• 제목/요약/키워드: optimal error estimate

검색결과 163건 처리시간 0.025초

$L^{\infty}$-CONVERGENCE OF MIXED FINITE ELEMENT METHOD FOR LAPLACIAN OPERATOR

  • Chen, Huan-Zhen;Jiang, Zi-Wen
    • Journal of applied mathematics & informatics
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    • 제7권1호
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    • pp.61-82
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    • 2000
  • In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

수정 SPR 기법에 의한 휨을 받는 평판문제의 적응적 p-체눈 세분화 (p-Adaptive Mesh Refinement of Plate Bending Problem by Modified SPR Technique)

  • 조준형;이희정;우광성
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 2007년도 정기 학술대회 논문집
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    • pp.481-486
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    • 2007
  • The Zienkiewicz-Zhu(Z/Z) error estimate is slightly modified for the hierarchical p-refinement, and is then applied to L-shaped plates subjected to bending to demonstrate its effectiveness. An adaptive procedure in finite element analysis is presented by p-refinement of meshes in conjunction with a posteriori error estimator that is based on the superconvergent patch recovery(SPR) technique. The modified Z/Z error estimate p-refinement is different from the conventional approach because the high order shape functions based on integrals of Legendre polynomials are used to interpolate displacements within an element, on the other hand, the same order of basis function based on Pascal's triangle tree is also used to interpolate recovered stresses. The least-square method is used to fit a polynomial to the stresses computed at the sampling points. The strategy of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed such that a particular element has to be refined automatically to obtain an acceptable level of accuracy by increasing p-levels non-uniformly or selectively. It is noted that the error decreases rapidly with an increase in the number of degrees of freedom and the sequences of p-distributions obtained by the proposed error indicator closely follow the optimal trajectory.

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물체의 분광반사율 추정을 위한 최적필터의 선정 (Optimization of color filters selection to estimate surface spectral reflectance of Munsell colors)

  • 이승희;이을환;유미옥;노상철;안석출
    • 한국인쇄학회지
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    • 제16권3호
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    • pp.121-131
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    • 1998
  • The object color does not look same under the different light source. It depends on the surface spectral reflectance and the spectral distribution of light source. Therefore we should find the surface spectral reflectance of object color and the spectral distribution of light source for color reproduction. Using Wiener estimation, we can estimate the spectral reflectance from low dimensional images obtained with multi-band image acquisition system. The kind and the number of imaging filters have the effect on the estimation of the spectral reflectance. Therefore it is important that optimal filters are selected to minimize the error of the result. In this paper, we describe methods to select optimal filters with minimum error between measured and estimated surface spectral reflectance and to estimate surface spectral reflectance of Munsell color chart from six multi-band images by using Wiener estimation.

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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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    • 제24권1호
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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 CONSISTENT DISCONTINUOUS BUBBLE SCHEME FOR ELLIPTIC PROBLEMS WITH INTERFACE JUMPS

  • KWONG, IN;JO, WANGHYUN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제24권2호
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    • pp.143-159
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    • 2020
  • We propose a consistent numerical method for elliptic interface problems with nonhomogeneous jumps. We modify the discontinuous bubble immersed finite element method (DB-IFEM) introduced in (Chang et al. 2011), by adding a consistency term to the bilinear form. We prove optimal error estimates in L2 and energy like norm for this new scheme. One of the important technique in this proof is the Bramble-Hilbert type of interpolation error estimate for discontinuous functions. We believe this is a first time to deal with interpolation error estimate for discontinuous functions. Numerical examples with various interfaces are provided. We observe optimal convergence rates for all the examples, while the performance of early DB-IFEM deteriorates for some examples. Thus, the modification of the bilinear form is meaningful to enhance the performance.

QUADRATURE BASED FINITE ELEMENT METHODS FOR LINEAR PARABOLIC INTERFACE PROBLEMS

  • Deka, Bhupen;Deka, Ram Charan
    • 대한수학회보
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    • 제51권3호
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    • pp.717-737
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    • 2014
  • We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal $L^2(L^2)$ and $L^2(H^1)$ error estimates are shown to hold for semidiscrete problem under suitable regularity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal $L^2(L^2)$ norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

Gaussian noise addition approaches for ensemble optimal interpolation implementation in a distributed hydrological model

  • Manoj Khaniya;Yasuto Tachikawa;Kodai Yamamoto;Takahiro Sayama;Sunmin Kim
    • 한국수자원학회:학술대회논문집
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    • 한국수자원학회 2023년도 학술발표회
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    • pp.25-25
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    • 2023
  • The ensemble optimal interpolation (EnOI) scheme is a sub-optimal alternative to the ensemble Kalman filter (EnKF) with a reduced computational demand making it potentially more suitable for operational applications. Since only one model is integrated forward instead of an ensemble of model realizations, online estimation of the background error covariance matrix is not possible in the EnOI scheme. In this study, we investigate two Gaussian noise based ensemble generation strategies to produce dynamic covariance matrices for assimilation of water level observations into a distributed hydrological model. In the first approach, spatially correlated noise, sampled from a normal distribution with a fixed fractional error parameter (which controls its standard deviation), is added to the model forecast state vector to prepare the ensembles. In the second method, we use an adaptive error estimation technique based on the innovation diagnostics to estimate this error parameter within the assimilation framework. The results from a real and a set of synthetic experiments indicate that the EnOI scheme can provide better results when an optimal EnKF is not identified, but performs worse than the ensemble filter when the true error characteristics are known. Furthermore, while the adaptive approach is able to reduce the sensitivity to the fractional error parameter affecting the first (non-adaptive) approach, results are usually worse at ungauged locations with the former.

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THE HP-VERSION OF THE FINITE ELEMENT METHOD UNDER NUMERICAL QUADRATURE RULES

  • Kim, Ik-Sung
    • East Asian mathematical journal
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    • 제14권1호
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    • pp.63-76
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    • 1998
  • we consider the hp-version to solve non-constant coefficients elliptic equations $-div(a{\nabla}u)=f$ with Dirichlet boundary conditions on a bounded polygonal domain $\Omega$ in $R^2$. In [6], M. Suri obtained an optimal error-estimate for the hp-version: ${\parallel}u-u^h_p{\parallel}_{1,\Omega}{\leq}Cp^{(\sigma-1)}h^{min(p,\sigma-1)}{\parallel}u{\parallel}_{\sigma,\Omega}$. This optimal result follows under the assumption that all integrations are performed exactly. In practice, the integrals are seldom computed exactly. The numerical quadrature rule scheme is needed to compute the integrals in the variational formulation of the discrete problem. In this paper we consider a family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties, which can be used for calculating the integrals. Under the numerical quadrature rules we will give the variational form of our non-constant coefficients elliptic problem and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_{1,\Omega}$.

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물체의 분광반사 추정을 위한 최적필터의 선정 (Optimization of color filters selection to estimate surface spectral reflectance of Munsell colors)

  • 이승희;김종필;이을환;노상철;안석출
    • 한국인쇄학회:학술대회논문집
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    • 한국인쇄학회 1998년도 추계 논문 발표회 논문집
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    • pp.1-6
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    • 1998
  • The object color does not look same under the different light source. It depends on the surface spectral reflectance and the spectral distribution of light source. Therefore we should find the surface spectral reflectance of object color and the spectral distribution of light source for color reproduction. Using Winer estimation, we can reconstruct the spectral reflectance from low dimensional images obtained with a few filters. The kind and the number of filters have the effect on the estimation of the spectral reflectance. Therefore it is important that optimal filters are selected to minimize the error of the result. In this paper, we describe methods to select optimal filters with minimum error between measured and estimated surface spectral reflectance and to estimate surface spectral reflectance of Munsell color from six band images by using Wiener estimation.

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ERROR ESTIMATES FOR A SEMI-DISCRETE MIXED DISCONTINUOUS GALERKIN METHOD WITH AN INTERIOR PENALTY FOR PARABOLIC PROBLEMS

  • Ohm, Mi Ray;Lee, Hyun Young;Shin, Jun Yong
    • East Asian mathematical journal
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    • 제32권1호
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    • pp.101-115
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    • 2016
  • In this paper, we consider a semi-discrete mixed discontinuous Galerkin method with an interior penalty to approximate the solution of parabolic problems. We define an auxiliary projection to analyze the error estimate and obtain optimal error estimates in $L^{\infty}(L^2)$ for the primary variable u, optimal error estimates in $L^2(L^2)$ for ut, and suboptimal error estimates in $L^{\infty}(L^2)$ for the flux variable ${\sigma}$.