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For elliptic interface problems in two and three dimensions, this paper studies a priori and residual-based a posteriori error estimations for the Crouzeix–Raviart nonconforming and the discontinuous Galerkin finite element approximations. It is shown that both the a priori and the a posteriori error estimates are robust with respect to the diffusion coefficient, i.e., constants in the error bounds are independent of the jump of the diffusion coefficient. The a priori estimates are also optimal with respect to local regularity of the solution. Moreover, we obtained these estimates with no assumption on the distribution of the diffusion coefficient.

Three prominent low order implicit time integration schemes are the first order implicit Euler-method, the second order trapezoidal rule and the second order Ellsiepen method. Its advantages are stability and comparatively low computational cost, however, they require the solution of a nonlinear system of equations. This paper presents a general approach for the construction of third order Runge–Kutta methods by embedding the above mentioned implicit schemes into the class of ELDIRK-methods. These will be defined to have an Explicit Last stage in the general Butcher array of Diagonal Implicit Runge–Kutta (DIRK) methods, with the consequence, that no additional system of equations must be solved. The main results—valid also for non-linear ordinary differential equations—are as follows: Two extra function calculations are required in order to embed the implicit Euler-method and one extra function calculation is required for the trapezoidal-rule and the Ellsiepen method, in order to obtain the third order properties, respectively. Two numerical examples are concerned with a parachute with viscous damping and a two-dimensional laser beam simulation. Here, we verify the higher order convergence behaviours of the proposed new ELDIRK-methods, and its successful performances for asymptotically exact global error estimation of so-called reversed embedded RK-method are shown.

Data leakage is a common issue that can lead to misleading generalisation error estimation and incorrect hyperparameter tuning. However, its mechanisms are not always well understood. In this work, we consider the case of clustered data and investigate the distribution of the number of elements in leakage when the data set is uniformly split. For both the validation and test sets, the first and second moments of the number of elements in leakage are derived analytically. Modelling consequences are investigated and exemplified on simulated data. In addition, the case of an actual agronomic feasibility study is presented. We demonstrate how data leakage can distort model performance estimation when an inadequate data splitting strategy is used. We provide an understanding of data leakage in the context of clustered data by quantifying its role in predictive modelling. This sheds light on related challenges that may impact the practice in agronomy and beyond.

There have been many studies and much attention paid to spatial sharpening for thermal imagery. Among them, TsHARP, based on the good correlation between vegetation index and land surface temperature (LST), is regarded as a standard technique because of its operational simplicity and effectiveness. However, as LST is affected by other factors (e.g., soil moisture) in the areas with low vegetation cover, these areas cannot be well sharpened by TsHARP. Thin plate spline (TPS) is another popular downscaling technique for surface data. It has been shown to be accurate and robust for different datasets; however, it has not yet been attempted in thermal sharpening. This paper proposes to combine the TsHARP and TPS methods to enhance the advantages of each. The spatially explicit errors of these two methods were firstly estimated in theory, and then the results of TPS and TsHARP were combined with the estimation of their errors. The experiments performed across various landscapes and data showed that the proposed combined method performs more robustly and accurately than TsHARP.

Under the high dynamic conditions, Global Navigation Satellite System (GNSS) signals produce great Doppler frequency shifts, which hinders the fast acquisition of signals. Inertial Navigation System (INS)-aided acquisition can improve the acquisition performance, whereas the accuracy of Doppler shift and code phase estimation are mainly determined by the INS precision. The relation between the INS accuracy and Doppler shift estimation error has been derived, while the relation between the INS accuracy and code phase estimation error has not been deduced. In this paper, in order to theoretically analyze the effects of INS errors on the performance of Doppler shift and code phase estimations, the connections between them are re-deduced. Moreover, the curves of the corresponding relations are given for the first time. Then, in order to have a better verification of the INS-aided acquisition, a high dynamic scenario is designed. Furthermore, by using the deduced mathematical relation, the effects of different grade INS on the GNSS (including Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS)) signal acquisition are analyzed. Experimental results demonstrate that the INS-aided acquisition can reduce the search range of local frequency and code phase, and achieve fast acquisition. According to the experimental results, a suitable INS can be chosen for the deeply coupled integration.

In the last few years, considerable attention has been paid to the roof cladding systems due to their progressive use in the construction of low-rise buildings. The design of such systems has been gaining importance since they are subjected to severe damage and failure caused by high wind events, particularly at their fastener connection points. To offer a solution for predicting the maximum pull-out force capacity of cladding fasteners, this article presents a mathematical model for a fastener made of high strength steel austenitic 316. In this model, the two basic parameters of the fastener, namely the thread depth and the thread angle are included as the main elements of the contact surface between threads and the low carbon mild steel batten/purlin sheets. This mathematical model will be proposed to estimate the maximum pull-out force capacity of the cladding fasteners made of cold-formed A2 316 stainless steel. After finding the parameters of the mathematical model by using an optimization method based on a genetic algorithm (GA), a comparison will be made between the mean estimation error of the new model and the formerly proposed ones.

In this work, we realize goal-oriented error estimation using the dual-weighted residual method on general polygonal meshes. Such meshes are of current interest in various applications thanks to their great flexibility. Specifically the discrete problems are treated on BEM-based FEM. Our dual-weighted residual estimator is derived for two localization procedures. Firstly, a classical (strong) localization. Secondly, a weak form is adopted in which localization is achieved with the help of a partition-of-unity. The dual (i.e., adjoint) solution is obtained via a local higher-order approximation using a single element. Our algorithmic developments are substantiated with the help of several numerical tests.

This study investigates estimation errors due to hidden costs—the costs of implementation that are neglected in strategic decision-making processes—in the context of services offshoring. Based on data from the Offshoring Research Network, we find that decision makers are more likely to make cost-estimation errors given increasing configuration and task complexity in captive offshoring and offshore outsourcing, respectively. Moreover, we show that experience and a strong orientation toward organizational design in the offshoring strategy reduce the cost-estimation errors that follow from complexity. Our findings contribute to research on the effectiveness of sourcing and global strategies by stressing the importance of organizational design and experience in dealing with increasing complexity.

A goal-oriented a posteriori error estimator is derived to control the error obtained while approximately evaluating a quantity of engineering interest, represented in terms of a given linear or nonlinear functional, using extended finite elements of type. The same approximation method is used to solve the dual problem as required for the a posteriori error analysis. It is shown that for both problems to be solved numerically the same singular enrichment functions can be used. The goal-oriented error estimator presented can be classified as explicit residual type, i.e. the residuals of the approximations are used directly to compute upper bounds on the error of the quantity of interest. This approach therefore extends the explicit residual-type error estimator for classical energy norm error control as recently presented in Gerasimov et al. (Int J Numer Meth Eng 90:1118–1155, 2012a ). Without loss of generality, the a posteriori error estimator is applied to the model problem of linear elastic fracture mechanics. Thus, emphasis is placed on the fracture criterion, here the -integral, as the chosen quantity of interest. Finally, various illustrative numerical examples are presented where, on the one hand, the error estimator is compared to its finite element counterpart and, on the other hand, improved enrichment functions, as introduced in Gerasimov et al. ( 2012b ), are discussed.

This research introduces a novel convex methodology for estimating transmission loss coefficients ( B -coefficients) in power systems using a data-driven approach based on power system measurements. To enhance estimation accuracy and practical relevance, the model is evaluated across a wide spectrum of operating conditions, incorporating random variations in active power injections and demand profiles modeled via uniform and Gaussian distributions. A semi-definite programming (SDP) model leveraging p -norm formulations is proposed to derive the B -coefficients efficiently. Numerical evaluations on IEEE 14-, 39-, 57-, and 118-bus test feeders demonstrate the effectiveness and robustness of the approach, yielding average estimation errors between − 6 % and 5 % across diverse scenarios. These results confirm the reliability of the proposed methodology, contributing to improved accuracy in transmission loss modeling and supporting more efficient power system operations.