mild solutions of non autonomous second order problems with nonlocal initial conditions abstract in this paper we establish the existence of mild solutions for a non autonomous abstract semi linear second order differential equation submitted to nonlocal initial conditions our approach relies on the existence of an evolution operator for the corresponding linear equation and the properties of the hausdorff measure of non compactness

analysis of locking and stress oscillations in a general curved beam element the exactly integrated general quadratic curved beam element has both membrane and shear locking and significant quadratic oscillations in the axial force and cubic oscillations in the shear force the functional re constitution technique is applied to derive accurate error estimates for the manner in which locking is relieved and for the magnitude of the stress oscillations the orthogonally correct field consistent interpolations are determined for the optimal form of the element and it is shown that the popular two point gaussian integrated13 version of the element is non orthogonal and has a cubic13 oscillation in the shear force that curiously vanishes at the barlow points

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

existence of solutions for a class of neutral partial differential equations with nonlocal conditions in the α norm abstract this paper is concerned with the existence of mild and strong solutions for some neutral partial differential equations with nonlocal conditions in the norm the linear part of the equations is assumed to generate a compact analytic semigroup of uniformly bounded linear operators and the nonlinear part satisfies some lipschitz conditions with respect to the norm by using a fixed point theorem of sadovskii we establish some existence results which generalize the recent conclusions on this issue in the end the obtained results will be applied to a class of partial differential equations with nonlocal conditions

numerical schemes for one dimensional parabolic equations with nonstandard initial condition parabolic partial differential equations with nonstandard initial condition feature in the mathematical modelling of many phenomena while a significant body of knowledge about the theory and numerical methods for parabolic partial differential equations with classical initial condition has been accumulated not much has been extended to parabolic partial differential equations with nonstandard initial condition in this paper finite difference approximations to the solution of one dimensional parabolic equation with nonstandard initial condition are studied several finite difference schemes are presented for solving a parabolic partial differential equation with nonlocal time weighting initial condition these schemes are based on the forward time centred space explicit formula the backward time centred space implicit technique the crank nicolson implicit formula the crandall s implicit scheme and the saulyev s 2 2 explicit methods the results of a numerical experiment are presented

three level techniques for one dimensional parabolic equation with nonlinear initial condition in this paper a boundary value problem for one dimensional heat equation is considered under the constraint of a nonlocal initial condition in place of the classical specification of initial data we impose the nonlocal initial condition efficient higher order algorithms are developed for solving this parabolic partial differential equation with nonstandard initial condition several three level finite difference schemes are presented these schemes are based on the modification of the centred time centred space explicit formula the three level 1 3 1 explicit technique the sixth order 1 3 3 explicit method and the dufort frankel finite difference scheme numerical computations combined with a simple iteration procedure of some examples are given to demonstrate the efficiency and accuracy of the new algorithms

geometrically non linear formulation for three dimensional curved beam elements with large rotations this paper presents a geometrically non linear formulation gnl for the three dimensional curved beam elements using the total lagrangian approach the element geometry is constructed using co ordinates of the nodes on the centroidal or reference axis and the orthogonal nodal vectors representing the principal bending directions the element displacement field is described using three translations at the element nodes and three rotations about the local axes the gnl three dimensional beam element formulations based on these element approximations are restricted to small nodal rotations between two successive load increments the element formulation presented here removes such restrictions this is accomplished by retaining non linear nodal terms in the definition of the element displacement field and the consistent derivation of the element properties the formulation presented here is very general and yet can be made specific by selecting proper non linear functions representing the effects of nodal rotations the details of the element properties are presented and discussed numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements a comparison of the results obtained from the present formulation with those available in the literature using a linearized element approximation clearly demonstrate the superiority of the formulation in terms of large load steps large rotations between two load steps and extremely good convergence characteristics during equilibrium iterations the displacement approximation of these elements is fully compatible with the isoparametric curved shell elements with large rotations and since the elements possess offset capability these elements can also serve as stiffeners for the curved shells

impulsive degenerate nonlinear parabolic functional differential inequalities abstract the aim of the paper is to give a theorem about impulsive degenerate strong nonlinear parabolic functional differential inequalities in arbitrary parabolic domain and two corollaries about weak and strong inequalities the paper is a direct generalization and a continuation among other things of the author s previous work the results obtained in this paper can be applied for some impulsive problems in the theories of diffusion and heat conduction with better effects than analogous known classical parabolic problems

strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with arbitrary functionals abstract in l byszewski z angew math mech 70 1990 3 202 206 l byszewski j appl math stochastic ann 3 1990 5 65 79 the author studied strong maximum principles for nonlinear parabolic problems with nonlocal inequalities together with particular functionals our purpose here is to extend results in l byszewski z angew math mech 70 1990 3 202 206 l byszewski j appl math stochastic ann 3 1990 5 65 79 to strong maximum principles for nonlinear parabolic problems with nonlocal inequalities together with arbitrary functionals the results obtained in this paper can be applied in the theories of diffusion and heat conduction

the two level finite difference schemes for the heat equation with nonlocal initial condition abstract in this paper the two level finite difference schemes for the one dimensional heat equation with a nonlocal initial condition are analyzed as the main result we obtain conditions for the numerical stability of the schemes in addition we revise the stability conditions obtained in 21 for the crank nicolson scheme we present several numerical examples that confirm the theoretical results within linear as well as nonlinear problems in some particular cases it is shown that for small regions of the time step size values the explicit ftcs scheme is stable while certain implicit methods such as crank nicolson scheme are not

combining metamodels with rational function representations of discretization error for uncertainty quantification abstract techniques for producing metamodels for the efficient monte carlo simulation of high consequence systems are presented the bias of f e m mesh discretization errors is eliminated or minimized by extrapolation using rational functions rather than the power series representation of richardson extrapolation examples including estimation of the vibrational frequency of a one dimensional bar show that the rational function model gives more accurate estimates using fewer terms than richardson extrapolation an important consideration for computational reliability assessment of high consequence systems where small biases in solutions can significantly affect the accuracy of small magnitude probability estimates rational function representation of discretization error enable the user to accurately extrapolate to the continuum from numerical experiments performed outside the asymptotic region of the usual power series allowing use of coarser meshes in the numerical experiments resulting in significant savings

method for treating discretization error in nondeterministic analysis a response surface methodology based technique is presented for treating discretization error in non deterministic analysis the response surface or metamodel is estimated from computer experiments which vary both uncertain physical parameters and the fidelity of the computational mesh the resultant metamodel is then used to propagate the variabilities in the continuous input parameters while the mesh size is taken to zero its asymptotic limit with respect to mesh size the metamodel is equivalent to richardson extrapolation in which solutions on coarser and finer meshes are used to estimate discretization error the method is demonstrated on a one dimensional prismatic bar in which uncertainty in the third vibration frequency is estimated by propagating variations in material modulus density and bar length the results demonstrate the efficiency of the method for combining non deterministic analysis with error estimation to obtain estimates of total simulation uncertainty the results also show the relative sensitivity of failure estimates to solution bias errors in a reliability analysis particularly when the physical variability of the system is low

controllability of systems with a general nonlocal condition abstract in this work we are concerned with the controllability of first order distributed systems with a general nonlocal condition specifically by a general nonlocal condition we understand a nonlocal condition modeled in terms of an inclusion in this context assuming that the underlying linear system is approximately controllable we present three types of conditions under which the nonlinear system is also approximately controllable

a new adi technique for two dimensional parabolic equation with an integral condition abstract nonclassical parabolic initial boundary value problems arise in the study of several important physical phenomena this paper presents a new approach to treat complicated boundary conditions appearing in the parabolic partial differential equations with nonclassical boundary conditions a new fourth order finite difference technique based upon the noye and hayman n h alternating direction implicit adi scheme is used as the basis to solve the two dimensional time dependent diffusion equation with an integral condition replacing one boundary condition this scheme uses less central processor time cpu than a second order fully implicit scheme based on the classical backward time centered space btcs method for two dimensional diffusion it also has a larger range of stability than a second order fully explicit scheme based on the classical forward time centered space ftcs method the basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyeet this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference methods the results of numerical experiments for the new method are presented the central processor times needed are also reported error estimates derived in the maximum norm are tabulated

existence for a class of partial differential equations with nonlocal conditions abstract this paper is concerned with the existence of mild and classical solutions of nonlocal cauchy problems we assume that the linear part generates an analytic compact bounded semigroup and that the nonlinear part is a holder continuous function with respect to the fractional power norm of the linear part considering the nonlocal conditions in the norm we generalize the recent conclusions on this topic the results obtained will be applied to a class of functional partial differential equations with nonlocal conditions in 1 2 norm

validation of a posteriori error estimators by numerical approach abstract a numerical methodology which determines the quality or robustness of a posteriori error estimators is described the methodology accounts precisely for the factors which affect the quality of error estimators for finite element solutions of linear elliptic problems namely the local geometry of the grid and the structure of the solution the methodology can be employed to check the robustness of any estimator for the complex grids which are used in engineering computations

issues in computational fluid dynamics code verification and validation a broad range of mathematical modeling errors of fluid flow physics and numerical approximation errors are addressed in computational fluid dynamics cfd it is strongly believed that if cfd is to have a major impact on the design of engineering hardware and flight systems the level of confidence in complex simulations must substantially improve to better understand the present limitations of cfd simulations a wide variety of physical modeling discretization and solution errors are identified and discussed here discretization and solution errors refer to all errors caused by conversion of the original partial differential or integral conservation equations representing the physical process to algebraic equations and their solution on a computer the impact of boundary conditions on the solution of the partial differential equations and their discrete representation will also be discussed throughout the article clear distinctions are made between the analytical mathematical models of fluid dynamics and the numerical models lax s equivalence theorem and its frailties in practical cfd solutions are pointed out distinctions are also made between the existence and uniqueness of solutions to the partial differential equations as opposed to the discrete equations two techniques are briefly discussed for the detection and quantification of certain types ofmore discretization and grid resolution errors less

existence of mild solutions for semilinear evolution equations with non local initial conditions abstract in this paper we study the existence of mild solutions for a class of semilinear evolution equations with non local initial conditions and extend some related results in this direction

consistency aspects of out of plane bending torsion and shear in a quadratic curved beam element curved beams in civil engineering applications call for out of plane bending and torsion under the action of out of plane transverse shear loads the design of a quadratic displacement type curved beam element capable of representing shear deformation as in the timoshenko beam theory will call for special attention to be paid to the manner in which the shear strain is to be represented field inconsistent representations of the out of plane transverse shear strain will result in a loss gf efficiency and introduce spuriou oscillations in the bending moment torsional moment and shear force the optimal field consistent assumed strain interpolation for the shear is derived here and it is demonstrated that it has very high accuracy and is free from spurious force and moment oscillations

finite difference solutions for parabolic equations with the time weighting initial conditions abstract a class of nonlinear parabolic boundary value problems with time weighting initial condition is considered instead of studying the existence uniqueness and continuous dependence of the solution upon the data we give a brief review of the known results and then concentrate on the performance of the backward euler and crank nicolson finite difference schemes 1 the results of some numerical examples are presented which demonstrate the efficiency and rapid convergence

a new approach to the finite element modelling of beams with warping effect as a first step toward developing a finite element formulation that can model coupling among extensional bending and torsional behaviour of beams a new method is proposed to properly represent the warping of arbitrary cross sections the basic approach is to introduce a small warping displacement superimposed over flat cross sections of a shear flexible beam in a deformed configuration numerical tests involving simple isotropic beams undergoing a small elastic displacement demonstrate the validity of the new approach the present approach can be extended to composite beams as well as isotropic beams experiencing a large deflection or finite rotation

uniqueness of solutions of parabolic semilinear nonlocal boundary problems abstract the purpose of the paper is to give two theorems about the uniqueness of solutions of parabolic semilinear nonlocal boundary problems the paper is a continuation of previous papers by byszewski and the generalization of some results from r rabczuk introduction to differential inequalities pwn warsaw 1976 polish j chabrowski on nonlocal problems for parabolic equations nagoya math j 93 1984 109 131 the theorems obtained in this paper can be applied in the theories of diffusion and heat conduction with better effects than the analogous theorems about parabolic initial boundary problems and than the analogous theorems about parabolic periodic boundary problems