technique and a monotonicity argument to establish an equivalence theorem which provides three different equivalent formulations of the inequality problem without compactness for one of operators in the problem a general existence theorem for mvhvi is proved by using the fan knaster kuratowski mazurkiewicz principle combined with methods of nonsmooth analysis furthermore we demonstrate several crucial properties of the solution set to mvhvi which include boundedness convexity weak closedness and continuity finally a uniqueness result with respect to the first component of the solution for the inequality problem is proved by using the ladyzhenskaya babuska brezzi lbb condition all results are obtained in a general functional framework in reflexive banach spaces

finite element analysis of a holonomic elastic plastic problem a thorough analysis of the finite element method is given for a holonomic elastic plastic problem an inequality of the cea s lemma type is proved which is the basis of error estimates for various finite element solutions difficulty caused by a non differentiable term in the problem can be overcome by using two convergent procedures an iterative procedure and a regularization procedure an a posteriori quantitative error estimate is derived for the regularized solution

isomorphism of two realizations of quantum affine algebra u_q widehat mathfrak g mathfrak l text n text we establish an explicit isomorphism between two realizations of the quantum affine algebra u q widehat mathfrak g mathfrak l text n text given previously by drinfeld and reshetikhin semenov tian shansky our result can be considered as an affine version of the isomorphism between the drinfield jimbo and the faddeev reshetikhin takhtajan constructions of the quantum algebra u q mathfrak g mathfrak l n

yang baxter equation in long range interacting systems we consider the su p spin chains with long range interactions and the spin generalization of the calogero sutherland models we show that their properties derive from a transfer matrix obeying the yang baxter equation we obtain the expression of the conserved quantities of the dynamical models and we diagonalise them in the spin chain case we establish the connection between the degeneracies of the spectrum and the representation theory of the yangians we use a correspondence with the dynamical models to diagonalise the hamiltonian finally we extend the previous results to the case of a trigonometric r matrix

a new locking free equilibrium mixed element for plane elasticity with continuous displacement interpolation with reference to plane elastic problems we first show that using the johnson and mercier jm element c johnson b mercier numer math 30 1978 103 for the stresses and an h 1 piecewise linear interpolation for the displacements leads to a severe locking when the lamcoefficient k tends to infinity i e in the case of an incompressible material motivated by the need to have a continuous displacement field that emerges in several engineering applica tions we use an eigenvalue argument to prove that locking is due to the presence of the element average pressure among the degrees of freedom we therefore relax the incompressibility constraint by introducing a quadrilateral macroelement basically consisting of two adjacent jm triangles sharing the same average pressure in a sense switching from a locking t1p0 approximation to a locking free q1p0 numerical tests on the pathological cook cantilever are performed to assess the validity of the proposed approach in which comparisons between the newly devised element and the original jm element with l 2 displacements are presented 2001 published by elsevier science b v

the breather type and periodic type soliton solutions for the 2 1 dimensional breaking soliton equation exact breather type and periodic type soliton solutions including the double breather type soliton solutions the breather type periodic soliton solutions and breather type two soliton solutions and the periodic type two soliton and three soliton solutions for the 2 1 dimensional breaking soliton equation are obtained using the extended three wave method etm the results show that the etm may provide us with a straightforward and effective mathematical tool for seeking multi wave solutions of higher dimensional nonlinear evolution equations

new multi soliton solutions of a 3 1 dimensional nonlinear evolution equation in this paper applying homoclinic test approach to a 3 1 dimensional nonlinear evolution equation new kink breather soliton solutions are obtained in addition some new multi soliton solutions are obtained via three wave method it is shown that the homoclinic test approach and the three wave method can be used for constructing multi soliton solutions of nonlinear evolution equations in mathematical physics

efficient numerical computations of yield stress fluid flows using second order cone programming abstract this work addresses the numerical computation of the two dimensional flow of yield stress fluids with bingham and herschel bulkley models based on a variational approach and a finite element discretization the main goal of this paper is to propose an alternative optimization method to existing procedures such as penalization and augmented lagrangian techniques it is shown that the minimum principle for bingham and herschel bulkley yield stress fluid steady flows can indeed be formulated as a second order cone programming socp problem for which very efficient primal dual interior point solvers are available in particular the formulation does not require any regularization of the visco plastic model as is usually the case for existing techniques avoiding therefore the difficult choice of the regularization parameter besides it is also unnecessary to adopt a mixed stress velocity approach or discretize explicitly auxiliary variables as frequently proposed in existing methods finally the performance of dedicated socp solvers like the mosek software package enables us to solve large scale problems on a personal computer within seconds only the proposed method will be validated on classical benchmark examples and used to simulate the flow generated around a plate during its withdrawal from a bath of yield stress fluid

semi discrete stabilized finite element methods for navier stokes equations with nonlinear slip boundary conditions based on regularization procedure based on the pressure projection stabilized methods the semi discrete finite element approximation to the time dependent navier stokes equations with nonlinear slip boundary conditions is considered in this paper because this class of boundary condition includes the subdifferential property then the variational formulation is the navier stokes type variational inequality problem using the regularization procedure we obtain a regularized problem and give the error estimate between the solutions of the variational inequality problem and the regularized problem with respect to the regularized parameter varepsilon which means that the solution of the regularized problem converges to the solution of the navier stokes type variational inequality problem as the parameter varepsilon longrightarrow 0 moreover some regularized estimates about the solution of the regularized problem are also derived under some assumptions about the physical data the pressure projection stabilized finite element methods are used to the regularized problem and some optimal error estimates of the finite element approximation solutions are derived

a new mixed formulation for elasticity we propose a new mixed variational formulation for the equations of linear elasticity it does not require symmetric tensors and consequently is easy to discretize by adapting mixed finite elements developed for scalar second order elliptic equations

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

extend three wave method for the 1 2 dimensional ito equation abstract in this work extend three wave method etm is used to construct the novel multi wave solutions of the 1 2 dimensional ito equation as a result three soliton solution doubly periodic solitary wave solutions periodic two solitary wave solutions are obtained it is shown that the extend three wave method may provide us with a straightforward and effective mathematical tool for seeking multi wave solutions of higher dimensional nonlinear evolution equations

new exact travelling wave solutions of two nonlinear physical models abstract in this paper an improved tanh function method is used with a computerized symbolic computation for constructing new exact travelling wave solutions on two nonlinear physical models namely the quantum zakharov equations and the 2 1 dimensional broer kaup kupershmidt bkk system the main idea of this method is to take full advantage of the riccati equation which has more new solutions the exact solutions are obtained which include new soliton like solutions trigonometric function solutions and rational solutions the method is straightforward and concise and its applications are promising

well posedness of the fundamental boundary value problems for constrained anisotropic elastic materials we consider the equations of linear homogeneous anisotropic elasticity admitting the possibility that the material is internally constrained and formulate a simple necessary and sufficient condition for the fundamental boundary value problems to be well posed for materials fulfilling the condition we establish continuous dependence of the displacement and stress on the elastic moduli and ellipticity of the elasticity system as an application we determine the orthotropic materials for which the fundamental problems are well posed in terms of their young s moduli shear moduli and poisson ratios finally we derive a reformulation of the elasticity system that is valid for both constrained and unconstrained materials and involves only one scalar unknown in addition to the displacements for a two dimensional constrained material a further reduction to a single scalar equation is outlined

single and multiple soliton solutions for the 2 1 dimensional kdv equation abstract the 2 1 dimensional kdv equation is studied by four distinct methods the hirota s bilinear method is used to derive multiple soliton solutions for this completely integrable equation the tanh coth method and the cosh ansatz are used to obtain single soliton solutions and travelling wave solutions the exp function method gives travelling wave solutions with some free parameters the work highlights the reliability of the four methods

on a numerical strategy to compute gravity currents of non newtonian fluids this paper is devoted to the presentation of a numerical scheme for the simulation of gravity currents of non newtonian fluids the two dimensional computational grid is fixed and the free surface is described as a polygonal interface independent from the grid and advanced in time by a lagrangian technique navier stokes equations are semi discretized in time by the characteristic galerkin method which finally leads to solve a generalized stokes problem posed on a physical domain limited by the free surface to only a part of the computational grid to this purpose we implement a galerkin technique with a particular approximation space defined as the restriction to the fluid domain of functions of a finite element space the decomposition coordination method allows to deal without any regularization with a variety of non linear and possibly non differentiable constitutive laws beside more analytical tests we revisit with this numerical method some simulations of gravity currents of the literature up to now investigated within the simplified thin flow approximation framework

nonlinear complementarity functions for plasticity problems with frictional contact in this paper a unifying framework for the numerical treatment of frictional contact in combination with elastoplasticity with hardening is presented both kinds of problems lead to the mathematical structure of variational inequalities which are discretized by introducing additional variables for the contact stresses or the deviatoric stresses leading to a mixed formulation by defining a family of nonlinear complementarity functions which can be applied to both frictional and plastic yield conditions these inequality constraints are reformulated as equalities combined with the equilibrium equations a system of nonlinear equations is obtained that is solved in terms of a semismooth newton method to obtain a larger domain of convergence and better stability properties the introduction of additional scaling parameters is motivated and their benefit to the convergence of the scheme is demonstrated due to the locality of the contact and plastic constraints the resulting method can be interpreted as a primal dual active set strategy furthermore for linear hardening laws our method is a generalization of the well known radial return algorithm which is obtained for a special suboptimal choice of the plastic scaling parameters the efficiency and the generality of the proposed quasi newton scheme is demonstrated by several numerical examples including the simulation of a three dimensional contact problem with several elastoplastic bodies exponential isotropic hardening and coulomb friction

a regularized stabilized mixed finite element formulation for viscoplasticity of bingham type abstract in this article we present a new mixed stabilized regularized finite element formulation in primitive variables with continuous velocity and discontinuous pressure interpolations for the steady flow of an incompressible fluid of bingham type this formulation is based on an augmented lagrangian regularization technique and a least squares stabilization method mathematical analyses are performed for the new formulation in terms of stability existence and uniqueness of the solution optimal orders of convergence are obtained mathematically improving on classical methods which also present limitations as regards the values of the yield stress numerical results are presented confirming the theory developed here and they show the robustness of the new method with stability obtained for the velocity and especially for the pressure when the yield stress is very high

dromion like structures in a 3 1 dimensional kdv type equation dromion structures have been found in many 2 1 dimensional models the similar structure in 3 1 dimensions is studied in this paper for a kdv type equation starting from the bilinear form of the model we found that there are five types of multi dromion solutions for its potentials say the first type of multi dromion solution is driven by multi camber solitons with one of them being non parallel to the x axis the second third and fourth types of multi dromion solutions are driven by two camber solitons and one two and three sets of parallel plane solitons respectively the fifth type of multi dromion solution is driven by one set of parallel plane solitons one set of camber solitons which are parallel to the x axis and one camber soliton which is non parallel to the x axis phase shifts may be involved in the interactions among the multi dromions for the first and fifth types of solutions a single dromion solution of the model may possess quite a free shape for instance the point like dromions ring type dromions extended and sharp dromions and oscillatory dromions can be obtained by selecting some arbitrary functions appropriately