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Numerical methods for the Rosenau equation. (English) Zbl 1021.65048
Summary: A continuous in time finite element Galerkin method is first discussed for a Korteweg-de Vries-like Rosenau equation in several space variables and optimal error estimates in \(L^2\), \(H^1\) as well as in \(H^2\)-norms are derived for conforming \(C^1\)-finite element spaces. Finally, several fully discrete schemes like backward Euler, Crank-Nicolson and two step backward methods are proposed and related convergence results are established.

MSC:
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
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods 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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