• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.953-966
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• 2010

In this paper, we develop discontinuous Galerkin methods with penalty terms, namaly symmetric interior penalty Galerkin methods to solve nonlinear parabolic equations. By introducing an appropriate projection of u onto finite element spaces, we prove the optimal convergence of the fully discrete discontinuous Galerkin approximations in ${\ell}^2(L^2)$ normed space.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.5
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• pp.2140-2149
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• 2013

Managing uncertainty or discontinuity in an innovation is still a challenge to most companies. For sustainable corporate survival over the long term, one of the problems caused by discontinuous innovation is the innovator's dilemma. In specific, the dynamics between discontinuous innovation and incumbents inspires the interestof researchers and managers. This paper employs catastrophe theory as a theoretical basis to explain the driving force of new discontinuous change. In other words, we extract the control variables overcoming innovation dilemma by interpreting the dynamics of corporate strategy for discontinuous innovation from the perspective of catastrophe theory. First, we define four types of discontinuity such as technology discontinuity, product discontinuity, business discontinuity, and consumer preference discontinuity. Second, we analyze the dynamics of the competition between companies by interpreting the cases of discontinuous innovation. This analyzing process enables us to identify the control variable which can, in advance, respond to the discontinuous situation.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.4
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• pp.386-394
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• 2011

This paper is concerned with the application of the vision control scheme for robot's point placement task in discontinuous trajectory caused by obstacle. The proposed vision control scheme consists of four models, which are the robot's kinematic model, vision system model, 6-parameters estimation model, and robot's joint angles estimation model. For this study, the discontinuous trajectory by obstacle is divided into two obstacle regions. Each obstacle region consists of 3 cases, according to the variation of number of cameras that can not acquire the vision data. Then, the effects of number of cameras on the proposed robot's vision control scheme are investigated in each obstacle region. Finally, the practicality of the proposed robot's vision control scheme is demonstrated experimentally by performing the robot's point placement task in discontinuous trajectory by obstacle.

• Proceedings of the Korea Society for Simulation Conference
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• 2001.10a
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• pp.373-379
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• 2001

There is a big issue to generate 3D hexahedral finite element (FE) model, since a process to divide the whole domain into several simple-shaped sub-domains is required before generating a continuous mesh with mapped mesh generators. In general, it is nearly impossible to set up proper division numbers interactively to keep mesh connectivity between sub-domains on a complicated arbitrary-shaped domain. If mesh continuity between sub-domains is not required in an analysis, this complicated process can be omitted. Element-free Galerkin method (EFGM) can accept discontinuous meshes, which only requires nodal information. However it is difficult to choose a reasonable influenced domain in moving least squares scheme with non-uniformly distributed nodes in discontinuous FE models. A new FE scheme fur discontinuous mesh is proposed in this paper by applying improved EFGM with some modification to derive FE approximated function in discontinuous parts. Its validity is evaluated on linear elastic problems.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.534-541
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• 2010

A high-order accurate Euler flow solver based on a discontinuous Galerkin method has been developed for the numerical simulation of unsteady flows on unstructured meshes. A multi-level solution-adaptive mesh refinement/coarsening technique was adopted to enhance the resolution of numerical solutions efficiently by increasing mesh density in the high-gradient region. An acoustic wave scattering problem was investigated to assess the accuracy of the present discontinuous Galerkin solver, and a supersonic flow in a wind tunnel with a forward facing step was simulated by using the adaptive mesh refinement technique. It was shown that the present discontinuous Galerkin flow solver can capture unsteady flows including the propagation and scattering of the acoustic waves as well as the strong shock waves.

• Journal of the Korea Concrete Institute
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• v.12 no.6
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• pp.83-90
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• 2000

This paper presents an analytical prediction of the elastic behavior of discontinuous displacement in reinforced concrete column-footing joint under earthquake. Material nonlinearity is taken into account by comprising tensile, compressive and shear models of cracked concrete and a model of reinforcing steel. The smeared crack approach is incorporated. In boundary plane at which each member with different thickness is connected, local discontinuous deformation due to the abrupt change in their stiffness can be taken into account by introducing interface element. The proposed numerical method for hysteretic behavior of discontinuous displacement in reinforced concrete column-footing joint will be verified by comparison with reliable experimental results.

• Korean Journal of Child Studies
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• v.26 no.6
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• pp.161-171
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• 2005

In Experiment 1, 4- and 5-year-olds were shown either continuous(i.e., pizza) or discontinuous Stimuli(i.e., biscuit) by the experimenter. After a proportion(e.g., 2/8, 4/8, or 6/8) was removed, children were asked to remove an equivalent proportion. Whereas 4-year-olds proportional reasoning was correct only when they shared the same stimulus with the experimenter, 5-year-olds reasoned correctly regardless whether or not they shared the stimulus with the experimenter. In Experiment 2, where the discontinuous stimulus was changed, 4-year-olds also made correct proportional reasoning even when their stimulus was different from the experimenter's. Contrary to other studies, quantity didn't affect children's proportional reasoning except the proportion 1/4, where problems with discontinuous quantity were solved more successfully than problems with continuous quantity.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.311-326
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• 2011

In this paper, we adopt discontinuous Galerkin methods with penalty terms namely symmetric interior penalty Galerkin methods, to solve nonlinear viscoelasticity type equations. We construct finite element spaces and define an appropriate projection of u and prove its optimal convergence. We construct extrapolated fully discrete discontinuous Galerkin approximations for the viscoelasticity type equation and prove ${\ell}^{\infty}(L^2)$ optimal error estimates in both spatial direction and temporal direction.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.337-350
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• 2014

In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori ${\ell}^{\infty}(L^2)$ error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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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.