• East Asian mathematical journal
• /
• v.32 no.1
• /
• pp.101-115
• /
• 2016

In this paper, we consider a semi-discrete mixed discontinuous Galerkin method with an interior penalty to approximate the solution of parabolic problems. We define an auxiliary projection to analyze the error estimate and obtain optimal error estimates in $L^{\infty}(L^2)$ for the primary variable u, optimal error estimates in $L^2(L^2)$ for ut, and suboptimal error estimates in $L^{\infty}(L^2)$ for the flux variable ${\sigma}$.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1221-1234
• /
• 2009

In this paper, we construct fully discrete discontinuous Galerkin approximations to the solution of linear Sobolev equations. We apply a symmetric interior penalty method which has an interior penalty term to compensate the continuity on the edges of interelements. The optimal convergence of the fully discrete discontinuous Galerkin approximations in ${\ell}^{\infty}(L^2)$ norm is proved.

• Proceedings of the KIEE Conference
• /
• 1997.07b
• /
• pp.499-503
• /
• 1997

In this paper, we present a fuzzy ICC using a self-tuning method. To provide robustness and adaptiveness over the vehicle nonlinearities and changes of the driving environments, an on-line self-tuning scheme based on 'Interior Penalty Function' was developed. Road test and computer simulation results verify the feasible performance of the suggested ICC algorithm.

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

• East Asian mathematical journal
• /
• v.26 no.5
• /
• pp.615-626
• /
• 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 the Korean Society for Industrial and Applied Mathematics
• /
• v.13 no.3
• /
• pp.169-180
• /
• 2009

A discontinuous Galerkin method with interior penalty terms is presented for linear Sobolev equation. On appropriate finite element spaces, we apply a symmetric interior penalty Galerkin method to formulate semidiscrete approximate solutions. To deal with a damping term $\nabla{\cdot}({\nabla}u_t)$ included in Sobolev equations, which is the distinct character compared to parabolic differential equations, we choose special test functions. A priori error estimate for the semidiscrete time scheme is analyzed and an optimal $L^\infty(L^2)$ error estimation is derived.

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

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.25 no.6
• /
• pp.988-995
• /
• 2001

Functionally graded materials(FGMs) are highlighted to be suitable for high temperature engineering due to their continuous distribution of material properties. In this paper, an optimal design is executed for determining the optimal material volume distribution pattern that minimizes the steady-state thermal stress of FGM heat-resisting composites. The interior penalty function method and the golden section method are employed as optimization techniques while the finite element method is used for thermal stress analysis. Through numerical simulations we suggest the volume fraction distributions that considerably improve initial thermal stress distributions.

• Journal of Institute of Control, Robotics and Systems
• /
• v.4 no.1
• /
• pp.68-75
• /
• 1998

The Intelligent Cruise Control system, ICC, is a driver assisting system for controlling relative speed and distance between two vehicles in the same lane. The ICC may be considered as an extension of a traditional cruise control, not only keeping a fixed speed of the vehicle, but correcting the speed also to that of a slower one ahead. This paper presents a real-time self-tuning fuzzy control algorithm to develop ICC. The self-tuning fuzzy control law is adopted to reduce the effects of nonlinearities of the vehicle and various road environments. In the self-tuning algorithm an interior penalty method is applied to preserve the inherent order of membership functions and is modified as an on-line algorithm for real time application. Via simulations, the performance of the suggested control algorithm is compared with a PID and a fuzzy control without self-tuning. The suggested control algorithm is implemented on PRV III and the results of the test driving on a local road are given.

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