• Journal of applied mathematics & informatics
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• 제5권3호
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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.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.311-320
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• 2002

For second order linear elliptic problems over smooth domains, it is well known that the rate of convergence of the error in the $L_2$norm is one order higher than that in the $H^1$norm. For polygonal domains with reentrant corners, it has been shown in [15] that this extra order cannot be fully recovered when the h-version is used. We present theoretical and computational examples showing the sharpness of our results.

• 대한수학회보
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• 제51권1호
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• pp.139-156
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• 2014

In this paper, we investigate the error estimates of a quadratic elliptic control problem with pointwise control constraints. The state and the co-state variables are approximated by the order k = 1 Raviart-Thomas mixed finite element and the control variable is discretized by piecewise linear but discontinuous functions. Approximations of order $h^{\frac{3}{2}}$ in the $L^2$-norm and order h in the $L^{\infty}$-norm for the control variable are proved.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.151-164
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• 2005

The regularized structured total least norm (RSTLN) method finds an approximate solution x and error matrix E to the overdetermined linear system (H + E)x $\approx$ b, preserving structure of H. A new separation scheme by parts of variables for the regularized structured total least norm on blind deconvolution problem is suggested. A method combining the regularized structured total least norm method with a separation by parts of variables can be obtain a better approximated solution and a smaller residual. Computational results for the practical problem with Block Toeplitz with Toeplitz Block structure show the new method ensures more efficiency on image restoration.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.707-719
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• 2014

In this paper, we investigate a variational discretization approximation of elliptic optimal control problems with control constraints. The state and the co-state are approximated by piecewise linear functions, while the control is not directly discretized. By using some proper intermediate variables, we derive a second-order convergence in $L^2$-norm and superconvergence between the numerical solution and elliptic projection of the exact solution in $H^1$-norm or the gradient of the exact solution and recovery gradient in $L^2$-norm. Then we construct a posteriori error estimates by using the superconvergence results and do some numerical experiments to confirm our theoretical results.

• 대한수학회지
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• 제58권3호
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• pp.553-569
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• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권2호
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• pp.31-40
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• 1998

Spectral analysis by energy method is given for a fully discrete methods for hyperbolic integro-differential equations with a weakly singular kernel. Stability and error estimates in $H^1$-norm are derived.

• 한국정보통신학회논문지
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• 제5권6호
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• pp.1089-1093
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• 2001

다중비 필터뱅크의 합성 필터 선계 문제에 H$\infty$ 제어기법을 적용한다. 순수한 시간 지연 시스템을 기준 모델로 설정하여 이 지연 시스템과 다중비 필터 뱅크와의 오차 시스템을 고려한다. 설계 하고자 하는 합성 필터는 오차 시스템의 ι$_2$-유도된 노름을 최소화하도록 설계한다.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.53-68
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• 2004

Numerical solutions for the viscous Cahn-Hilliard equation are considered using the Crank-Nicolson type finite difference method which conserves the mass. The corresponding stability and error analysis of the scheme are shown. The decay speeds of the solution in $H^1-norm$ are shown. We also compare the evolution of the viscous Cahn-Hilliard equation with that of the Cahn-Hilliard equation numerically and computationally, which has been given as an open question in Novick-Cohen[13].

• 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.