Name
Title | ||
|---|---|---|
A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect |
Abstract | ||
|---|---|---|
A local discontinuous Galerkin method for solving Korteweg-de Vries (KdV)-type equations with non-homogeneous boundary effect is developed. We provide a criterion for imposing appropriate boundary conditions for general KdV-type equations. The discussion is then focused on the KdV equation posed on the negative half-plane, which arises in the modeling of transition dynamics in the plasma sheath formation [H. Liu, M. Slemrod, KdV dynamics in the plasma-sheath transition, Appl. Math. Lett. 17(4) (2004) 401-410]. The guiding principle for selecting inter-cell fluxes and boundary fluxes is to ensure the L^2 stability and to incorporate given boundary conditions. The local discontinuous Galerkin method thus constructed is shown to be stable and efficient. Numerical examples are given to confirm the theoretical result and the capability of this method for capturing soliton wave phenomena and various boundary wave patterns. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.jcp.2005.10.016 | J. Comput. Physics |
Keywords | Field | DocType |
various boundary wave pattern,boundary flux,korteweg-de vries equation,plasma-sheath transition,boundary condition,kdv dynamic,non-homogeneous boundary effect,appropriate boundary condition,kdv equation,local discontinuous galerkin method,soliton wave phenomenon,korteweg de vries equation | Discontinuous Galerkin method,Soliton,Boundary value problem,Mathematical analysis,Debye sheath,Korteweg–de Vries equation,Mathematics,Mixed boundary condition | Journal |
Volume | Issue | ISSN |
215 | 1 | Journal of Computational Physics |
Citations | PageRank | References |
16 | 2.03 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hailiang Liu | 1 | 88 | 14.62 |
| Jue Yan | 2 | 198 | 24.23 |