explicit and averaging a posteriori error estimates for adaptive finite volume methods local mesh refining algorithms known from adaptive finite element methods are adopted for locally conservative and monotone finite volume discretizations of boundary value problems for steady state convection diffusion reaction equations the paper establishes residual type explicit error estimators and averaging techniques for a posteriori finite volume error control with and without upwind in global h1 and l2 norms reliability and efficiency are verified theoretically and confirmed empirically with experimental support for the superiority of the suggested adaptive mesh refining algorithms over uniform mesh refining a discussion of adaptive computations in the simulation of contaminant concentration in a nonhomogeneous water reservoir concludes the paper

a posteriori error estimations of some cell centered finite volume methods for diffusion convection reaction problems this paper presents an a posteriori residual error estimator for diffusion convection reaction problems approximated by some cell centered finite volume methods on isotropic or aniso tropic meshes in rd d 2 or 3 for that purpose we built a reconstructed approximation which is an appropriate interpolant of the finite volume solution the error is then the difference between the exact solution and this interpolant the residual error estimator is based on the jump of the normal derivative of the interpolant we then prove the equivalence between the energy norm of the error and the residual error estimator some numerical tests confirm our theoretical results

adaptive finite element methods for elliptic equations with non smooth coefficients nous considerons une equation elliptique du second ordre a coefficients discontinus ou anisotropes dans un domaine borne en dimension 2 ou 3 et sa discretisation par elements finis le but de cet article est de demontrer des estimations d erreur a priori et a posteriori dans une norme appropriee qui soient independantes de la variation des coefficients

prebending effects upon the vibrational modes of thermally prestressed planar beams abstract in this paper the linear vibrations of thermally prestressed beams are studied including the effects of predisplacement due to prebending and initial imperfections only low prestressed states far from the buckling stage are considered one of the motivations of this paper being the issue of taking into account climatic temperature effects in damage detection based on modal techniques a brief general review is first presented in order to give some theoretical and physical insights upon structural vibrations superimposed on an initial static state both the total lagrangian and the updated lagrangian formulations are applied to a planar euler bernouli beam under the assumption of small prestrains and large predisplacements the governing equilibrium equations are solved using a finite element method some illustrative numerical results are given the model is then validated through experiments inside a climatic chamber it is concluded that in addition to the axial prestress the presence of prebending is also likely to have a significant effect upon some eigenfrequencies even in the case of rather small predisplacements

an a posteriori error estimate for a first kind integral equation in this paper we present a new a posteriori error estimate for the boundary element method applied to an integral equation of the first kind the estimate is local and sharp for quasi uniform meshes and so improves earlier work of ours the mesh dependence of the constants is analyzed and shown to be weaker than expected from our previous work besides the galerkin boundary element method the collocation method and the qualocation method are considered a numerical example is given involving an adaptive feedback algorithm

guaranteed and robust discontinuous galerkin a posteriori error estimates for convection diffusion reaction problems we propose and study a posteriori error estimates for convection diffusion reaction problems with inhomogeneous and anisotropic diffusion approximated by weighted interior penalty discontinuous galerkin methods our twofold objective is to derive estimates without undetermined constants and to analyze carefully the robustness of the estimates in singularly perturbed regimes due to dominant convection or reaction we first derive locally computable estimates for the error measured in the energy semi norm these estimates are evaluated using h div w conforming diffusive and convective flux reconstructions thereby extending the previous work on pure diffusion problems the resulting estimates are semi robust in the sense that local lower error bounds can be derived using suitable cutoff functions of the local peclet and damkohler numbers fully robust estimates are obtained for the error measured in an augmented norm consisting of the energy semi norm a dual norm of the skew symmetric part of the differential operator and a suitable contribution of the interelement jumps of the discrete solution numerical experiments are presented to illustrate the theoretical results

coupling of the finite volume element method and the boundary element method an a priori convergence result the coupling of the finite volume element method and the boundary element method is an interesting approach to simulate a coupled system of a diffusion convection reaction process in an interior domain and a diffusion process in the corresponding unbounded exterior domain this discrete system maintains naturally local conservation and a possible weighted upwind scheme guarantees the stability of the discrete system also for convection dominated problems we show existence and uniqueness of the continuous system with appropriate transmission conditions on the coupling boundary provide a convergence and an a priori analysis in an energy semi norm and provide an existence and an uniqueness result for the discrete system all results are also valid for the upwind version numerical experiments show that our coupling is an efficient method for the numerical treatment of transmission problems which can also be convection dominated

on landau damping going beyond the linearized study has been a longstanding problem in the theory of landau damping in this paper we establish exponential landau damping in analytic regularity the damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables rather than exchanges of energy phase mixing is the driving mechanism the analysis involves new families of analytic norms measuring regularity by comparison with solutions of the free transport equation new functional inequalities a control of non linear echoes sharp deflection estimates and a newton approximation scheme our results hold for any potential no more singular than coulomb or newton interaction the limit cases are included with specific technical effort as a side result the stability of homogeneous equilibria of the non linear vlasov equation is established under sharp assumptions we point out the strong analogy with the kam theory and discuss physical implications finally we extend these results to some gevrey non analytic distribution functions

nondestructive determination of buckling for plates and bars including shear it will be shown that the generic integral equation for nondestructive determination of the buckling loads obtained previously baruch m integral equations for nondestructive determination of buckling loads for elastic bars and plates israel journal of technology vol 11 no 1 2 1973 pp 1 8 includes the influence of the transverse shear strains on the buckling load this can not be said for the integral equations obtained by differentiation of the generic integral equation

a nonconforming a posteriori estimator for the coupling of cell centered finite volume and boundary element methods the coupling of the cell centered finite volume method and the boundary element method is an interesting approach to solve elliptic problems on an unbounded domain where local flux conservation is important based on the piecewise constant interior finite volume solution we define a morley type interpolant built on a nonconforming finite element together with the cauchy data of the exterior boundary element solution this allows us to define a residual based a posteriori error estimator with respect to an energy norm we prove reliability and efficiency of this estimator and use its local contributions to steer an adaptive mesh refining algorithm in two examples we illustrate the effectiveness of the new adaptive coupling method and compare it with the coupling approach with a conforming morley interpolant

residual based a posteriori error estimate for hypersingular equation on surfaces the hypersingular integral equation of the first kind equivalently describes screen and neumann problems on an open surface piece the paper establishes a computable upper error bound for its galerkin approximation and so motivates adaptive mesh refining algorithms numerical experiments for triangular elements on a screen provide empirical evidence of the superiority of adapted over uniform mesh refining the numerical realisation requires the evaluation of the hypersingular integral operator at a source point this and other details on the algorithm are included

a posteriori error estimate and h adaptive algorithm on surfaces for symm s integral equation a residual based a posteriori error estimate for boundary integral equations on surfaces is derived in this paper a localisation argument involves a lipschitz partition of unity such as nodal basis functions known from finite element methods the abstract estimate does not use any property of the discrete solution but simplifies for the galerkin discretisation of symm s integral equation if piecewise constants belong to the test space the estimate suggests an isotropic adaptive algorithm for automatic mesh refinement an alternative motivation from a two level error estimate is possible but then requires a saturation assumption the efficiency of an anisotropic version is discussed and supported by numerical experiments

spectral theory of the linearized vlasov poisson equation etude de la theorie spectrale de l equation de vlasov poisson linearisee dont la solution se comporte comme une somme d ondes planes pour de grandes valeurs du temps prolongement analytique de la resolvante de l equation

a posteriori error estimators for convection diffusion equations we derive a posteriori error estimators for convection diffusion equations with dominant convection the estimators yield global upper and local lower bounds on the error measured in the energy norm such that the ratio of the upper and lower bounds only depends on the local mesh peclet number the estimators are either based on the evaluation of local residuals or on the solution of discrete local dirichlet or neumann problems

on the coupled bem and fem for a nonlinear exterior dirichlet problem in r2 in this paper we apply the coupling of boundary integral and finite element methods to solve a nonlinear exterior dirichlet problem in the plane specifically the boundary value problem consists of a nonlinear second order elliptic equation in divergence form in a bounded inner region and the laplace equation in the corresponding unbounded exterior region in addition to appropriate boundary and transmission conditions the main feature of the coupling method utilized here consists in the reduction of the nonlinear exterior boundary value problem to an equivalent monotone operator equation we provide sufficient conditions for the coefficients of the nonlinear elliptic equation from which existence uniqueness and approximation results are established then we consider the case where the corresponding operator is strongly monotone and lipschitz continuous and derive asymptotic error estimates for a boundary finite element solution we prove the unique solvability of the discrete operator equations and based on a strang type abstract error estimate we show the strong convergence of the approximated solutions moreover under additional regularity assumptions on the solution of the continous operator equation the asymptotic rate of convergenceo h is obtained

time asymptotics for solutions of vlasov poisson equation in a circle we prove that there exists a class of solutions of the nonlinear vlasov poisson equation vpe on a circle that converges weakly as t to a stationary homogeneous solution of vpe this behavior is called in the linear case landau damping the result is obtained by constructing a suitable scattering problem for the solutions of the vlasov poisson problem a consequence of this result is that a class of stationary solutions of the vlasov poisson equation is unstable in a weak topology

a study of landau damping with random initial inputs abstract for the vlasov poisson equation with random uncertain initial data we prove that the landau damping solution given by the deterministic counterpart caglioti and maffei 1998 3 depends smoothly on the random variable if the time asymptotic profile does under the smoothness and smallness assumptions similar to the deterministic case the main idea is to generalize the deterministic contraction argument to more complicated function spaces to estimate derivatives in space velocity and random variables this result suggests that the random space regularity can persist in long time even in time reversible nonlinear kinetic equations

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

critical contrasting of three versions of vibrating bresse timoshenko beam with a crack abstract this paper deals with natural frequencies of short or thick beams taking into account effects of rotary inetria and shear deformation three versions of the bresse timoshenko beam theory are considered and contrasted in the context of the problem of beam vibration in presence of the single crack namely the a original bresse timoshenko theory b elishakoff s truncated version and c the proposed slope inertia based version the original bresse timoshenko equations contain fourth order derivative with respect to time that is not present in the classical bernoulli euler theory whose correction was the declared goal of s p timoshenko who himself did not overestimate the importance of this term the truncated version of the bresse timoshenko was suggested by elishakoff with no fourth order time derivative incorporated in the theory in this paper variational derivation of the truncated version of the bresse timoshenko beam theory is conducted with attendant additional term containing the fourth derivative with respect to axial coordinate and second derivative with respect to time it appears imperative to conduct thorough comparison of the above three theories in the context of beams containing a crack which is often present in engineering structures the applicability of these three versions with attendant extensive numerical calculations is specifically studied for the titled problem it is demonstrated that the original bresse timoshenko beam theory as an overcomplicated theory is not needed for crack analysis simpler theories namely the truncated version of this theory or the one based on slope inertia are sufficient for crack analysis in all treated cases

the application of chebyshev polynomials to the solution of the nonprismatic timoshenko beam vibration problem abstract chebyshev series approximation is applied to solve the problem of vibration of the nonprismatic timoshenko beam resting on a two parameter elastic foundation as a result a system of equations whose coefficients have a closed form for calculating the coefficients of the sought solution is obtained the method is used to solve the free vibration problem for simple supported and clamped free nonprismatic beams the results are compared with the results obtained by other authors also the nonprismatic beam stability problem is solved and the results are compared with those obtained for euler beams to demonstrate the method s applicability to more complex systems the problem of stability of a frame system is solved

a posteriori error estimates and adaptive mesh refinement for the coupling of the finite volume method and the boundary element method we consider the coupling of the finite volume method and the boundary element method of erath siam j numer anal 50 2012 pp 574 594 in two and three dimensions this method can be used for example to approximate a solution of the transport of a concentration in a fluid where no boundary conditions are available we derive residual based a posteriori estimates also for an upwind version these upper and lower bounds measure the error in an energy semi norm between the exact solution and the numerical solution the upper bound is robust in the sense that it does not depend on the variation of the model data the lower bound however depends additionally on the local peclet number the local contributions of the a posteriori estimates are used to steer an adaptive mesh refining algorithm this strategy turns out to be very suitable for the numerical treatment of transmission problems which have singularities or boundary internal layers several numerical examples illustrate the effectivenes

on transverse vibrations of a vertical timoshenko beam in this paper the transverse vibrations of a standing uniform timoshenko beam will be considered due to gravity and the self weight of the beam a linearly varying compression force is acting on the beam it will be assumed that this compression force is small but not negligible the transverse vibrations of the beam can be described by an initial boundary value problem approximations of the solution of this problem will be constructed by using a multiple time scales perturbation method also approximations of the frequencies will be obtained moreover the effect of the linearly varying compression force on the magnitude of the frequencies of the oscillation modes of the beam will be discussed

hypocoercivity for a bgk model for gas mixtures abstract we consider a kinetic model for a two component gas mixture without chemical reactions our goal is to study hypocoercivity for the linearized bgk model for gas mixtures in continuous phase space by constructing an entropy functional we can prove exponential relaxation to equilibrium with explicit rates our strategy is based on the entropy and spectral methods adapting lyapunov s direct method as presented in 1 for the one species linearized bgk model in comparison to the one species case we start with two partial differential equations one for each species these equations are coupled due to interspecies interactions which requires additional estimates on these interspecies terms

a posteriori error estimates for boundary element methods this paper deals with a general framework for a posteriori error estimates in boundary element methods which is specified for three examples namely symm s integral equation an integral equation with a hypersingular operator and a boundary integral equation for a transmission problem based on these estimates an analog of eriksson and johnson s adaptive finite element method is proposed for the h version of the galerkin boundary element method for integral equations of the first kind the efficiency of the approach is shown by numerical experiments which yield almost optimal convergence rates even in the presence of singularities the construction of an adaptive mesh refinement procedure is of very high practical importance in the numerical analysis of partial differential equations and we refer to the pioneering work of babuska and miller 3 and eriksson and johnson 10 11 whereas the main features ofadaptivity for finite element methods now seem to be visible and the door is open to implementation 15 comparably little is known for boundary element methods for integral equations see e g 1 13 18 19 24 in this paper a new adaptive version of the galerkin discretization for the boundary element method is presented based on a posteriori error estimates a general framework for these a posteriori error estimates is derived in 2 and three examples are discussed in 3 5 involving the dirichlet problem the neumann problem for a closed and an open surface and a transmission problem for the laplacian leading to integral equations with strongly elliptic pseudodifferential operators even for smooth data the lack of regularity of the solution near corners of a polygonal domain q leads to poor solutions of the numerical schemes unless appropriate singular functions are incorporated in the trial space or a suitable mesh refinement is used in practical problems such information is missing e g when we have singular or nearly singular data and the main problem is how to balance a graded mesh refinement towards singularities and a global

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

a new conservative numerical scheme for flow problems on unstructured grids and unbounded domains abstract we consider the prototype of a flow and transport problem in two dimensions in particular in many fluid dynamics problems the boundary conditions may be unknown or the domain may be unbounded furthermore only numerical schemes which conserve mass and are stable with respect to dominating convection are appropriate to solve these problems therefore we develop a new discrete scheme to address these issues more precisely we couple the cell centered finite volume method and the boundary element method and introduce suitable transmission conditions also semi robust a posteriori estimates of residual type are developed which allow us to use an adaptive mesh refinement algorithm to treat efficiently problems which have singularities or boundary internal layers several examples illustrate the effectiveness of our new adaptive coupling method

each averaging technique yields reliable a posteriori error control in fem on unstructured grids part i low order conforming nonconforming and mixed fem averaging techniques are popular tools in adaptive finite element methods for the numerical treatment of second order partial differential equations since they provide efficient a posteriori error estimates by a simple postprocessing in this paper their reliablility is shown for conforming nonconforming and mixed low order finite element methods in a model situation the laplace equation with mixed boundary conditions emphasis is on possibly unstructured grids nonsmoothness of exact solutions and a wide class of averaging techniques theoretical and numerical evidence supports that the reliability is up to the smoothness of given right hand sides

robust a posteriori error estimates for stationary convection diffusion equations we analyze a posteriori error estimators for finite element discretizations of convection dominated stationary convection diffusion equations using locally refined isotropic meshes the estimators are based on either the evaluation of local residuals or the solution of discrete local problems with dirichlet or neumann boundary conditions all estimators yield global upper and lower bounds for the error measured in a norm that incorporates the standard energy norm and a dual norm of the convective derivative they are fully robust in the sense that the ratio of the upper and lower bounds is uniformly bounded with respect to the size of the convection the estimates are also uniform with respect to the size of the zero order reaction term and also hold for the limit case of vanishing reaction