Numerical analysis of two frictionless elastic-piezoelectric contact problems

In this work, we consider two frictionless contact problems between an elastic-piezoelectric body and an obstacle. The linear elastic-piezoelectric constitutive law is employed to model the piezoelectric material and either the Signorini condition (if the obstacle is rigid) or the normal compliance condition (if the obstacle is deformable) are used to model the contact. The variational formulations are derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a discrete scheme is introduced based on the finite element method to approximate the spatial variable. Error estimates are derived on the approximate solutions and, as a consequence, the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, some two-dimensional examples are presented to demonstrate the performance of the algorithm.     

Error analysis of the numerical solution of split differential equations

The operator splitting method is a widely used approach for solving partial differential equations describing physical processes. Its application usually requires the use of certain numerical methods in order to solve the different split sub-problems. The error analysis of such a numerical approach is a complex task. In the present paper we show that an interaction error appears in the numerical solution when an operator splitting procedure is applied together with a lower-order numerical method. The effect of the interaction error is investigated by an analytical study and by numerical experiments made for a test problem.     

控制电位滴定法的误差分析

研究了影响控制电位滴定法测定结果准确度的因素,得到的结论是:第一,电位的控制误差及滴定剂体积的测定误差是影响控制电位滴定法测定结果准确度的主要因素.计算模型中的比例系数越大,滴定曲线的变化率越大,这种影响越小.第二,多组分体系的测定误差,与组分在计算模型中比例系数的相对大小有关.比例系数越大,测定误差越小.第三,不同浓度(或不同浓度比)待测溶液滴定曲线的差异越大,对控制电位滴定法的测定越有利.     

CONVERGENCE OF AN IMMERSED INTERFACE UPWIND SCHEME FOR LINEAR ADVECTION EQUATIONS WITH PIECEWISE CONSTANT COEFFICIENTS I： L^1-ERROR ESTIMATES

We study the L^l-error estimates for the upwind scheme to the linear advection equations with a piecewise constant coefficients modeling linear waves crossing interfaces. Here the interface condition is immersed into the upwind scheme. We prove that, for initial data with a bounded variation, the numerical solution of the immersed interface upwind scheme converges in L^l-norm to the differential equation with the corresponding interface condition. We derive the one-halfth order L^l-error bounds with explicit coefficients following a technique used in [25]. We also use some inequalities on binomial coefficients proved in a consecutive paper [32].     

Error bounds for asymptotic expansions of the distribution of the MLE in a GMANOVA model

Summary In this paper we obtain asymptotic expansions for the distribution function and the density function of a linear combination of the MLE in a GMANOVA model, and for the density function of the MLE itself. We also obtain certain error bounds for the asymptotic expansions.     

On simplifying ‘incremental remap’–based transport schemes

The flux-form incremental remapping transport scheme introduced by Dukowicz and Baumgardner [1] converts the transport problem into a remapping problem. This involves identifying overlap areas between quadrilateral flux-areas and regular square grid cells which is non-trivial and leads to some algorithm complexity. In the simpler swept area approach (originally introduced by Hirt et al. [2]) the search for overlap areas is eliminated even if the flux-areas overlap several regular grid cells. The resulting simplified scheme leads to a much simpler and robust algorithm.     

Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations

We study a family of generalized slope limiters in two dimensions for Runge–Kutta discontinuous Galerkin (RKDG) solutions of advection-diffusion systems. We analyze the numerical behavior of these limiters applied to a pair of model problems, comparing the error of the approximate solutions, and discuss each limiter’s advantages and disadvantages. We then introduce a series of coupled p-enrichment schemes that may be used as standalone dynamic p-enrichment strategies, or may be augmented via any in the family of variable-in-p slope limiters presented.     

On the robustness of Harris detector in image watermarking attacks

This paper investigates the misplacement issue presented on the detection of feature points by using the well-known Harris detector, under several watermarking attacks. Harris detector, as a powerful tool in finding image's points of high importance, called “interest points”, has been widely used to locate specific image portions where watermarks are embedded, according to some watermarking insertion procedure. Although Harris detector constitutes a significant part of a typical feature-based watermarking process, no work dealing with its performance under certain attacks has been reported yet. This work studies the accuracy of Harris detector in finding the feature points, which define the watermarked regions of attacked images, firstly as an individual processing module and secondly as a part of a feature-based watermarking methodology. Detailed theoretical analysis followed by appropriate simulation experiments has shown that the incorporation of the Harris detector into the watermarking procedure presents misplacement issues that can lead the watermarking algorithm to unreliable results. In the way of decreasing these misplacement errors, a novel algorithm that extracts more stable interest points, with promising performance is also proposed.     

Sub-pixel processing algorithm based on boundary recursion and error optimization in staring FPA nonuniform micro-scanning imaging

For the 2 × 2 nonuniform micro-scanning, of which the interframe displacement is no longer equivalent to accurate half-pixel, a sub-pixel processing algorithm based on boundary recursion and error optimization is proposed in this paper. Boundary recursive technique is introduced to solve the ill-posed problem in the process of nonuniform micro-scanning sub-pixel image reconstruction, but the manually predefined boundary values in boundary recursion inevitably result in error. Aiming at eliminating the error in boundary recursion, error optimization based on gray statistical principle is used in this paper. All the simulation results and experiment data show that the algorithm proposed in this paper can realize accurate sub-pixel imaging and improve image resolution. The algorithm is robust, simple and effective, and it is hopeful to be used in actual system.     

An enhanced finite volume method to model 2D linear elastic structures

This paper details the evaluation and enhancement of the vertex-centred finite volume method for the purpose of modelling linear elastic structures undergoing bending. A matrix-free edge-based finite volume procedure is discussed and compared with the traditional isoparametric finite element method via application to a number of test-cases. It is demonstrated that the standard finite volume approach exhibits similar disadvantages to the linear Q4 finite element formulation when modelling bending. An enhanced finite volume approach is proposed to circumvent this and a rigorous error analysis conducted. It is demonstrated that the developed finite volume method is superior to both standard finite volume and Q4 finite element methods, and provides a practical alternative to the analysis of bending-dominated solid mechanics problems.