On some high-order accurate fully discrete Galerkin methods for the Korteweg-de Vries equation. (English) Zbl 0609.65064
The Galerkin finite element method for the construction of a numerical solution for the Korteweg-de Vries equation is discussed in many papers, for example, see R. Winther [ibid. 34, 23-34 (1980; Zbl 0422.65063)]. In this paper, the authors establish fully discrete Galerkin methods of high order of accuracy for the Korteweg-de Vries equation. For the time stepping, two schemes of modified diagonally implicit Runge- Kutta methods are used. \(L^ 2\)-error estimates of convergence for both schemes are established.
Reviewer: Boling Guo
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
