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ERROR ESTIMATES FOR FULLY DISCRETE DISCONTINUOUS GALERKIN METHOD FOR NONLINEAR PARABOLIC EQUATIONS  

Ohm, Mi-Ray (Division of Information Systems Engineering, Dongseo University)
Lee, Hyun-Yong (Department of Mathematics, Kyungsung University)
Shin, Jun-Yong (Division of Mathematical Sciences, Pukyong National University)
Publication Information
Journal of applied mathematics & informatics / v.28, no.3_4, 2010 , pp. 953-966 More about this Journal
Abstract
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.
Keywords
Discontinuous Galerkin approximation; nonlinear parabolic equation; fully discrete approximations;
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1 M.R. Ohm, H.Y. Lee, and J.Y. Shin, Error estimates for discontinuous Galerkin method for nonlinear parabolic equations, Jour. Math. Anal. and Appl. 315(2006), 132-143.   DOI   ScienceOn
2 D.N. Arnold, An interior penalty finite element method with discontinuous elements, SIAM J. Numer. Anal. 19(1982), 724-760.
3 J. Douglas and T. Dupont, Interior penalty procedures for elliptic and parabolic Galerkin methods, Lecture Notes in Physics 58(1976), 207-216.   DOI
4 J.A. Nitsche (check on the MR), Uber ein Variationspringzip zur Losung von Dirichlet Problemen bei Verwendung von Teilraumen, die keinen Randbedingungen unterworfen sind, Abh. Math. Sem. Univ. Hamburg. 36(1971), 9-15.   DOI
5 J.T. Oden, I. Babuska, and C.E. Baumann, A discontinuous hp finite element method for diffusion problems, J. Compu. Phys. 146(1998), 491-519.   DOI   ScienceOn
6 B. Riviere Discontinuous Galerkin finite element methods for solving the miscible displacement problem in porous media, Ph. D. Thesis, The University of Texas at Austin, 2000.
7 B. Riviere and M.F. Wheeler, Nonconforming methods for transport with nonlinear reaction, Contemporary Mathematics 295(2002), 421-432.
8 B. Riviere and M.F. Wheeler, A discontinuous Galerkin method applied to nonlinear parabolic equations, Discontinuous Galerkin methods: theory, computation, and applications [Eds. by B. Cockburn, G.E. Karniadakis, and C.-W. Shu], Lecture notes in computational science and engineering, Springer-Verlag 11(2000), 231-244.
9 M.F. Wheeler, An elliptic collocation-finite element method with interior penalties, SIAM J. Numer. Anal. 15(1978), 152-161.   DOI   ScienceOn
10 B. Riviere, M.F. Wheeler, and V. Girault, Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems, Part I., Compo Geo. 3(1999), 337-360.   DOI