Error estimates for a sixth-order theory of plate bending

A refined linear theory for the bending of anisotropic, homogeneous plates which takes account of transverse shear deformation and transverse normal stress is rigorously validated by imbedding it in the linear theory of elasticity. Three-dimensional displacement and stress fields are constructed from the two-dimensional plate theory and shown by the hypersphere theorem to approximate exact elasticity solutions with a relative mean square error proportional to the plate thickness cubed. This improves previous estimates for sixth-order theories involving error bounds proportional to the square of thickness.     

Error estimates and adaptive refinement for plate bending problems

The Zienkiewicz–Zhu error estimator is shown to be effective in problems of plate flexure. When used in conjunction with triangular elements and an adaptive mesh generator allowing a prescribed size of elements to be developed, very fast adaptive convergence for results of specified accuracy is achieved.     

Error estimates and convergence rates for various incompressible elements

This note reports numerical experiments on the efficiency of simple error estimates derived earlier¹ applied to incompressible mixed or related penalty type formulations. The rate of convergence and performance of various mixed elements is compared. Numerical results from a driven cavity and an incompressible elastic problem demonstrate that the T6B1/3D and T6/3C elements give a faster rate of convergence than the T6/1D element. However, in the case of a plane extrusion analysis (stronger singularity), the rate of convergence for the T6B1/3D element drops and is inferior to that of the T6/1D, while the T6/3C element still proves superior to the other two elements.     

Bounds on frequency response estimates derived from uncertain stepresponse data

The frequency response of a system can be estimated from measurements of its step response; however, many error sources affect the accuracy of such estimates. This paper investigates the effects of uncertainty in the knowledge of the step response. Methods for establishing uncertainty bounds for the frequency response estimates are developed, based on the corresponding time-domain uncertainties associated with the measured step response. Two methods are described. One method produces bounds that are often very conservative. The other method produces bounds that are more realistic. End effects that influence the bounds are also considered. A simulation example and an application of the bounds are presented     

Error estimates of numerical solutions for a cyclic plasticity problem

A cyclic plasticity problem is numerically analyzed in [13], where a sub-optimal order error estimate is shown for a spatially discrete scheme. In this note, we prove an optimal order error estimate for the spatially discrete scheme under the same solution regularity condition. We also derive an error estimate for a fully discrete scheme for solving the plasticity problem.     

Error estimates for mixed finite element approximations of nonlinear problems

The finite element methods have proved a very effective tool for the numerical solutions of nonlinear problems arising in elasticity and other related engineering sciences. Relative to linear elliptic theory, little is known about the accuracy and convergence properties of mixed finite element approximation of nonlinear elliptic boundary value problems. The nonlinear problems are much more complicated, since each problem has to be treated individually. This is one of the reasons that there is no unified and general theory for the nonlinear problems. In this paper, the application of the mixed finite element method to a highly nonlinear Dirichlet problem, which arises in the field of oceanography and elasticity is studied and new results involving the error estimates are derived. In fact, some of the results and methods to be described in this paper may be extended to more complicated problems or problems with other boundary conditions. As a special case, we obtain the well known error estimates for the corresponding linear and mildly nonlinear elliptic boundary value problems.     

Error estimates of mixed methods for optimal control problems governed by parabolic equations

In this paper, we investigate the error estimates for the solutions of parabolic optimal control problem by mixed finite element methods. The state and co‐state are approximated by the lowest‐order Raviart–Thomas mixed finite element spaces, and the control is approximated by piecewise constant functions. The convergence for the states, co‐states and the control is demonstrated. Copyright © 2008 John Wiley & Sons, Ltd.     

Reliability estimates for data recovered from compact discs

Data reliability at the output of the error-correction code decoderin a compact-disc system is influenced by the decoding strategyemployed by the decoder, as well as by the statistical distribution oferrors that contaminate the recorded data. Recovered-datareliability estimates have been computed by use of error statisticsobtained from the measurement of errors that contaminate the actualdata stored on clean write-once and read-only-memory compactdiscs. These estimates consist of probabilities that specify theoccurrence of residual errors in the data that appear at the output ofa compact-disc player's cross-interleaved Reed-Solomon code(CIRC) decoder. Data reliability estimates that apply to fivespecific CIRC decoding strategies are reported.     

Measured and calculated angular responses of panasonic UD-809 thermoluminescence dosemeters to neutrons

Multi-element thermoluminescence dosemeters (TLD), such as the Panasonic UD-809, are used in personal dosimetry. The Panasonic UD-809 dosemeter consists of one gamma sensitive and three neutron sensitive TLD elements with different filter materials. In this work, the neutron energy responses (the number of (n,alpha) reactions per neutron) of the neutron-sensitive TLD elements of the Panasonic UD-809 dosemeter were calculated using the MCNP Monte Carlo transport code. Experiments were performed in a calibration geometry with an unmoderated 252Cf neutron source. These measurements were made with the dosemeter placed on the centre front face of a polymethylmethacrylate (PMMA) slab phantom. The phantom was rotated in the horizontal plane from -90 to +90 degrees, in 15 degree increments. Good agreement between calculated and measured element responses was observed. The angular dependency of personal dose equivalent was also calculated for parallel beams of 252Cf neutrons and compared to the TLD element angular responses.     

Error estimates for isoparametric mixed finite element solution of 4th order elliptic problems with variable coefficients

 Considering the combined effect of boundary approximation and numerical integration, error estimates for the isoparametric mixed finite element solution of fourth order elliptic problems with variable coefficients in convex domains, which, in the particular case of aniso-/ortho-/ isotropic plate bending problems, gives a direct and simultaneous approximation to bending moment tensor field Ψ=(ψ _ij ) _1≤i,j≤2 and displacement field `u', have been developed. Results of numerical experiments justify the theoretical results. Received 20 July 2001 / Accepted 28 November 2001     

Comparisons of polymer/gas partition coefficients calculated from responses of thickness shear mode and surface acoustic wave vapor sensors

Apparent partition coefficients, K, for the sorption of toluene by four different polymer thin films on thickness shear mode (TSM) and surface acoustic wave (SAW) devices are compared. The polymers examined were poly(isobutylene) (PIB), poly(epichlorohydrin) (PECH), poly(butadiene) (PBD), and poly(dimethylsiloxane) (PDMS). Independent data on partition coefficients for toluene in these polymers were compiled for comparison, and TSM sensor measurements were made using both oscillator and impedance analysis methods. K values from SAW sensor measurements were about twice those calculated from TSM sensor measurements when the polymers were PIB and PECH, and they were also at least twice the values of the independent partition coefficient data, which is interpreted as indicating that the SAW sensor responds to polymer modulus changes as well as to mass changes. K values from SAW and TSM measurements were in agreement with each other and with independent data when the polymer was PBD. Similarly, K values from the PDMS-coated SAW sensor were not much larger than values from independent measurements. These results indicate that modulus effects were not contributing to the SAW sensor responses in the cases of PBD and PDMS. However, K values from the PDMS-coated TSM device were larger than the values from the SAW device or independent measurements, and the impedance analyzer results indicated that this sensor using our sample of PDMS at the applied thickness did not behave as a simple mass sensor. Differences in behavior among the test polymers on SAW devices are interpreted in terms of their differing viscoelastic properties.     

Error sources and error estimates in flow-injection determination of oxidizing and reducing agents

We have determined the sources of the greatest error in determination of oxidizing and reducing agents in a flow-injection approach using a platinum electrode. We have numerically estimated each of the error components. Translated from Izmeritel'naya Tekhnika, No.5, pp. 62–64, May, 1998.     

Error estimates in coordinate measurements of the cross section parameters of cylindrical surfaces

A simulation method and the results of simulating the errors in coordinate measurements of the cross section parameters of cylindrical surfaces are discussed. Data are presented from experimental studies that confirm the simulations.     

Using rays better. III. Error estimates and illustrative applications in smooth media

A new method for computing ray-based approximations to optical wave fields is demonstrated through simple examples involving wave propagation in free space and in a gradient-index waveguide. The analytic solutions that exist for these cases make it easy to compare the new estimates with exact results. A particularly simple RMS error estimate is developed here, and corrections to the basic field estimate are also discussed and tested. A key step for any ray-based method is the choice of a family of rays to be associated with the initial wave field. We show that, for maximal accuracy, not only must the initial field be considered in choosing the rays, but so too must the medium that is to carry the wave.     

Velocity distributions calculated from the Fourier transforms ofRamsey lineshapes

A computerized method for finding velocity distributions from the Fourier transforms of Ramsey lineshapes has been developed. Experimental and numerical tests of the method show that it works very well for broad distributions and lineshapes where the drift time is much longer than the excitation time. The method is routinely used to find velocity distributions for the primary frequency standard NIST-7. The second-order Doppler shift is calculated from these distributions with an uncertainty of a few tenths of 1 percent     

Non-Newtonian flow between concentric cylinders calculated from thermophysical properties obtained from simulations

A study of the Weissenberg effect (rod climbing in a stirred system) based on nonequilibrium molecular dynamics (NEMD) is reported. Simulation results from a soft-sphere fluid are used to obtain a self-consistent free-surface profile of the fluid of finite compressibility undergoing Couette flow between concentric cylinders. A numerical procedure is then applied to calculate the height profile for a hypothetical fluid with thermophysical properties of the soft-sphere liquid and of a dense colloidal suspension. The height profile calculated is identified with shear thickening and the forms of the viscometric functions. The maximum climb occurs between the cylinders rather than at the inner cylinder.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.