Acknowledgement
Supported by : Korea Research Foundation
References
- D.N. Arnold, An interior penalty finite element method with discontinuous elements, SIAM J. Numer. Anal. 19(1982), 724-760.
- J. Douglas and T. Dupont, Interior penalty procedures for elliptic and parabolic Galerkin methods, Lecture Notes in Physics 58(1976), 207-216. https://doi.org/10.1007/BFb0120591
- 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. https://doi.org/10.1007/BF02995904
- 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. https://doi.org/10.1006/jcph.1998.6032
- 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. https://doi.org/10.1016/j.jmaa.2005.07.027
- 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.
- B. Riviere and M.F. Wheeler, Nonconforming methods for transport with nonlinear reaction, Contemporary Mathematics 295(2002), 421-432.
- 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.
- 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. https://doi.org/10.1023/A:1011591328604
- M.F. Wheeler, An elliptic collocation-finite element method with interior penalties, SIAM J. Numer. Anal. 15(1978), 152-161. https://doi.org/10.1137/0715010