• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.5
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• pp.850-858
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• 1997

A new a posteriori error estimator is introduced and applied to variational inequalities occurring in problems of flow through porous media. In order to construct element-wise a posteriori error estimates the global error is localized by a special mixed formulation in which continuity conditions at interfaces are treated as constraints. This approach leads to error indicators which provide rigorous upper bounds of the element errors. A discussion of a compatibility condition for the well-posedness of the local error analysis problem is given. Two numerical examples are solved to check the compatibility of the local problems and convergence of the effectivity index both in a local and a global sense with respect to local refinements.

• 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].

• 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 Institute of Intelligent Systems
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• v.20 no.1
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• pp.101-108
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• 2010

In this paper, we proposed a new lazy classifier with fuzzy k-nearest neighbors approach and feature selection which is based on reconstruction error. Reconstruction error is the performance index for locally linear reconstruction. When a new query point is given, fuzzy k-nearest neighbors approach defines the local area where the local classifier is available and assigns the weighting values to the data patterns which are involved within the local area. After defining the local area and assigning the weighting value, the feature selection is carried out to reduce the dimension of the feature space. When some features are selected in terms of the reconstruction error, the local classifier which is a sort of polynomial is developed using weighted least square estimation. In addition, the experimental application covers a comparative analysis including several previously commonly encountered methods such as standard neural networks, support vector machine, linear discriminant analysis, and C4.5 trees.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.12
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• pp.1046-1052
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• 2016

For the safe driving of autonomous vehicles, accurate position estimation is required. Generally, position error must be less than 1m because of lane keeping. However, GPS positioning error is more than 1m. Therefore, we must correct this error and a map matching algorithm is generally used. Especially, road marking intensity map have been used in many studies. In previous work, 3D LIDAR with many vertical layers was used to generate a local intensity map. Because it can be obtained sufficient longitudinal information for map matching. However, it is expensive and sufficient road marking information cannot be obtained in rush hour situations. In this paper, we propose a localization algorithm using an accumulated intensity local map. An accumulated intensity local map can be generated with sufficient longitudinal information using 3D LIDAR with a few vertical layers. Using this algorithm, we can also obtain sufficient intensity information in rush hour situations. Thus, it is possible to increase the reliability of the map matching and get accurate position estimation result. In the experimental result, the lateral RMS position error is about 0.12m and the longitudinal RMS error is about 0.19m.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.409-438
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• 2000

In this paper we develop a new procedure to control stepsize for Runge- Kutta methods applied to both ordinary differential equations and semi-explicit index 1 differential-algebraic equation In contrast to the standard approach, the error control mechanism presented here is based on monitoring and controlling both the local and global errors of Runge- Kutta formulas. As a result, Runge-Kutta methods with the local-global stepsize control solve differential of differential-algebraic equations with any prescribe accuracy (up to round-off errors)

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.4
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• pp.203-214
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• 2017

In this paper we propose and analyze two a posteriori error estimators for the stabilized $P_1/P_1$ finite element discretization of the Stokes equations. These error estimators are computed by solving local Poisson or Stokes problems on elements of the underlying triangulation. We establish their asymptotic exactness with respect to the velocity error under certain conditions on the triangulation and the regularity of the exact solution.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.167-177
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• 2012

In this article, we propose exponentially fitted error correction methods(EECM) which originate from the error correction methods recently developed by the authors (see [10, 11] for examples) for solving nonlinear stiff initial value problems. We reduce the computational cost of the error correction method by making a local approximation of exponential type. This exponential local approximation yields an EECM that is exponentially fitted, A-stable and L-stable, independent of the approximation scheme for the error correction. In particular, the classical explicit Runge-Kutta method for the error correction not only saves the computational cost that the error correction method requires but also gives the same convergence order as the error correction method does. Numerical evidence is provided to support the theoretical results.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.8
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• pp.678-687
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• 2005

This paper describes a relative localization algorithm using odometry data and consecutive local maps. The purpose of this paper is the odometry error correction using the area matching of two consecutive local maps. The local map is built up using a sensor module with dual laser beams and USB camera. The range data form the sensor module is measured using the structured lighting technique (active stereo method). The advantage in using the sensor module is to be able to get a local map at once within the camera view angle. With this advantage, we propose the AVS (Aligned View Sector) matching algorithm for. correction of the pose error (translational and rotational error). In order to evaluate the proposed algorithm, experiments are performed in real environment.