• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.615-622
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• 2002

In this paper, the modification of double projection method for the adaptive analysis of Element-free Galerkin(EFG) method were proposed. As results of the double projection method, the smoothed error profile that is adequate for adaptive analysis was obtained by re-projection of error that means the differences of EFG stress and projected stress. However, it was found that the efficiency of double projection method is degraded as increase of the numerical integration order. Since, the iterative refinement to single step error estimation made the same effect as increasing of integration order, the application of the iterative refinement base on double projection method could be produced the inadequately refined analysis model. To overcome this defect, a modified scheme of double projection were proposed. In the numerical example, the results did not show degradation of double projection effect in iterative refinement and the efficiency of proposed scheme were proved.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.897-915
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• 2011

In this paper, we develop a symmetric Galerkin method with interior penalty terms to construct fully discrete approximations of the solution for nonlinear Sobolev equations. To analyze the convergence of discontinuous Galerkin approximations, we introduce an appropriate projection and derive the optimal $L^2$ error estimates.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.829-850
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• 2012

In this paper, we adopt symmetric interior penalty discontinuous Galerkin (SIPG) methods to approximate the solution of nonlinear viscoelasticity-type equations. We construct finite element space which consists of piecewise continuous polynomials. We introduce an appropriate elliptic-type projection and prove its approximation properties. We construct semidiscrete discontinuous Galerkin approximations and prove the optimal convergence in $L^2$ normed space.

• East Asian mathematical journal
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• v.26 no.5
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• pp.615-626
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• 2010

In this paper, we analyze discontinuous Galerkin methods with penalty terms, namly symmetric interior penalty Galerkin methods, to solve nonlinear parabolic equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ${\ell}^{\infty}$ ($L^2$) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

• 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 applied mathematics & informatics
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• v.5 no.1
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• pp.171-180
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• 1998

In this paper we analyze the convergence of the semidis-crete solution of the Roseneau equation. We introduce the auxiliary projection of the solution and derive the optimal convergence of the semidiscrete solution as well as the auxiliary projection in L2 normed space.

• 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.20 no.4
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• pp.295-308
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• 2016

We propose a projection-based analysis of a new hybridizable discontinuous Gale-rkin method for second order elliptic equations. The method is more advantageous than the standard HDG method in a sense that the new method has higher-order accuracy and lower computational cost, and is more flexible. Notable distinctions of our new method, when compared to the standard HDG emthod, are that our method uses $L^2$-projection and suitable stabilization parameter depending on a mesh size for superconvergence. We show that the error for the solution of the equation converges with order p + 2 when we only use polynomials of degree p + 1 as a finite element space without postprocessing. After establishing the theory, we carry out numerical tests to demonstrate and ensure that the proposed method is effective and accurate in practice.

• Journal of Advanced Marine Engineering and Technology
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• v.25 no.2
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• pp.304-310
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• 2001

This paper describes the analysis of flow field using a projection finite element method. The projection scheme with a pressure correction is presented for the analysis of an incompressible Navier-Stokes flow. The projection scheme is analyzed numerically and applied to the well-known bench marking problems such as lid driven cavity. Finally, the projection scheme is applied to a flow through the automobiles front. In the automobiles cooling system, the flow through its front is very important to a cooling performance. The results show that the flow quantity increases by locating the position of bumper to the further front position of a car. And, the improvement on the suction part below a bumper achieves the more passing flow quantity. The attachment of an air dam increases passing flow quantity causing the pressure rise to the front part and the pressure drop beneath a car.