• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.9
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• pp.2887-2893
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• 1996

Governing equations infrictional contact problems are introduced using variational inequality formulations which are regularized to overcome the diffculties of non-differentiability of the friction functional. Also finite element approximations and a priori error estimations are derived based on those formulations. Numerical simulations are performed illustrating the theoretical results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.80-86
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• 1997

Recently, the box-girder bridge became quite popular because of the effectiveness of the box section against torsional deformation, and the finite element method has been one of the powerful and versatile method for obtaining the solution of box-girder bridge. The finite element method is used to solve a box girder which is built up with flat plates such as flanges, webs and diaphragm, and box girder is idealized by 8-nodes 2-dimensional isoparmetric finite element. To investigate the stress of diaphragm, substructure analysis is performed with two Parameters which are the location of support and slope of web.

• East Asian mathematical journal
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• v.29 no.5
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• pp.503-510
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• 2013

A quadratic B-spline finite element method for the spatial variable combined with a Newton method for the time variable is proposed to approximate a solution of Benjamin-Bona-Mahony-Burgers (BBMB) equation. Two examples were considered to show the efficiency of the proposed scheme. The numerical solutions obtained for various viscosity were compared with the exact solutions. The numerical results show that the scheme is efficient and feasible.

• 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.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1331-1345
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• 2010

This paper describes a numerical solution of Navier-Stokes equations. It includes algorithms for discretization by finite element methods and a posteriori error estimation of the computed solutions. In order to evaluate the performance of the method, the numerical results are compared with some previously published works or with others coming from commercial code like ADINA system.

• Journal of Industrial Technology
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• v.9
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• pp.109-117
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• 1989

In the finite element analysis of semiconductor devices analysis, the solution often be diverged due to the numerical instability of discretized equations. To overcome this problems, a noble finite element code which guarantees a successful convergence is developed. The factor of divergence in the current continuity equation of semiconductor governing equations is derived using stability test and an adaptive mesh refine scheme is introduced to eliminates the divergence properties. A test calculation of GaAs MESFET model reveals that the proposed scheme has a robust self-convergence property and is suitable for the semiconductor devices analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.4
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• pp.203-214
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• 2017

In this paper we propose and analyze two a posteriori error estimators for the stabilized $P_1/P_1$ finite element discretization of the Stokes equations. These error estimators are computed by solving local Poisson or Stokes problems on elements of the underlying triangulation. We establish their asymptotic exactness with respect to the velocity error under certain conditions on the triangulation and the regularity of the exact solution.

• 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.

• Structural Engineering and Mechanics
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• v.6 no.7
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• pp.727-746
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• 1998

Finite element models and numerical results are presented for bending and natural vibration using the unified third-order plate theory developed in Part 1 of this paper. The unified third-order theory contains the classical, first-order, and other third-order plate theories as special cases. Analytical solutions are developed using the Navier and L$\acute{e}$vy solution procedures (see Part 1 of the paper). Displacement finite element models of the unified third-order theory are developed herein. The finite element models are based on $C^0$ interpolation of the inplane displacements and rotation functions and $C^1$ interpolation of the transverse deflection. Numerical results of bending and natural vibration are presented to evaluate the accuracy of various plate theories.

• Structural Engineering and Mechanics
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• v.31 no.3
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• pp.297-314
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• 2009

When the temperature of a structure varies, there is a tendency to produce changes in the shape of the structure. The resulting actions may be of considerable importance in the analysis of the structures having non-prismatic members. Therefore, this study aimed to investigate the modeling, analysis and behavior of the non-prismatic members subjected to temperature changes with the aid of finite element modeling. The fixed-end moments and fixed-end forces of such members due to temperature changes were computed through a comprehensive parametric study. It was demonstrated that the conventional methods using frame elements can lead to significant errors, and the deviations can reach to unacceptable levels for these types of structures. The design formulas and the dimensionless design coefficients were proposed based on a comprehensive parametric study using two-dimensional plane-stress finite element models. The fixed-end actions of the non-prismatic members having parabolic and straight haunches due to temperature changes can be determined using the proposed approach without necessitating a detailed finite element model solution. Additionally, the robust results of the finite element analyses allowed examining the sources and magnitudes of the errors in the conventional analysis.