• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.257-270
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• 2018

An extrapolated Crank-Nicolson characteristic finite element method is introduced for approximate solutions of nonlinear Sobolev equations with a convection term. And we obtain the higher order of convergence for approximate solutions in the temporal and the spatial directions with respect to $L^2$ norm.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.385-395
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• 2005

A finite element scheme is considered for the viscous Cahn-Hilliard equation with the nonconstant gradient energy coefficient. The scheme inherits energy decay property and mass conservation as for the classical solution. We obtain the corresponding error estimate using the extended Lax-Richtmyer equivalence theorem.

• East Asian mathematical journal
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• v.30 no.3
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• pp.327-334
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• 2014

In this paper, we construct extrapolated expanded mixed finite element approximations to approximate the scalar unknown, its gradient and its flux of semilinear Sobolev equations. To avoid the difficulty of solving the system of nonlinear equations, we use an extrapolated technique in our construction of the approximations. Some numerical examples are used to show the efficiency of our schemes.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.2
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• pp.100-105
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• 1989

This paper presents an adaptive finite element method for magnetostatic force computation using Maxwell's stress tensor. Mesh refinements are performed automatically by interelement magnetic field intensity discontinuity errors and element force errors. In initial mesh, the computed forces for different integration paths give great differences, but converge to a certain value as mesh division is performed by the adaptive scheme, We obtained good agreement between analytic solutions and numerical values in typical examples.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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• pp.394-401
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• 2006

This study developed two dimensional finite element program(FE-SCP) for the analysis of a composite ground reinforced by sand compaction piles with a low area replacement ratio based on the Mohr-Coulomb elastic perfectly plastic constitutive model. Program FE-SCP give some conveniences to users such as automatic mesh generation according to the replacement ratio and the effective sand pile diameter in the post processor. Also, it contains optimum processor in calculation of In-situ stress equilibrium considering different coefficient of earth pressure between sand pile and surrounding clay. Estimated stress-strain behavior using FE-SCP and the measured one from a centrifuge test showed good agreement comparing to the result from a general finite element program.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.654-659
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• 2003

PVAP (Pressure Vessel Analysis Program V1.0) was developed by adopting the finite element analysis program ANSYS V6.0, and Microsoft Visual Basic V6.0 was also utilized for the interfacing and handling of input and output data during the analysis. PVAP offers the end user the ability to design and analyze vessels in strict accordance with ASME Section VIII, Division 2. More importantly, the user is not required to make any design decisions during the input of the vessel. PVAP consists of three analysis modules for the finite element analysis of the primary components of pressure vessel such as head, shell, nozzle, and skirt. In each module, finite element analysis can be performed automatically only if the end user gives the dimension of the vessel. Furthermore, the calculated results are compared and evaluated in accordance with the criteria given in ASME Boiler and Pressure Vessel Code, Section VIII, Division 2. In particular, heat transfer analysis and consecutive thermal stress analysis for the junction between skirt and head can be carried out automatically in the skirt-tohead module. Finally, report including the above results is created automatically in Microsoft Word format.

• Journal of the Korean institute of surface engineering
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• v.49 no.4
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• pp.344-348
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• 2016

Stainless steel is widely applied in many industrial fields due to its excellent anti-corrosion and durability characteristics. However, stainless steel is very vulnerable to cavitation attack caused by high speed flow of fluid in the chloride environments such as marine environment. These conditions promote intergranular corrosion and cavitation-erosion, leading to degradation of the structural integrity and service life. In order to prevent these problems, the stabilized stainless steel is applied to the offshore and shipbuilding industries. In this study, Ti was added to 19%Cr-9%Ni as the stabilizer element with different concentrations (0.26%, 0.71%), and their durabilities were evaluated with cavitation-erosion experiment by a modified ASTM G32 method. The microstructural change was observed with the stabilizer element contents. The result of the observation indicated that the amount of carbide precipitation was decreased and its size became finer with increasing Ti content. In the cavitation-erosion experiment, both weight loss and surface damage depth represented an inverse proportional relationship with the amount of Ti element. Consequently, the stainless steel containing 0.71% of Ti had excellent durability characteristics.

• Structural Engineering and Mechanics
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• v.40 no.6
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• pp.813-827
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• 2011

This paper provides a numerical solution for a finite internally cracked plate using hybrid crack element method (HCE). In the formulation, an inclined crack is placed in any place of a rectangular element and the complex variable method is used. The complex potentials are expressed in a series form, and several undetermined coefficients are involved. The complex potentials for the cracked rectangle are first suggested in this paper. Based on a variational principle, the element stiffness matrix can be evaluated. The next steps are same as in the usual finite element method. Several numerical examples with computed stress intensity factor and T-stress are presented.

• East Asian mathematical journal
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• v.35 no.5
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• pp.569-587
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• 2019

In this paper, we consider a split least-squares characteristic mixed element method for Sobolev equations with a convection term. First, to manipulate both convection term and time derivative term efficiently, we apply a characteristic mixed element method to get the system of equations in the primal unknown and the flux unknown and then get a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares characteristic mixed element scheme for the given problem whose system is uncoupled in the unknowns. We prove the optimal order in $L^2$ and $H^1$ normed spaces for the primal unknown and the suboptimal order in $L^2$ normed space for the flux unknown.

• East Asian mathematical journal
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• v.38 no.3
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• pp.293-319
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• 2022

In this paper, we introduce a higher order split least-squares characteristic mixed element scheme for Sobolev equations. First, we use a characteristic mixed element method to manipulate both convection term and time derivative term efficiently and obtain the system of equations in the primal unknown and the flux unknown. Second, we define a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares characteristic mixed element scheme for the given problem whose system is uncoupled in the unknowns. We establish the convergence results for the primal unknown and the flux unknown with the second order in a time increment.