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A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect. (English) Zbl 1092.65083

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.

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.

MSC:
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
65M12Stability and convergence of numerical methods (IVP of PDE)
82D10Plasmas (statistical mechanics)