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Zbl 1092.65083
Liu, Hailiang; Yan, Jue
A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect. (English)
[J] J. Comput. Phys. 215, No. 1, 197-218 (2006). ISSN 0021-9991

A Korteweg-de Vries (KdV) equation with admissible boundary conditions is considered. Then an energy estimate for the KdV problem on the negative quarter-plane is obtained. \par A local discontinuous Galerkin method for solving KdV type equations with non-homogeneous boundary effect is proposed and its nonlinear $L^2$ stability is proved. Some wave patterns near the boundary are discussed and numerical results, consistent with these wave patterns, are presented.
[Ruxandra Stavre (Bucureşti)]

MSC 2000:: *65M60 Finite numerical methods (IVP of PDE)
35Q53 KdV-like equations
65M12 Stability and convergence of numerical methods (IVP of PDE)
82D10 Plasmas

Keywords: Korteweg-de Vries equation; local discontinuous Galerkin method; non-homogeneous boundary effect; stability; numerical results

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