[1] Arnold D N. An interior penalty finite element method with discontinuous element. SIAM J Numer Anal, 1982, 19: 742--760
[2] Arnold D N, Brezzi F, Cockburn B, et al. Discontinuous Galerkin Methods for Elliptic Problems//Cockburn B, Karniadakis G, Shu C W. Discontinuous Galerkin Methods: Theory, Computation and Applications. Lecture Notes in Comput Sci Engrg 11. New York: Springer-Verlag, 2000: 89--101
[3] Arnold D N, Brezzi F, Cockburn B, et al. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J Numer Anal, 2002, 39: 1749--1779
[4] Ciarlet P G. The Finite Element Method for Elliptic Problems. Amsterdam: North-Holland, 1978
[5] Cockburn B, Shu C W. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J Sci Comput, 2001, 16: 173--261
[6] Cockburn B, Shu C W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J Numer Anal,
1998, 35: 2440--2463
[7] Dawson C N, Du Q, Dupont T F. A finite difference domain decomposition procedure for the heat equation. Math Comp, 1991, 57: 63--71
[8] Dawson C N, Dupont T F. Explicit/implicit conservative Galerkin domain decomposition procedures for parabolic problems. Math Comp, 1992, 58: 21--34
[9] Dawson C N, Dupont T F. Explicit/implicit conservative Galerkin domain decomposition procedures for parabolic problems based on block-centered finite differences. SIAM J Numer Anal, 1994, 31: 1045--1061
[10] Epshteyn Y, Riviére B. Estimation of penalty parameters for symmetric interior penalty Galerkin methods. J Comput Appl Math,
2007, 206(2): 843--872
[11] Hughes T J R, Engel G, Mazzei L, et al. A Comparison of Discontinuous and Continuous Galerkin Methods Based on Error Estimates, Conservation, Robustness and Dfficiency//Cockburn B, Karniadakis G, Shu C W. Discontinuous Galerkin Methods: Theory, Computation and Applications. Lecture Notes in Comput Sci Engrg 11. New York: Springer-Verlag, 2000: 136--146
[12] Riviére B. Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation. Philadelphia: SIAM, 2008
[13] Riviére B, Wheeler M F, Girault G. A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. SIAM J Numer Anal, 2001: 39: 902--931
[14] Sun S, Wheeler M F. Symmetric and nonsymmetric discontinuous Galerkin methods for reactive transport in porous media. SIAM J Numer Anal, 2005, 43: 195--219
[15] Wang K, Wang H, Sun S, et al. An optimal-order L2-error estimate for nonsymmetric discontinuous Galerkin methods for a parabolic
equation in mutiple space dimensions. Comput Methods Appl Mech Engrg, 2009, 198: 2190--2197 |