• Title, Summary, Keyword: Local Error

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Finite Element Analysis and Local a Posteriori Error Estimates for Problems of Flow through Porous Media (다공매체를 통과하는 유동문제의 유한요소해석과 부분해석후 오차계산)

  • Lee, Choon-Yeol
    • 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.

A Modified Mesh Generation Algorithm Using Pollution Error (Pollution error를 이용한 개선된 요소생성 알고리즘)

  • 유형선;장준환
    • Proceedings of the Computational Structural Engineering Institute Conference
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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.

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Error Control Strategy in Error Correction Methods

  • KIM, PHILSU;BU, SUNYOUNG
    • 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].

Design of Lazy Classifier based on Fuzzy k-Nearest Neighbors and Reconstruction Error (퍼지 k-Nearest Neighbors 와 Reconstruction Error 기반 Lazy Classifier 설계)

  • Roh, Seok-Beom;Ahn, Tae-Chon
    • Journal of 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.

A mesh generation based on the pollution error (Pollution 오차를 이용한 요소생성에 관한 연구)

  • 유형선;편수범
    • 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.

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Intensity Local Map Generation Using Data Accumulation and Precise Vehicle Localization Based on Intensity Map (데이터 누적을 이용한 반사도 지역 지도 생성과 반사도 지도 기반 정밀 차량 위치 추정)

  • Kim, Kyu-Won;Lee, Byung-Hyun;Im, Jun-Hyuck;Jee, Gyu-In
    • 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.

OPTIMAL ERROR ESTIMATE OF A DECOUPLED CONSERVATIVE LOCAL DISCONTINUOUS GALERKIN METHOD FOR THE KLEIN-GORDON-SCHRÖDINGER EQUATIONS

  • YANG, HE
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.24 no.1
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    • pp.39-78
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    • 2020
  • In this paper, we propose a decoupled local discontinuous Galerkin method for solving the Klein-Gordon-Schrödinger (KGS) equations. The KGS equations is a model of the Yukawa interaction of complex scalar nucleons and real scalar mesons. The advantage of our scheme is that the computation of the nucleon and meson field is fully decoupled, so that it is especially suitable for parallel computing. We present the conservation property of our fully discrete scheme, including the energy and Hamiltonian conservation, and establish the optimal error estimate.

A POSTERIORI ERROR ESTIMATORS FOR THE STABILIZED LOW-ORDER FINITE ELEMENT DISCRETIZATION OF THE STOKES EQUATIONS BASED ON LOCAL PROBLEMS

  • KIM, KWANG-YEON
    • 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.

Edge Enhanced Error Diffusion Based on Local Average of Original Image

  • Kang, Tae-Ha;Lee, Tae-Seung;Park, Hyeong-Taek;Hwang, Byong-Won
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.612-615
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    • 2003
  • The error diffusion is a good method to reconstruct the continuous tones of an image to the bilevel tones However the reconstruction of edge characteristic by the nor diffusion is represented work when power spectrum is analyzed fer display error. In this paper, we present an edge enhanced error diffusion method to preprocess original image to achieve the enhancement for the edge characteristic. The preprocessing algorithm consist of two processes. First the difference value between the current pixel and the local average of the surrounding pixel in original image is obtained. Second, the weighting function is composed by the magnitude and the sign of the local average. To confirm the effect of the proposed method, it is compared with the conventional edge enhanced error diffusion methods by measuring the radially averaged power spectrum densities (RAPSDs) for their display errors. The comparison result demonstrate the superiority of the proposed method over the conventional ones.

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Exponentially Fitted Error Correction Methods for Solving Initial Value Problems

  • Kim, Sang-Dong;Kim, Phil-Su
    • 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.