A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect.

*(English)*Zbl 1092.65083A 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.

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.

Reviewer: Ruxandra Stavre (Bucureşti)

##### MSC:

65M60 | Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE) |

35Q53 | KdV-like (Korteweg-de Vries) equations |

65M12 | Stability and convergence of numerical methods (IVP of PDE) |

82D10 | Plasmas (statistical mechanics) |