A posteriori error estimates of discontinuous Galerkin methods for the Signorini problem

A reliable and efficient a posteriori error estimator is derived for a class of discontinuous Galerkin (DG) methods for the Signorini problem. A common property shared by many DG methods leads to a unified error analysis with the help of a constraint preserving enriching map. The error estimator of DG methods is comparable with the error estimator of the conforming methods. Numerical experiments illustrate the performance of the error estimator. (C) 2015 Elsevier B.V. All rights reserved.

A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.

Evaluation and Minimization of Low-Order Harmonic Torque in Low-Switching-Frequency Inverter-Fed Induction Motor Drives

A low-order harmonic pulsating torque is a major concern in high-power drives, high-speed drives, and motor drives operating in an overmodulation region. This paper attempts to minimize the low-order harmonic torques in induction motor drives, operated at a low pulse number (i.e., a low ratio of switching frequency to fundamental frequency), through a frequency domain (FD) approach as well as a synchronous reference frame (SRF) based approach. This paper first investigates FD-based approximate elimination of harmonic torque as suggested by classical works. This is then extended into a procedure for minimization of low-order pulsating torque components in the FD, which is independent of machine parameters and mechanical load. Furthermore, an SRF-based optimal pulse width modulation (PWM) method is proposed to minimize the low-order harmonic torques, considering the motor parameters and load torque. The two optimal methods are evaluated and compared with sine-triangle (ST) PWM and selective harmonic elimination (SHE) PWM through simulations and experimental studies on a 3.7-kW induction motor drive. The SRF-based optimal PWM results in marginally better performance than the FD-based one. However, the selection of optimal switching angle for any modulation index (M) takes much longer in case of SRF than in case of the FD-based approach. The FD-based optimal solutions can be used as good starting solutions and/or to reasonably restrict the search space for optimal solutions in the SRF-based approach. Both of the FD-based and SRF-based optimal PWM methods reduce the low-order pulsating torque significantly, compared to ST PWM and SHE PWM, as shown by the simulation and experimental results.

Evaluation of the Effectiveness of Representative Methods for Determining Young's Modulus and Hardness from Instrumented Indentation Data

The effectiveness of Oliver & Pharr's (O&P's) method, Cheng & Cheng's (C&C's) method, and a new method developed by our group for estimating Young's modulus and hardness based on instrumented indentation was evaluated for the case of yield stress to reduced Young's modulus ratio (sigma(y)/E-r) >= 4.55 x 10(-4) and hardening coefficient (n) <= 0.45. Dimensional theorem and finite element simulations were applied to produce reference results for this purpose. Both O&P's and C&C's methods overestimated the Young's modulus under some conditions, whereas the error can be controlled within +/- 16% if the formulation was modified with appropriate correction functions. Similar modification was not introduced to our method for determining Young's modulus, while the maximum error of results was around +/- 13%. The errors of hardness values obtained from all the three methods could be even larger and were irreducible with any correction scheme. It is therefore suggested that when hardness values of different materials are concerned, relative comparison of the data obtained from a single standard measurement technique would be more practically useful. It is noted that the ranges of error derived from the analysis could be different if different ranges of material parameters sigma(y)/E-r and n are considered.

Development of a classical force field for the oxidized Si surface: application to hydrophilic wafer bonding.

We have developed a classical two- and three-body interaction potential to simulate the hydroxylated, natively oxidized Si surface in contact with water solutions, based on the combination and extension of the Stillinger-Weber potential and of a potential originally developed to simulate SiO(2) polymorphs. The potential parameters are chosen to reproduce the structure, charge distribution, tensile surface stress, and interactions with single water molecules of a natively oxidized Si surface model previously obtained by means of accurate density functional theory simulations. We have applied the potential to the case of hydrophilic silicon wafer bonding at room temperature, revealing maximum room temperature work of adhesion values for natively oxidized and amorphous silica surfaces of 97 and 90 mJm(2), respectively, at a water adsorption coverage of approximately 1 ML. The difference arises from the stronger interaction of the natively oxidized surface with liquid water, resulting in a higher heat of immersion (203 vs 166 mJm(2)), and may be explained in terms of the more pronounced water structuring close to the surface in alternating layers of larger and smaller densities with respect to the liquid bulk. The computed force-displacement bonding curves may be a useful input for cohesive zone models where both the topographic details of the surfaces and the dependence of the attractive force on the initial surface separation and wetting can be taken into account.