On one approach to a posteriori error estimates for evolution problems solved by the method of lines

Summary. In this paper, we describe a new technique for a posteriori error estimates suitable to parabolic and hyperbolic equations solved by the method of lines. One of our goals is to apply known estimates derived for elliptic problems to evolution equations. We apply the new technique to three distinct problems: a general nonlinear parabolic problem with a strongly monotonic elliptic operator, a linear nonstationary convection-diffusion problem, and a linear second order hyperbolic problem. The error is measured with the aid of the -norm in the space-time cylinder combined with a special time-weighted energy norm. Theory as well as computational results are presented. Received September 2, 1999 / Revised version received March 6, 2000 / Published online March 20, 2001     

η%-Superconvergence of Finite Element Solutions and Error Estimators

This paper is a summary of our study on the superconvergence of the finite element solutions and error estimators. We will persent the analysis of %-superconvergence for finite element solutions of the Poisson equation in the interior of meshes of triangles with straight edges, as well as the analysis at the boundary. The %-superconvergence via local averaging will also be presented, and the error estimators are compared in the sense of %-superconvergence.     

Multi-level scheduling decisions in a class of FMS using simulation based metamodels

This paper pertains to a detailed simulation study conducted on a typical Flexible Manufacturing System (FMS). Initially, the configurations of the FMS under study have been established. Two types of FMSs have been evolved: one is failure free and the other is failure prone. For each of these cases, simulation models have been developed using SLAMSYSTEM. Orders arriving randomly at the FMS are subjected to three levels of scheduling decisions namely, launching of parts into the system, routing of parts through machines and sequencing of parts on AGVs at a central buffer. The simulation results have been used to develop metamodels for the two types of FMSs. These metamodels have been subjected to statistical analysis to ascertain their adequacy to represent the simulation models. These metamodels have been found to be useful for simulating the FMSs under study so as to evaluate various multi-level scheduling decisions in the FMS.     

Thermal post-buckling analysis of square plates resting on elastic foundation: A simple closed-form solutions

Thermal post-buckling paths of homogeneous, isotropic, square plate configurations resting on elastic foundation (Winkler type) subjected to biaxial compressive thermal loads are expressed as simple closed-form solutions by using the Rayleigh–Ritz method based on coupled displacement fields. Geometric non-linearity of von-Karman type is considered. The in-plane displacement field variations used in the formulation of Rayleigh–Ritz method are derived by using the governing in-plane static differential equations of the plate which in turn simplifies the difficulty of assuming an in-plane displacement field variations of the square plate. Accuracy and robustness of the proposed closed-form solutions are demonstrated by using the non-linear finite element formulation results which are obtained from an equilibrium path approach.     

Dimensional reduction for Helmholtz's equation on a bounded domain

Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain by replacing them with systems of equations in dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution and the dimensionally reduced solution of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference between and in is estimated as and are fixed. Finally, some numerical experiments in a domain are given in order to compare theretical results. Received April 2, 1996 / Revised version received July 30, 1990     

Voice responses to changes in pitch of voice or tone auditory feedback

The present study was undertaken to examine if a subject's voice F0 responded not only to perturbations in pitch of voice feedback but also to changes in pitch of a side tone presented congruent with voice feedback. Small magnitude brief duration perturbations in pitch of voice or tone auditory feedback were randomly introduced during sustained vowel phonations. Results demonstrated a higher rate and larger magnitude of voice F0 responses to changes in pitch of the voice compared with a triangular-shaped tone (experiment 1) or a pure tone (experiment 2). However, response latencies did not differ across voice or tone conditions. Data suggest that subjects responded to the change in F0 rather than harmonic frequencies of auditory feedback because voice F0 response prevalence, magnitude, or latency did not statistically differ across triangular-shaped tone or pure-tone feedback. Results indicate the audio-vocal system is sensitive to the change in pitch of a variety of sounds, which may represent a flexible system capable of adapting to changes in the subject's voice. However, lower prevalence and smaller responses to tone pitch-shifted signals suggest that the audio-vocal system may resist changes to the pitch of other environmental sounds when voice feedback is present.