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Stability and convergence of the spectral Galerkin method for the Cahn-Hilliard equation. (English) Zbl 1157.65053
The authors give a full analysis for the spectral Galerkin method of the periodic Cahn-Hilliard equation on the time interval $$[0, \infty)$$. Using some techniques in partial differential equation and a known compactness result, it is shown that the spectral Galerkin approximate solution converges towards the weak solution of the considered Cahn–Hilliard equation. An error estimate between the exact solution and the spectral Galerkin approximate solution is given when the exact initial function $$u_0$$ satisfies $$u_0\in H_{per}^4(\Omega)$$.

##### MSC:
 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35Q53 KdV equations (Korteweg-de Vries equations)
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