Application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system

Communications in Computational Physics

Volumn 5, Issue 2-4, 2009, Pages 821-835

  Xia, Yinhua ^a   Xu, Yan ^a   Shu, Chi Wang ^b  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b BROWN UNIVERSITY   (United States)

Author keywords

Allen Cahn Cahn Hilliard system; Free energy; Local discontinuous Galerkin method; Stability

Indexed keywords

EID: 61349172519     PISSN: 18152406     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (13)

1. J.W. Barrett and J.F. Blowey, Finite element approximation of a degenerate Allen-Cahn/Cahn-Hilliard system, SIAM J. Numer. Anal., 39 (2001), pp.1598-1624.
2. J.W. Barrett and J.F. Blowey, Finite element approximation ofan Allen-Cahn/Cahn-Hilliard system, MA J. Numer. Anal., 22 (2002), pp. 11-71.
3. J.W Cahn and A. Novick-Cohen, Evolution equations for phase separation and ordering in binary alloys, J. Stat. Phys., 76 (1994), pp. 877-909.
4. B. Cockburn, Discontinuous Galerkin methods for methods for convection-dominated problems, in High-Order Methods for Computational Physics, T.J. Barth and H. Deconinck, editors, Lecture Notes in Computational Science and Engineering, volume 9, Springer, 1999, pp.69-224.
5. B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diflusion systems, SIAM J. Numer. Anal., 35 (1998), pp.2440-2463.
6. B. Cockburn and C.-W Shu, Runge-Kutta Discontinuous Galerkin methods for convection-dominated problems, J. Sci. Comput., 16 (2001), pp.173-261.
7. B. Cockburn and C.-W. Shu, Foreword for the special issue on discontinuous Galerkin method, J. Sci. Comput., 22-23 (2005), pp.1-3.
8. C. Dawson, Foreword for the special issue on discontinuous Galerkin method, Comput. Meth. Appl. Mech. Engin., 195 (2006), p.3183.
9. D. Levy, C.-W Shu and J. Yan, Local discontinuous Galerkin methods for nonlinear dispersive equations, J. Comput. Phys., 196 (2004), pp.751-772.
10. Y. Xia, Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the Cahn-Hilliard type equations, J. Comput. Phys., 227 (2007), pp.472-491.
11. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for nonlinear Schrödinger equations, J. Comput. Phys., 205 (2005), pp.72-97.
12. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for two classes of two dimensional nonlinear wave equations, Physica D, 208 (2005), pp.21-58.
13. J. Yan and C.-W. Shu, A local discontinuous Galerkin methodfor KdV type equations, SIAM J. Numer. Anal., 40 (2002), pp.769-791.