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A splitting method for the Cahn-Hilliard equation with inertial term. (English) Zbl 1205.65246
The authors analyze a finite element space semi-discretization splitting method for the Cahn-Hilliard equation with inertial term, based on a scheme introduced by C.M. Elliott et al. [Numer. Math. 54, No. 5, 575–590 (1989; Zbl 0668.65097)] for the same equation. They have also proved that the semi discrete solution converges weakly to the continuous solution as the grid size tends to zero. Assuming enough regularity on the solution, they have obtained optimal a priori error estimates in energy norm and related norms. They have also given simple finite difference version of the scheme and shown that the semi-discrete solution converges to an equilibrium as time tends to infinity.

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
65M20 Method of lines 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
35Q99 Partial differential equations of mathematical physics and other areas of application
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
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