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