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The convergence of finite element Galerkin solution for the Roseneau equation. (English) Zbl 0977.65080
Summary: We analyze the convergence of the semidiscrete solution of the Roseneau equation. We introduce the auxiliary projection of the solution, and derive the optimal convergence of the semidiscrete solution as well as the auxiliary projection in $$L^2$$ normed space.

##### MSC:
 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35Q53 KdV equations (Korteweg-de Vries equations) 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs