(J-KSIAM) Volume 23 Number 2 (June 2019 issue) TOC
글쓴이 : KSIAM
작성일 : 2019-07-01

Dear colleagues and researchers,

The Journal of the Korean Society for Industrial and Applied Mathematics (J-KSIAM) Volume 23 Number 2 (June 2019 issue) has been posed on https://www.ksiam.org/archive or other information on the journal is available on the KSIAM website http://www.ksiam.org or https://www.ksiam.org/journal

The journal is one of Korea Citation Indexed (KCI) journals since 2007 and is indexed in Emerging Sources Citation Index (ESCI) since 2017.

Readers interested in the following articles may download each of articles free of charge from our website and authors are encouraged to submit a paper via the online submission site http://submission.ksiam.org/journal.do?method=journalintro&journalSeq=J000039

Sincerely yours,

Hi Jun Choe, Editor-in-Chief

Zhiming Chen, Hyeong-Ohk Bae, Tao Tang, Associate Editors-In-Chief

Jae Hoon Jung, Jaemyung Ahn, Wanho Lee, Managing Editors

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JKSIAM-v23n2 pp65-92

Recent  development of immersed  FEM for elliptic and elastic interface problems

Gwanghyun Jo, Do Young Kwak

https://s3-ap-northeast-2.amazonaws.com/ksiam-editor/1561950687384-jksiam-2019v23p065.pdf

We survey a recently developed immersed finite element method (IFEM) for the interface problems. The IFEM uses structured grids such as uniform grids, even if the interface is a smooth curve. Instead of fitting the curved interface, the bases are modified so that they satisfy the jump conditions along the interface.

The early versions of IFEM [1, 2] were suboptimal in convergence order [3]. Later, the consistency terms were added to the bilinear forms [4 5], thus the scheme became optimal and the error estimates were proven.

For elasticity problems with interfaces, we modify the Crouzeix-Raviart based element to satisfy the traction conditions along the interface [6], but the consistency terms are not needed. To satisfy the Korn's inequality, we add the stabilizing terms to the bilinear form.

The optimal error estimate was shown for a triangular grid.

Lastly, we describe the multigrid algorithms for the discretized system arising from IFEM.

The prolongation operators are designed so that the prolongated function satisfy the flux continuity condition along the interface. The $\mathcal{W}$-cycle convergence was proved, and the number of $\mathcal{V}$-cycle is independent of the mesh size.

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JKSIAM-v23n2 pp93-114

An Energy-stable and Second-order accurate method for Solving the Incompressible Navier-Stokes equations

Jeongho Kim, Jinwook Jung, Yesom Park, Chohong Min, Byungjoon Lee

https://s3-ap-northeast-2.amazonaws.com/ksiam-editor/1561950693587-jksiam-2019v23p093.pdf

In this article, we introduce a finite difference method for solving the Navier-Stokes equations in rectangular domains. The method is proved to be energy stable and shown to be second-order accurate in several benchmark problems. Due to the guaranteed stability and the second order accuracy, the method can be a reliable tool in real-time simulations and physics-based animations with very dynamic fluid motion. We first discuss a simple convection equation, on which many standard explicit methods fail to be energy stable. Our method is an implicit Runge-Kutta method that preserves the energy for inviscid fluid and does not increase the energy for viscous fluid. Integration-by-parts in space is essential to achieve the energy stability, and we could achieve the integration-by-parts in discrete level by using the Marker-And-Cell configuration and central finite differences. The method, which is implicit and second-order accurate, extends our previous method \cite{lee2018L2stable} that was explicit and first-order accurate. It satisfies the energy stability and assumes rectangular domains. We acknowledge that the assumption on domains is restrictive, but the method is one of the few methods that are fully stable and second-order accurate.

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JKSIAM-v23n2 pp115-138

Algorithms to apply finite element dual singular function method for the Stokes equations including corner singularities

Deok-Kyu Jang, Jae-Hong Pyo

https://s3-ap-northeast-2.amazonaws.com/ksiam-editor/1561950699857-jksiam-2019v23p115.pdf

The dual singular function method [DSFM] is a solver for corner sigulaity problem. We already construct DSFM in previous reserch to solve the Stokes equations including one singulairity at each reentrant corner, but we find out a crucial incorrection in the proof of well-posedness and regularity of dual singular function. The goal of this paper is to   prove accuracy and well-posdness of DSFM for Stokes equations including two singulairities at each corner. We also introduce new applicable algorithms to slove multi-singulrarity problems in a complicated domain.

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JKSIAM-v23n2 pp139-155

Dynamics of a modified Holling-Tanner predator-prey model with diffusion

M. Sambath, K. Balachandran, Il Hyo Jung

https://s3-ap-northeast-2.amazonaws.com/ksiam-editor/1561950704589-jksiam-2019v23p139.pdf

In this paper, we study the asymptotic behavior and Hopf bifurcation of the modified Holling-Tanner models for the predator-prey interactions in the absence of diffusion. Further the direction of Hopf bifurcation and stability of bifurcating periodic solutions are investigated. Diffusion driven instability of the positive equilibrium solutions and Turing instability region regarding the parameters are established. Finally we illustrate the theoretical results with some numerical examples.

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