• Water Engineering Research
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• v.4 no.1
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• pp.45-58
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• 2003

Two-dimensional depth-averaged advection-dispersion equation was simulated using FEM. In the straight rectangular channel, the advection-dispersion processes are simulated so that these results can be compared with analyti-cal solutions for the transverse line injection and the point injection. In the straight domain the standard Galerkin method with the linear basis function is found to be inadequate to the advection-dispersion analysis compared to the upwind finite element scheme. The experimental data in the S-curved channel were compared with the result by the numerical model using SUPG(Streamline upwind Petrov-Galerkin) method.

• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.621-657
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• 2024

In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.

• Coupled systems mechanics
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• v.5 no.3
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• pp.203-221
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• 2016

The present study deals with the numerical modelling for the one dimensional contaminant transport through saturated homogeneous and stratified porous media using meshfree method. A numerical algorithm based on element free Galerkin method is developed. A one dimensional form of the advectivediffusive transport equation for homogeneous and stratified soil is considered for the analysis using irregular nodes. A Fortran program is developed to obtain numerical solution and the results are validated with the available results in the literature. A detailed parametric study is conducted to examine the effect of certain key parameters. Effect of change of dispersion, velocity, porosity, distribution coefficient and thickness of layer is studied on the concentration of the contaminant.

• Journal of Mechanical Science and Technology
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• v.20 no.11
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• pp.1881-1890
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• 2006

In this paper, a Petrov-Galerkin natural element method (PG-NEM) based upon the natural neighbor concept is presented for the free vibration and dynamic response analyses of two-dimensional linear elastic structures. A problem domain is discretized with a finite number of nodes and the trial basis functions are defined with the help of the Voronoi diagram. Meanwhile, the test basis functions are supported by Delaunay triangles for the accurate and easy numerical integration with the conventional Gauss quadrature rule. The numerical accuracy and stability of the proposed method are verified through illustrative numerical tests.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.131-134
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• 2005

Conventional high order interpolation schemes are limitative in several aspects mainly because they need data of neighboring cells at the reconstruction step. However, discontinuous Galerkin method and spectral volume method, two high order flux schemes which will be analyzed and compared in this paper, have an important benefit that they are not necessary to determine the flow gradients from data of neighboring cells or elements. These two schemes construct polynomial of variables within a cell so that even near wall or discontinuity, the high order does not deteriorate.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.4
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• pp.174-186
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• 1998

A Galerkin's finite element model incorporating infinite elements for modeling of radiation condition at infinity has been developed, which is based on an extended mild-slope equation. To illustrate the validity and applicability of the present model, the example analyses were carried out for a resonance problem in the rectangular harbor of Ippen and Goda (1963) and for wave transformations over circular shoals of Sharp (1968) and Chandrasekera and Cheung (1997). Comparisons with the results obtained by hydraulic experiments and hybrid element method showed that the present model gives very good results in spite of the rapidly varying topography. Numerical experiments were also performed for wave transformations over a circular concave well which may be an alternative to conventional wave barriers.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.4
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• pp.485-500
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• 2000

In this paper the adaptive crack propagation analysis based on the estimated local and global error in the element-free Galerkin (EFG) method is presented. It is possible to keep consistency and accuracy of analysis in each propagation step by adaptive analysis. The adaptivity analysis in crack propagation is achieved by adding and removing the node along the background integration cell that are refined or recovered as estimated error. These errors are obtained by calculating the difference between the values of the projected stresses and original EFG stresses. To evaluate the performance of proposed adaptive procedure, the convergence behavior is investigated lot several examples. The results of these examples show the efficiency of proposed scheme in crack propagation analysis.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.161-176
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• 2005

We consider a model of population dynamics whose mortality function is unbounded. We note that the regularity of the solution depends on the growth rate of the mortality near the maximum age. We propose Gauss-Legendre methods along the characteristics to approximate the solution when the solution is smooth enough. It is proven that the scheme is convergent at fourth-order rate in the maximum norm. We also propose discontinuous Galerkin finite element methods to approximate the solution which is not smooth enough. The stability of the method is discussed. Several numerical examples are presented.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.159-171
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• 1999

We formulate and study a finite element method for a linearized steady state, compressible, viscous Navier-Stokes equations in 2D, based on the discontinuous Galerkin method. Dislike the standard discontinuous galerkin method, we do not assume that the triangle sides be bounded away from the characteristic direction. the unique stability follows from the inf-sup condition established on the finite dimensional spaces for the (incompressible) Stokes problem. An error analysis having a jump discontinuity for pressure is shown.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.43-55
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• 2007

In this paper, an $H^1-Galerkin$ mixed finite element method is used to approximate the solution as well as the flux of Burgers' equation. Error estimates have been derived. The results of the numerical experiment show the efficacy of the mixed method and justifies the theoretical results obtained in the paper.