• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.567-584
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• 2014

In this paper, we consider approximation of eigenelements of a two dimensional compact integral operator with a smooth kernel by discrete collocation and iterated discrete collocation methods. By choosing numerical quadrature appropriately, we obtain convergence rates for gap between the spectral subspaces, and also we obtain superconvergence rates for eigenvalues and iterated eigenvectors. We then apply Richardson extrapolation to obtain further improved error bounds for the eigenvalues. Numerical examples are presented to illustrate theoretical estimates.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.293-304
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• 2013

In this paper we analyze an error estimator for the lowest-order triangular Raviart-Thomas mixed finite element which is based on solution of local problems for the error. This estimator was proposed in [Alonso, Error estimators for a mixed method, Numer. Math. 74 (1996), 385{395] and has a similar concept to that of Bank and Weiser. We show that it is asymptotically exact for the Poisson equation if the underlying triangulations are uniform and the exact solution is regular enough.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.587-601
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• 2020

In this paper we propose a way of enhancing eigenvalue approximations with the Bank-Weiser error estimators for the P1 and P2 conforming finite element methods of the Laplace eigenvalue problem. It is shown that we can achieve two extra orders of convergence than those of the original eigenvalue approximations when the corresponding eigenfunctions are smooth and the underlying triangulations are strongly regular. Some numerical results are presented to demonstrate the accuracy of the enhanced eigenvalue approximations.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.891-906
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• 2015

In this work we analyze a postprocessing scheme for improving the guaranteed error bound based on the equilibrated fluxes for the P1 conforming FEM. The improved error bound is shown to be asymptotically exact under suitable conditions on the triangulations and the regularity of the true solution. We also present some numerical results to illustrate the effect of the postprocessing scheme.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.15-30
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• 1999

In this paper the second order semi-discrete and full dis-crete generalized difference schemes for one dimensional parabolic equa-tions are constructed and the optimal order $H^1$ , $L^2$ error estimates and superconvergence results in TEX>$H^1$ are obtained. The results in this paper perfect the theory of generalized difference methods.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.765-778
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• 2012

We construct a symmetric finite volume element (SFVE) scheme for a self-adjoint elliptic problem on tetrahedron grids and prove that our new scheme has optimal convergent order for the solution and has superconvergent order for the flux when grids are quasi-uniform and regular. The symmetry of our scheme is helpful to solve efficiently the corresponding discrete system. Numerical experiments are carried out to confirm the theoretical results.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.37 no.2
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• pp.133-140
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• 2024

This study offers a comprehensive evaluation of the role and impact of advanced power semiconductors in solar module systems. Focusing on silicon carbide (SiC) and gallium nitride (GaN) materials, it highlights their superiority over traditional silicon in enhancing system efficiency and reliability. The research underscores the growing industry demand for high-performance semiconductors, driven by global sustainable energy goals. This shift is crucial for overcoming the limitations of conventional solar technology, paving the way for more efficient, economically viable, and environmentally sustainable solar energy solutions. The findings suggest significant potential for these advanced materials in shaping the future of solar power technology.

• KIPS Transactions on Computer and Communication Systems
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• v.12 no.6
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• pp.189-196
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• 2023

Today, in the era of the 4th industrial revolution based on the paradigm of hyper-connectivity, super-intelligence, and superconvergence, the remote work environment is becoming central based on technologies such as mobile, cloud, and big data. This remote work environment has been accelerated by the demand for non-face-to-face due to COVID-19. Since the remote work environment can perform various tasks by accessing services and resources anytime and anywhere, it has increased work efficiency, but has caused a problem of incapacitating the traditional boundary-based network security model by making the internal and external boundaries ambiguous. In this paper, we propse a method to improve the limitations of the traditional boundary-oriented security strategy by building a security model centered on core components and their relationships based on the zero trust idea that all actions that occur in the network beyond the concept of the boundary are not trusted.