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Finite element Galerkin solutions for the Rosenau equation. (English) Zbl 0830.65097
Finite element Galerkin approximate solutions for a KdV-like Rosenau equation which models the dynamics of dense discrete systems are considered. Existence and uniqueness of exact solutions are shown and the error estimates of the continuous time Galerkin solutions are discussed. For the fully discrete time Galerkin solutions, we consider the backward Euler method which results in the first-order convergence in the temporal direction. For the second-order convergence in time, we consider a three- level backward method and the Crank-Nicolson method which give optimal convergence in the spatial direction.
Reviewer: S.K.Chung (Seoul)

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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References:
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