• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.735-748
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• 1998

We analyze the error in the p version of the of the finite element method when the effect of the quadrature error is taken in the load vector. We briefly study some results on the $H^{1}$ norm error and present some new results for the error in the $L^{2}$ norm. We inves-tigate the quadrature error due to the numerical integration of the right hand side We present theoretical and computational examples showing the sharpness of our results.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.311-327
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• 2016

In this paper, we propose an error embedded Runge-Kutta method to improve the traditional embedded Runge-Kutta method. The proposed scheme can be applied into most explicit embedded Runge-Kutta methods. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, the van der Pol equation and another one having a difficulty for the global error control are numerically solved. Finally, a two-body Kepler problem is also used to assess the efficiency of the proposed algorithm.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.34-42
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• 2001

In this paper, we study on a modified mesh generation method based on the pollution error estimate. This method is designed for the control of the pollution error in any patch of elements of interest. It is a well-known fact that the pollution error estimates are much more than the local one. Reliable a posteriori error estimation is possible by controlling the pollution error in the patch through proper design of the mesh outside the patch. This design is possible by equally distributing the pollution error indicators over the mesh outside the patch. The conventional feedback pollution-adaptive mesh generation algorithm needs many iterations. Therefore, the solution time is significant. But we use the remeshing scheme in the proposed method. We will also show that the pollution error reduces less than the local error.

• Journal of the Korean Society for Railway
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• v.2 no.3
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• pp.46-53
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• 1999

In this paper, made was a study on a mesh generation method based on the pollution error. This method is designed for the control of the pollution error in any patch of elements of interest. It is a well-known fact that the pollution error estimates are much more than the local one. When the pollution error is significant, nothing can be said about the reliability of any estimator based on local computations in the patch. Reliable a posteriori error estimation is possible by controlling the pollution error in the patch through proper design of the mesh outside the patch. This design is possible by equally distributing the pollution error indicators over the mesh outside the patch. The mesh generated from the conventional feedback pollution-adaptive mesh generation algorithm needs many iterations. Therefore, the solution time is significant. But the remeshing scheme in the proposed method was used here. It was shown that the pollution-adaptive mesh improves the E.I., simply denoted as Effectivity Index, on the patch of interest, and the pollution error reduces less than the local error.

• Journal of the Korean Society for Precision Engineering
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• v.11 no.4
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• pp.158-164
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• 1994

A volumetric error compensation method was stueide with measuring systematic error of a Coordinate Measuring Machine(CMM). The volumetric error equations were proposed for a Moving Bridge type CMM. Using the error equations, error vectors in the measuring volume were corrected by a software method. The CMM was controlled by the compensation program separately in the measuring and moving function of the CMM proving. The linear accuracy of the CMM was measured by the Laser Interferometer and compared with the data before the volumetric error compensation. This method was proved as low cost and effective to reduce the systematic error of the CMM, as no hardware modification is required.

• Journal of Advanced Navigation Technology
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• v.15 no.5
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• pp.850-856
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• 2011

The error diffusion method is one of the digital halftoning methods that diffuses quantization errors of current processing pixel to neighboring pixels and get a high-quality black-white image. This method has the problematic case which partially increase or decrease summation of diffused errors in the process of diffusing the quantization error. In this paper, we analyze Floyd-Steinberg method, Jarvis-Judice-Ninke method, Stucki method, and Shiau-Fan method as a representative case of error diffusion methods and propose a solution method of this problem.

• Journal of Korean Society of Transportation
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• v.21 no.2
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• pp.119-130
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• 2003

SP data have been widely used in assessing new transport policies and transport related plans. However, one of criticisms of using SP is that respondents may show different reaction between hypothetical experiments and real life. In order to overcome the problem, combination of SP and RP data has been suggested and the combined methods have been being developed. The purpose of this paper is to suggest a new SP and RP combined method using error component method and to verify the method. The error component method decomposes IID extreme value error into non-IID error component(s) and an IID error component. The method estimates both of component parameters and utility parameters in order to obtain relative variance of SP data and RP data. The artificial SP and RP data was created by using simulation and used for the analysis, and the estimation results of the error component method were compared with those of existing SP and RP combined methods. The results show that regardless of data size, the parameters of the error component method models are similar to those assumed parameters much more than those of the existing SP and RP combined models, indicating usefulness of the error component method. Also the values of time for error component method are more similar to those assumed values than those of the existing combined models. Therefore, we can conclude that the error component method is useful in combining SP and RP data and more efficient than the existing methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.1
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• pp.1-13
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• 2012

In this paper we present an a posteriori error estimator for the stabilized P1 nonconforming finite element method of the linear elasticity problem based on a nonsymmetric H(div)-conforming approximation of the stress tensor in the first-order Raviart-Thomas space. By combining the equilibrated residual method and the hypercircle method, it is shown that the error estimator gives a fully computable upper bound on the actual error. Numerical results are provided to confirm the theory and illustrate the effectiveness of our error estimator.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.301-311
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• 2015

In this paper, we present the error control techniques for the error correction methods (ECM) which is recently developed by P. Kim et al. [8, 9]. We formulate the local truncation error at each time and calculate the approximated solution using the solution and the formulated truncation error at previous time for achieving uniform error bound which enables a long time simulation. Numerical results show that the error controlled ECM provides a clue to have uniform error bound for well conditioned problems [1].

• Transactions of Materials Processing
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• v.13 no.7
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• pp.594-599
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• 2004

In the sheet metal forming operations, the strain measurement of sheet panel is an essential work which provides the formability information needed in die design, process design, and product inspection. To measure efficiently complex geometry strains, the 3-dimensional automative strain measurement system, which theoretically has a high accuracy but practically has about 3～5％ strain error, is often used. For eliminating the strain error resulted in measuring the strains of formed panels using an automated strain measurement system, the position error calibration method is suggested, which computes accurate strains using the grids with accurate nodal coordinates. The accurate nodal coordinates are calculated by adding the nodal coordinates measured by the measurement system and the position error found using the multiple regression method as a function of the main error parameters obtained from the analysis of strain error in a standard cube. For the verification, the strain distributions of square and dome cups obtained from the position error calibration method are compared with those provided by the finite element analysis and ASAME.