a note on α β derivations abstract we show that every multiplicative derivation of a ring r is additive if there exists an idempotent e e 0 1 in r satisfying the conditions c1 c3 c1 e r x 0 implies x 0 c2 e x e r 1 e 0 implies e x e 0 c3 x r 0 implies x 0 in particular every multiplicative derivation of a prime ring with a nontrivial idempotent is additive as applications we could decompose a multiplicative derivation of the algebra m n c of all the n n complex matrices into a sum of an inner derivation and an derivation on m n c given by an additive derivation f on c

generic simplicity of the spectrum and stabilization for a plate equation in this work we prove the generic simplicity of the spectrum of the clamped plate equation in a bounded regular domain of mathbb r d that is given omega subset mathbb r d we show that there exists an arbitrarily small deformation of the domain u such that all the eigenvalues of the plate system in the deformed domain omega u are simple to prove this result we first prove a nonstandard unique continuation property for this system that also holds generically with respect to the perturbations of the domain both the proof of this generic uniqueness result and the generic simplicity of the spectrum use baire s lemma and shape differentiation finally we show an application of this unique continuation property to a result of generic stabilization for a plate system with one dissipative boundary condition

alternating direction iterative technique for mixed finite element methods for stokes equations alternating direction iterative technique for solving the algebraic systems associated with mixed finite element methods for two and three dimensional stokes equations and the navier stokes equations are formulated this method due to brown brown alternating direction iterative schemes for mixed finite element methods for second order elliptic problems thesis university of chicago 1982 is related to the uzawa iterative method for saddle point problems stabilization analysis for the uzawa iterative method is given

an equilibrium finite element method for fourth order elliptic equations with variable coefficients abstract an equilibrium finite element method for 4th order elliptic problems with variable coefficients on convex polygonal domains has been developed in the particular case of bending problems of elastic anisotropic orthotropic isotropic plates with variable constant thickness this new equilibrium method allows a simultaneous approximation to the displacement and the bending and twisting moment tensor error estimates for equilibrium finite element solution are given

ciarlet raviart mixed finite element approximation for an optimal control problem governed by the first bi harmonic equation the ciarlet raviart mixed finite element approximation is constructed to solve the constrained optimal control problem governed by the first bi harmonic equation the optimality conditions consisting of the state and the co state equations is derived also the a priori error estimates are analyzed in the analysis of the a priori error estimates the improved convergent rate of the higher order than existed results is proved some numerical experiments are performed to confirm the theoretical analysis for the a priori error estimate

multiplicative mappings of operator algebras nest algebras are the natural analogues of upper triangular matix algebras in an infinite dimensional hilbert space in this paper we study multiplicative isomorphisms of subalgebras of nest algebras which contain all finite rank operators but might contain no idempotents we prove that such multiplicative mappings are automatically additive and linear or conjugate linear

eigenvalue approximation by mixed and hybrid methods note univ maryland dept math college pk md 20742 ecole polytech ctr math appl f 91128 palaiseau france univ paris 6 f 75230 paris 05 france mercier b cea limeil f 94190 villeneuve france isi document delivery no lq584times cited 29cited reference count 44 reference asn article 1981 005doi 10 2307 2007651 record created on 2006 08 24 modified on 2017 05 12

performance of a parallel mixed finite element implementation for fourth order clamped anisotropic plate bending problems in distributed memory environments the paper deals with a parallel implementation of a mixed finite element method of solution of a fourth order elliptic partial differential equation which in the particular case of aniso ortho isotropic plate bending problems gives a simultaneous approximation to the bending moment tensor field j j i j 1 i j 2 and the displacement field u the parallel implementation has been done in silicon graphics origin 3800 a 4 processor intel xeon symmetric multiprocessor and a beowulf cluster of four intel pentium iii pcs the indefinite linear system obtained after discretization using mixed finite element method is solved in parallel using direct schur s complement approach and iterative method using argonne national laboratory s petsc package the numerical results obtained and the time speed up comparisons for the direct method and iterative methods for a few interesting examples are also given

analysis of mixed finite element methods for fourth order wave equations mixed finite element methods explicit and implicit in time for a fourth order wave equation are considered in this paper the optimal error estimates in the l 2 norm for velocity and moment and in the h 1 norm and l 2 norm for displacement are derived these error estimates are proved by using a special interpolation operator on quasi uniform rectangular meshes the stabilities of the two schemes are also analyzed in addition three other kinds of mixed scheme are constructed numerical examples are provided to verify the theoretical results

a mixed finite element method for fourth order elliptic equations with variable coefficients abstract a new mixed finite element method for the dirichlet problem of fourth order elliptic equations with variable coefficients on convex polygonal domain has been developed in this paper the biharmonic problem and bending problems of elastic plates being particular cases of the general problem considered in the paper for bending problems this method gives a simultaneous approximation to the displacement u and the actual bending and twisting moment ij i j 1 2 error estimate for the mixed finite element solution has been given

nonlinear equations with coefficients of bounded variation in two space variables abstract we consider the equation u t v x 0 x r 2 with v defined as a divergenceless vector valued function in the generalized sense and subject to initial data u 0 we prove the existence of a generalized global solution to this equation under assumptions of bounded variation for v and u 0 and smoothness for

adaptive finite element approximation for distributed elliptic optimal control problems in this paper sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems these error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adjustments and can save substantial computational work

analysis of new augmented lagrangian formulations for mixed finite element schemes two new augmented lagrangian formulations for mixed finite element schemes are presented the methods lead in some cases to an improvement in the order of the approximation an error analysis is provided together with some interesting examples of applications

extension of an ito based general approximation technique for random vibration of a bbw general hysteris model part ii non gaussian analysis abstract the work presented in this paper constitutes the second phase of on going research aimed at developing mathematical models for representing general hysteretic behavior of structures and approximation techniques for the computation and analysis of the response of hysteretic systems to random excitations in this second part the technique previously developed by the authors for the gaussian response analysis of non linear systems with general hysteretic behavior is extended for the non gaussian analysis of these systems this approximation technique is based on the approach proposed independently by ibrahim and wu lin in this work up to fourth order moments of the response co ordinates are obtained for the bouc baber wen smooth hysteresis model these higher order statistics previously have not been made available for general hysteresis models by using existing approximation methods second order moments obtained for the model by this non gaussian closure scheme are compared with equivalent linearization and gaussian closure results via monte carlo simulation mcs higher order moments are compared with the simulation results the study performed for a wide range of degradation parameters and input power spectral density psd levels shows that the non gaussian responses obtained by this approach are in better agreement with the mcs results than the linearized and gaussian ones this approximation technique can provide information on higher order moments for general hysteretic systems this information is valuable in random vibration and the reliability analysis of hysteretically yielding structures

convergence and performance of the h and p extensions with mixed finite element c0 continuity formulations for tension and buckling of a gradient elastic beam abstract mixed formulations with c 0 continuity basis functions are employed for the solution of some types of one dimensional fourth and sixth order equations resulting from axial tension and buckling of gradient elastic beams respectively a basic characteristic of gradient elasticity type equations is the appearance of boundary layers in the higher order derivatives of the displacements e g in the stress fields this is due to the small parameters related to the size of the microstructure entering the governing equations the proposed mixed formulations are based on generalizations of the well known ciarlet raviart mixed method where the new main variables are related to second order or fourth order for the buckling problem derivatives of the displacement field the continuous and discrete babuska brezzi inf sup conditions are established the mixed formulations are numerically tested for both the uniform h and p extensions with regard to the axial tension problem the standard quasi optimal rates of convergence are numerically verified in all cases i e algebraic rate of convergence for the h extension and exponential rate for the p extension on the other hand the h extension observed convergence rates of the critical buckling load for the second model problem are slightly higher than the theoretical ones found in the literature especially for polynomial order p 1 the respective observed rates of convergence of the buckling load for the p extension are still exponential

accurate free vibration analysis of clamped orthotropic plates by the method of superposition abstract the superposition method is exploited for the first time to analyze the free vibration frequencies and mode shapes of fully clamped rectangular orthotropic plates the method is found to work extremely well and excellent agreement is obtained when comparison is made between computed results and earlier reliable published data simple modifications required to adapt the method to orthotropic plate problems are described in detail accurate eigenvalues are tabulated for a wide range of plate geometries and vibration mode families with various levels of orthotropy

jordan maps of nest algebras abstract in this paper we prove that a bijective map from a a standard subalgebra of a nest algebra on a hilbert space onto an algebra that satisfies r ab ba r a b b a a b a where r is a fixed nonzero rational number is additive

a mixed finite element method for fourth order elliptic problems with variable coefficients a new mixed finite element method for the solution of the dirichlet problem of fourth order elliptic partial differential equations with variable coefficients on a convex polygon has been developed in this paper biharmonic and bending problems of elastic plates for which this technique allows a simultaneous approximation to the deflection components of the change in curvature tensor and the bending and twisting moments are the particular cases of the problem considered in the paper error estimate for the mixed finite element solution has been given

additivity of jordan maps on standard operator algebras abstract in this paper we prove that a bijective map form a a standard operator algebra on a banach space of dimension 1 onto a ring that satisfies ab ba a b b a a b a is additive

a mixed finite element method for fourth order eigenvalue problems a mixed finite element method for approximating eigenpairs of iv order elliptic eigenvalue problems with dirichlet boundary conditions has been given the method can be applied to the vibration analysis of anisotropic orthotropic isotropic biharmonic plates computer implementation procedures for this mixed method are given along with the results of numerical experiments

closed form numerical solutions of variable coefficient linear second order elliptic problems abstract in this work we develop an alternative numerical technique which allows to construct a numerical solution in closed form of variable coefficient linear second order elliptic problems with dirichlet boundary conditions the elliptic partial differential equation is approximated by a consistent explicit difference scheme and using a discrete separation of the variables method we determine a closed form solution of the two resulting discrete boundary value problems with the separated variables avoiding to have to solve large algebraic systems one of these boundary value problems is a discrete sturm liouville problem which guarantees the qualitative properties of the exact solution of elliptic problem a constructive procedure for the computation of the numerical solution is given and an illustrative example is included

mixed finite element and boundary element approximation in 3d magnetostatics for computation of the magnetic induction we describe a mixed method for the computation of the magnetic induction in three dimensional magnetostatics this method uses mixed finite elements in association with boundary elements we present numerical results and make a comparison between these results and those obtained from a classical method with magnetic scalar potential we conclude that our method leads to better numerical accuracy

some c0 continuous mixed formulations for general dipolar linear gradient elasticity boundary value problems and the associated energy theorems abstract the goal of this work is a systematic presentation of some classes of mixed weak formulations for general multi dimensional dipolar gradient elasticity fourth order boundary value problems the displacement field main variable is accompanied by the double stress tensor and the cauchy stress tensor case 1 or u formulation the double stress tensor alone case 2 or u formulation the double stress the cauchy stress the displacement second gradient and the standard strain field case 3 or e u formulation and the displacement first gradient along with the equilibrium stress case 4 or u formulation in all formulations the respective essential conditions are built in the structure of the solution spaces for cases 1 2 and 4 one dimensional analogues are presented for the purpose of numerical comparison moreover the standard galerkin formulation is depicted it is noted that the standard galerkin weak form demands c1 continuous conforming basis functions on the other hand up to first order derivatives appear in the bilinear forms of the current mixed formulations hence standard c0 continuous conforming basis functions may be employed in the finite element approximations the main purpose of this work is to provide a reference base for future numerical applications of this type of mixed methods in all cases the associated quadratic energy functionals are formed for the purpose of completeness

an interior penalty method for distributed optimal control problems governed by the biharmonic operator in this paper a c 0 interior penalty method has been proposed and analyzed for distributed optimal control problems governed by the biharmonic operator the state and adjoint variables are discretized using continuous piecewise quadratic finite elements while the control variable is discretized using piecewise constant approximations a priori and a posteriori error estimates are derived for the state adjoint and control variables under minimal regularity assumptions numerical results justify the theoretical results obtained the a posteriori error estimators are useful in adaptive finite element approximation and the numerical results indicate that the sharp error estimators work efficiently in guiding the mesh refinement

a numerical method for two phase flow with an unstable interface abstract the random choice method is used to compute the oil water interface for two dimensional porous media equations the equations used are a pair of coupled equations the elliptic pressure equation and the hyperbolic saturation equation the equations do not include the dispersive capillary pressure term and the computation does not introduce numerical diffusion the method resolves saturation discontinuities sharply the main conclusion of this paper is that the random choice is a correct numerical procedure for this problem even in the highly fingered case two methods of inducing fingers are considered deterministically through choice of cauchy data and heterogeneity through maximizing the randomness of the random choice method

a parallel mixed finite element implementation of fourth order plate bending problems in distributed memory environments the paper deals with a parallel implementation of a mixed finite element method of solution of general fourth order elliptic partial differential equations which in the case of aniso ortho isotropic plate bending problems simultaneously approximates the bending moment tensor field j j i j 1 i j 2 and the displacement field u the experiments on the performance of this method have been done in two parallel environments namely silicon graphics origin 3800 and cray t3e the details of the parallel computer implementation procedures for this mixed method with time speed up comparisons for a few illustrative examples are given

theoretical analysis of a class of mixed c0 continuity formulations for general dipolar gradient elasticity boundary value problems abstract mixed weak formulations with two or three main tensor variables are stated and theoretically analyzed for general multi dimensional dipolar gradient elasticity biharmonic boundary value problems the general structure of constitutive equations is considered with and without coupling terms the mixed formulations are based on various generalizations of the so called ciarlet raviart technique hence c 0 continuity conforming basis functions may be employed in the finite element approximations or even c 1 basis functions for the cauchy stress variable all the complicated boundary conditions especially in the multi dimensional scenario are naturally considered the main variables are the displacement vector the double stress tensor and the cauchy stress tensor the latter variable may be eliminated in some of the formulations depending on the structure of the constitutive equations the standard continuous and discrete babuska brezzi inf sup conditions for the constraint equation as well as solution uniqueness for both the continuous statements and discrete approximations are established in all cases for the purpose of completeness two one dimensional mixed formulations are also analyzed the respective constitutive equations possess general structure with coupling terms for the 1 d formulations all the inf sup conditions are satisfied for both the continuous and discrete statements assuming proper selection of the polynomial spaces for the main variables hence the general babuska brezzi theory results in quasi optimality and stability for multi dimensional problems the difficulty of deducing the inf sup condition on the kernel is examined certain aspects of methodologies employed to theoretically by pass this problem are also discussed

postprocessing and higher order convergence of the mixed finite element approximations of biharmonic eigenvalue problems a new procedure for accelerating the convergence of mixed finite element approximations of the eigenpairs and of the biharmonic operator is proposed it is based on a postprocessing technique that involves an additional solution of a source problem on an augmented finite element space this space could be obtained either by substantially refining the grid the two grid method or by using the same grid but increasing the order of polynomials by one the two space method the numerical results presented and discussed in the paper illustrate the efficiency of the postprocessing method

a parallel mixed finite element implementation for approximation of eigenvalues and eigenvectors of fourth order eigenvalue problems the paper deals with a parallel implementation of a mixed finite element method of approximation of eigenvalues and eigenvectors of fourth order eigenvalue problems with variable constant coefficients the implementation has been done in silicon graphics origin 3800 a four processor intel xeon symmetric multiprocessor and a beowulf cluster of four intel pentium iii pcs the generalised eigenvalue problem obtained after discretization using the mixed finite element method is solved using the package lanso the numerical results obtained are compared with existing results if available the time speedup comparisons in different environments for some examples of practical and research interest and importance are also given

iterative schemes for mixed finite element methods with applications to elasticity and compressible flow problems iterative schemes for mixed finite element methods are proposed and analyzed in two abstract formulations the first one has applications to elliptic equations and incompressible fluid flow problems while the second has applications to linear elasticity and compressible stokes problems these schemes are constructed through iteratively penalizing the mixed finite element scheme of which iterated penalty method and augmented lagrangian method are special cases convergence theorems are demonstrated in abstract formulations in hilbert spaces and applications to individual physical problems are considered as examples theoretical analysis and computational experiments both show that the proposed schemes have very fast convergence a few iterations are normally enough to reduce the iterative error to a prescribed precision numerical examples with continuous and discontinuous coefficients are presented

jordan maps on triangular algebras abstract let t be a triangular algebra and r be an arbitrary ring suppose that m t r and m r t are surjective maps such that m am x m x a m a x xm a m m a x xm a am x m x a for all a t x r in this paper we give sufficient conditions on t such that both m and m are additive in particular if t is a standard subalgebra of a nest algebra then both m and m are additive

new rectangular mixed finite element method for second order elliptic problems a low order rectangular mixed finite element for second order elliptic problems is constructed stability and optimal order error estimates will be derived

on gradient type optimization method utilizing mixed finite element approximation for optimal boundary control problem governed by bi harmonic equation in this paper a numerical method based on mixed finite element method for optimal boundary control problem governed by bi harmonic equation is presented the system of optimality equations consisting of state and costate function is derived based on the system a gradient type optimization method using a mixed finite approximation for solving the optimal boundary control is developed in our algorithm the trace of vortex function of costate equation on boundary plays a key role finally a local error analysis at every iteration for this gradient type optimization method is given

accuracy and convergence properties of the finite difference multigrid solution of an optimal control optimality system the finite difference multigrid solution of an optimal control problem associated with an elliptic equation is considered stability of the finite difference optimality system and optimal order error estimates in the discrete l2 norm and in the discrete h1 norm under minimum smoothness requirements on the exact solution are proved sharp convergence factor estimates of the two grid method for the optimality system are obtained by means of local fourier analysis a multigrid convergence theory is provided which guarantees convergence of the multigrid process towards weak solutions of the optimality system