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엄미례,이현영,신준용 영남수학회 2016 East Asian mathematical journal Vol.32 No.1
In this paper, we consider a semi-discrete mixed discontinuousGalerkin method with an interior penalty to approximate the solution ofparabolic problems. We de ne an auxiliary projection to analyze the errorestimate and obtain optimal error estimates in L∞(L2) for the primaryvariable u, optimal error estimates in L2(L2) for ut, and suboptimal errorestimates in L∞(L2) for theux variable σ.
엄미례,이현영,신준용 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.1
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 l^∞(L^2) optimal error estimates in both spatial direction and temporal direction.
ERROR ESTIMATES FOR FULLY DISCRETE DISCONTINUOUS GALERKIN METHOD FOR NONLINEAR PARABOLIC EQUATIONS
엄미례,이현영,신준용 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.3
In this paper, we develop discontinuousGalerkinmethods with penalty terms, namaly symmetric interior penalty Galerkin methods to solve nonlinear parabolic equations. By introducing an appropriate projection of u onto finite ele-ment spaces, we prove the optimal convergence of the fully discrete discontinuous Galerkin approximations in ℓ²(L²) normed space.
엄미례,이현영,신준용 영남수학회 2015 East Asian mathematical journal Vol.31 No.5
In this paper, we introduce fully discrete mixed discontinuous Galerkin approximations for parabolic problems. And we analyze the error estimates in l∞(L^2 ) norm for the primary variable and the error estimates in the energy norm for the primary variable and the flux variable.
DISCONTINUOUS GALERKIN METHOD FOR NONLINEAR PARABOLIC PROBLEMS WITH MIXED BOUNDARY CONDITION
엄미례,이현영,신준용 한국전산응용수학회 2014 Journal of applied mathematics & informatics Vol.32 No.5
In this paper we consider the nonlinear parabolic problems with mixed boundary condition. Under comparatively mild conditions of the coefficients related to the problem, we construct the discontinuous Galerkin approximation of the solution to the nonlinear parabolic problem. We discretize spatial variables and construct the finite element spaces consisting of discontinuous piecewise polynomials of which the semidiscrete approximations are composed. We present the proof of the convergence of the semidiscrete approximations in L∞(H¹) and L∞(L²) normed spaces.
A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR NONLINEAR SOBOLEV EQUATIONS
엄미례,신준용 영남수학회 2017 East Asian mathematical journal Vol.33 No.3
We introduce a Crank-Nicolson characteristic finite element method to construct approximate solutions of a nonlinear Sobolev equa- tion with a convection term. And for the Crank-Nicolson characteristic finite element method, we obtain the higher order of convergence in the temporal direction and in the spatial direction in L2 normed space.
A HIGHER ORDER SPLIT LEAST-SQUARES CHARACTERISTIC MIXED ELEMENT METHOD FOR SOBOLEV EQUATIONS
엄미례,신준용 영남수학회 2022 East Asian mathematical journal Vol.38 No.3
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.
A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS
엄미례,신준용 영남수학회 2016 East Asian mathematical journal Vol.32 No.5
A Crank-Nicolson characteristic finite element method is in troduced to construct approximate solutions of a Sobolev equation with a convection term. The higher order of convergences in the temporal direction and in the spatial direction in L2 normed space are verified for the Crank-Nicolson characteristic finite element method.
엄미례,이현영 대한수학회 2011 대한수학회보 Vol.48 No.5
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.
AN EXTRAPOLATED HIGHER ORDER CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS
엄미례,신준용 영남수학회 2017 East Asian mathematical journal Vol.33 No.5
We introduce an extrapolated higher order characteristic fi- nite element method to construct approximate solutions of a Sobolev equa- tion with a convection term. The higher order of convergence in both the temporal direction and the spatial direction in L2 normed space is estab- lished and some computational results to support our theoretical results are presented.