Local discontinuous Galerkin methods for the generalized Zakharov system

Authors:
Yinhua Xia;Yan Xu;Chi-Wang Shu
Affiliations:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China;Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

In this paper we develop a local discontinuous Galerkin (LDG) method for the generalized Zakharov system. Two energy conservations of the LDG scheme are proved for the generalized Zakharov system. Numerical experiments for the Zakharov system are presented to illustrate the accuracy and capability of the methods, including accuracy tests, plane waves, soliton-soliton collisions of the standard and generalized Zakharov system and a two-dimensional problem.